Turbulent Mixing in Experimental Ecosystem Studies

MARINE ECOLOGY PROGRESS SERIES Vol. 161: 265-293. 1997 Published December 31 Mar Ecol Prog Ser

REVIEW Turbulent mixing in experimental ecosystem studies

Lawrence P. Sanford*

University of Maryland, Center for Environmental Science, Horn Point Laboratory, PO Box 775, Cambridge. Maryland 21613, USA

ABSTRACT. Turbulent mixing is an integral aspect of aquatic ecosystems Turbulence affects ecosystem features ranglng from phytoplankton blooms at large scales through microscale interactions in the plankton. Enclosed experimental ecosystems, if they are to mimic the function of natural ecosystems, also must mimic natural turbulence and its effects. Large-scale velocity gradients and unstable buoyancy fluxes generate turbulent mixing in nature, most often at the surface and bottom boundaries and in the pycnocline. Large eddy sizes are controlled by the mixed layer depth, boundary layer thickness, or overturning length in the pycnocl~ne.Turbulent energy cascades through smaller and smaller eddy scales until it can be dissipated by molecular viscosity at the smallest scales. In contrast, artificial apparatuses frequently are used to generate turbulent m~xingin the interior of experimental ecosystem enclosures Large eddy sizes are controlled by the size of the generation apparatus, and they usually are much smaller than in nature Mismatched large eddy length scales and differences in turbulence generation mechanisms are responsible for the difficulties in mimicking natural turbulent mixing in experimental enclosures. The 2 most important turbulence parameters to consider in experimental ecosystem research are overall mixing time, T,,,, and turbulence dissipation rate, E. If the levels, spatial dlstribut~ons,and temporal variability of T,,, and E can be matched between an enclosure and the natural system it IS to model, then potential mixing artifacts can be minimized. An important additional consideration is that benthic ecosystems depend on the time-averaged boundary layer flow as much as the turbulence. Existing designs for mix~ngexperimental ecosystems are capable of reasonably representing some aspects of natural turbulent mixing Paddle and grid stirring are the best available techniques for water column mixing, and flumes are best for benthic turbulence. There is no design at present that represents both environments adequately. More work also is needed on mixing of flexible- wall in situenclosures. A more serious problem, however, is that turbulent mixing in experimental ecos)~stemstudies too often is ignored, inadequately characterized, or unreported. Several methods are available for reasonable characterlzation of mixing in enclosures without sophisticated technology, and the technology for direct velocity measurements is becoming more accessible. Experimental ecosystem researchers should make a concerted effort to implement, characterize, and report on turbulent mixing In the~renclosures.

KEY WORDS: Turbulent mixlng . Mesocosms Experimental ecosystems . Turbulence dissipation rate Mixing time Biolog~cal-physicalinteraction Mass transfer

INTRODUCTION with in situstudies, capturing and containing a piece of the natural aquatic environment gives experimental Aquatic ecologists and toxicologists have a long his- ecosystems the distinct advantages of controllability, tory of using experimental ecosystems to explore the replicability, and freedom from advective changes dynamics of aquatic ecosystems and mechanisms con- (Guanguo 1990, Oviatt 1994). However, isolating a trolling those dynamics (Banse 1982, SCOR Working small piece of an ecosystem from its natural environ- Group 85 1990, Daehler & Strong 1996). In companson ment risks a series of artifacts that may or may not affect seriously the course of an experiment (Conover & Paranjape 1977, Carpenter 1996). Mixing is one aspect of the natural aquatic environment that is

O Inter-Research 1997 Resale of full article not permitted 266 Mar Ecol Prog Ser 161: 265-293, 1997

important for realistic experimental ecosystem behav- boundary layer thickness to the mean flow speed ior (Eppley et al. 1978, Bakke 1990, Lasserre 1990) and (Cantwell 1981). A well-designed 15 cm deep labora- at the same time a challenge to generate and control in tory flume can simulate a 15 cm deep natural flow experimental containers (Steele et al. 1977, Nixon et al. accurately, but the effects of the large eddies in a 15 m 1980, Howarth et al. 1993). deep tidal channel are much more difficult to mimic. Mixlng in natural water bodies nearly always is tur- There also are significant differences between nat- bulent. Turbulence is generated by unstable excess ural turbulence generated by vertical shear of a hori- physical energy at large scales. This energy is trans- zontal mean flow (e.g at the surface, pycnocline, or ferred to smaller and smaller scales through a process bottom) and turbulence generated by a paddle or grid of cascading instability, saturating all intermediate stirring the tnterlor of an experimental ecosystem scales of motion, until it can be dissipated into heat by (Brumley & Jirka 1987, Fernando 1991). These differ- molecular viscosity (Richardson 1922, Batchelor 1967). ences particularly are important for transport across Because of the broad range of scales involved, turbu- interfaces (Jaehne et al. 1987, Dade 1993) and for ben- lence affects ecosystem features ranging from basin- thic ecology, where the time-averaged boundary layer scale phytoplankton blooms to the micro-environment flow can be as important as the turbulence (Snelgrove of the plankton. Turbulent mixing promotes rapid mix- & Butman 1994). ing and dispersion at large scales (Okubo 1980, Platt It is unreasonable to expect that any single mixing 1981, Lewis et al. 1984a, b, Bennett & Denman 1989). design for an enclosed experimental ecosystem will Turbulence plays an important role in mass transfer reproduce all of the important characteristics of natural processes at all scales (Jsrgensen & Revsbech 1985, turbulence. It is, however, quite reasonable to ask that Jaehne et al. 1987, Mann & Lazier 1991, Dade 1993, aquatic ecologists understand the choices that must be Denman & Gargett 1995, Karp-Boss et al. 1996). Tur- made with regard to mixing and the potential conse- bulence influences small-scale processes through its quences of making such choices. My intent in this roles in predator-prey interaction (Rothschild & Osborn paper is to provide a framework for exploring these 1988, Browman 1996, Dower et al. 1997), particle choices and consequences. An overview of relevant capture (Shimeta & Jumars 1991), aggregation and dis- characteristics and scales of natural turbulence follows aggregation (Kierrboe 1993, MacIntyre et al. 1995), this introduction. I then discuss the meaning and use of small-scale patchiness (Moore et al. 1992, Squires & important turbulence scales for experimental ecosys- Yamazaki 1995), and species-specific growth inhibi- tem studies, and fol.10~up with a discussion of some of tion (Gibson & Thomas 1995). Turbulence and turbu- the available techniques for generating and quantify- lent mixing are arguably equal in importance to light, ing turbulent mixing in experimental ecosystems. temperature, salinity, and, nutrien.t concentrations. Because of its broad scope, this paper only briefly Simulating natural small-scale turbulence and its addresses each topic. I have attempted to provide more effects in experimental enclosures is straightforward in-depth references whenever possible. (Hwang et al. 1994, Peters & Gross 1994). Small-scale turbulence is approximately isotropic and homogeneous, i.e. statistically independent of direction and CHARACTERISTICS AND SCALES OF NATURAL spatially uniform (Landahl & Mollo-Christensen 1986. TURBULENCE Kundu 1990). Turbulence characteristics at small scales are determined by the rate of turbulent energy Turbulence generation dissipation, E, and the kinematic viscosity of the fluid, v, and do not depend on the turbulence generation Turbulence in nature generally is classified as shear mechanism. generated or buoyancy generated, or some combina- In contrast, generation of realistic large-scale turbu- tion of the two. The likelihood of turbulence and the lence in experimental ecosystem enclosures can be a intensity of turbulence are expressed in terms of non- challenge, especially if a realistic turbulent cascade dimensional ratios between stabilizing and destabil- also is of interest. Stirring by large eddies is responsi- izing forces. The most common of these ratios are ble for the rapidity of turbulent mixing (e.g. Garrett named after the fluid dynamicists credited with their 1989). Problems arise at the reduced scale of experi- discovery. mental ecosystems because ch.aracteristic length and Unstratified shear-generated turbulence is common time scales of large eddies are related to the largest in the wind-mixed surface layer, the bottom boundary scales of the flow. For example, the size of the largest layer, and in flow around obstacles and through open- eddies in a turbulent boundary layer is set by the ings. The onset and intensity of unstratified shear tur- boundary layer thickness, and a characteristic large bulence are governed by the Reynolds number of the eddy recurrence interval is set by the ratio of the flow, Sanford: Turbulent mixing in experimental ecosystems 267

into turbulence. In general, there are multiple possible sources of shear in natural flows, which interact with the stratification and with each other in complex ways (Dyer where U is some characteristic velocity scale (e.g. the & New 1986, Geyer & Smith 1987). average flow speed in m S-'), L is some characteristic Turbulence generated by unstable buoyancy fluxes length scale (e.g. the depth in m), and v is the mole- also is common in nature. Examples include overturn- cular kinematic viscosity (in m2 s-'). The Reynolds ing of the surface mixed layer due to outward heat flux number may be thought of as the ratio of destabilizing (Tayloi- & Stephens 1993, Peters et al. 1994) or in- inertia to stabilizing viscosity. Reynolds numbers fre- creases in near surface salinity caused by evaporation quently are named after the length scale of interest, or freezing. These processes result in unstable density such that the Reynolds number for a horizontal flow of profiles with heavier water over lighter water. The speed U in water of depth h (Re, = Uh/v) is the depth onset and intensity of buoyancy driven turbulence are Reynolds number. Oftentimes several Reynolds num- controlled by the Rayleigh number, bers may be defined, each controlling a different aspect of the turbulence. In the present example a second Reynolds number based on the bottom roughness height may be defined (the roughness Reynolds number) which controls the state (smooth or rough) of the where Ap/p, the normalized unstable density differ- turbulent flow very near the bottom boundary (Nowell ence over depth h, is written as aAT for an imposed & Jumars 1984) and mass transfer across that boundary temperature difference AT (in "C) in a fluid with ther- (Dade 1993). mal expansion coefficient a (in "C-'), and the molecular Most unstratified shear flows in nature are turbulent. diffusivity of mass D,, (in m2 S-') is written as the mole- For example, flow in a water column of depth h is lam- cular thermal diffusivity DH (in m2 s-') for the same sit- inar (non-turbulent) if the depth Reynolds number uation. The Rayleigh number may be thought of as the (Re,) is ~500,turbulent if Re, > 2000, and transitional ratio of the tendency for the water column to overturn between laminar and turbulent for intermediate Rei, to the tendency for diffusion to eliminate unstable den- (Smith 1975). Setting v = 10-%' S-' (a typical value in sity differences. Well-defined convective rolls develop water), even a slow, shallo\v flow with U = 0.02 m SS' for Ra > 1.7 X 103,and the flow becomes fully turbulent and h = 0.1 m has a Reynolds number of 2000 and is for Ra > 106 (Landahl & Mollo-Christensen 1986). For very likely turbulent. example, taking a = 2 X 10-4 "C-' and DF, = 1.45 X Turbulence also can be generated by shear in the 10-' m2 S-' (fresh water at 20°C; Chapman 1974), a presence of stable stratification. In fact, stably stratified temperature increase of AT = O.Ol°C from the surface shear turbulence is the predominant form of turbu- to h = 0.2 m depth would correspond to Ra = 1.1 X 106 lence in the ocean, where it controls mixing across the and fully turbulent mixing would be expected. pycnocline. As a result, a great deal of research has concentrated on this subject in recent years (see reviews by Hopfinger 1987, Abraham 1988, Gargett Turbulence length scales and spectra 1989, Fernando 1991). The most important parameter controlling turbulence generation in the presence of In unstratified turbulence, the size of the largest stable stratification is the Richardson number, eddies, 1 (in m), usually approximates the overall scale of the flow, i.e. the depth of the water column, size of an obstacle, thickness of the bottom boundary layer, depth of the surface mixed layer, etc. In the presence of stable stratification, the largest eddies tend to be smaller than the overall scale of the flow. This is where g is gravitational acceleration (in m S-'), p is the because the largest eddies lose a substantial portion of density of the water (in kg m-3),z is distance normal to their energy working against the stratification (Turner the plane of motion of U (zusually is taken as the vertl- 1973). The maximum length scale for the largest cal direction, positive upwards, in m), and N is the Brunt- eddies in stably stratified turbulence is known as the Vaisala frequency (a measure of water column stability Ozmidov length, and the natural frequency of oscillation of a stably stratified water column, in S-').The Richardson number may be thought of as the ratio of stabilizing stratification to destabilizing shear. Ri >> 0.25 indicates strong stability (Turner 1973, Abraham 1988, Weinstock 1992), where and Ri < 0.25 usually indicates breakdown of the flow E is the energy dissipation rate of the turbulence (in 268 Mar Ecol Prog Ser 161: 265-293,1997

m' S?) (E is discussed below). If velocity data are avail- pressed in terms of wavenumber because Fourier able, 1 also may be defined statistically as the integral decomposition techniques that are central to the length scale of the turbulent velocity field, derivation of turbulent energy spectra are most easily expressed in terms of wavenumber At length scales smaller than 1, or equivalently at wavenumbers greater than k,, the theory predicts that the turbulent energy where UH~~Sis the root mean square of the u velocity spectrum E(k) (the wavenumber distribution of turbu- fluctuations, u is a velocity component (parallel to the X lent velocity variance, in mhs2) will be defined by a direction or perpendicular to the X direction, in m S-'), region known as the equilibrium range in which turbu- X, is an arbitrary fixed position, and X is distance away lent energy is transferred to successively smaller and from that position (in m; Tatterson 1991). Another way smaller eddies (e.g. Landahl & Mollo-Christensen of interpreting Eq. (5) is to think of 1 as the auto-corre- 1986, and Fig. 1). In the equilibrium range, there is no lation length scale of the turbulent velocity field, or the direct external input of turbulent energy. The rate of distance at which velocity fluctuations are no longer energy transfer through this range equals the rate of correlated. energy extraction from the mean flow b\. the large Large eddies in turbulent flows contain the most energy. This is because flows usual!y are most unstable at large scales, 10-2 10' and large eddies are the first to be gener- (a) 7 F ated. For example, large length scales, L, NE 10.3 in Eq. (1) lead to large values of Re and a g greater likelihood of turbulence. Large -E T1- depths h in Eq. (3) have an even greater 3 10~ - 10-2 1 0 0) effect, since Ra depends on h3. If there is Cllc NUX sufficient energy in the flow, the large '8 o eddies themselves become unstable and 10.5 0 10'3 break down into smaller eddies, which in (b) 1°.' turn become unstable and break down I 0-2 into smaller eddies, etc.; this process is known as the cascade of turbulent energy 1w3 (Richardson 1922). Large eddies fre- VISCOUS-ConvectiveSubrange quently are inhomogeneous and aniso- 1Od tropic, reflecting the character of their 10-5 generation mechanism (e.g. Grant et al. 9- 1962, Townsend 1976). Once energy has 10" entered the turbulent field and the tur- "E - bulent energy cascade to smaller and 2- 10'~ lnertlal Subrange smaller scales has begun, however, the 1o.8 character of the turbulence becomes pro- gressively more homogeneous and isotropic (spatially uniform and independent of orientation). The statistical behavior of turbulence once generated is described remarkably Equilibrium Range well by the idealized theory of homogeneous, isotropic turbulence (Batchelor 1967). This theory, which deals with the distribution of turbulent energy in eddies of different sizes, is expressed in terms of wavenumber, k (in m-'), instead of length or size. The wavenumber of an eddy is Fig. 1.Turbulence spectra observed by Grant et al. (1968) at a depth of 15 m just the inverse of its size, such that the near Vancouver Island, BC. Canada. Measurements were in the upper pycnocline under strong tidal forcing conditions; E = 0.52 cm2 S-? (a) Shear wavenumber of the integral length scale spectrum (0) and temperature gradient spectrum (0). (b) Velocity (0) and of turbulence is k, = 2d1.The theory of temperature (0) energy spectra. Adapted from Grant et al. (1968) by isotropic, homogeneous turbulence is ex- permission of Cambridge University Press Sanford: Turbulent mixing in experimental ecosystems

eddies, which also equals the rate of energy diss~pation by molecular viscosity at the smallest scales of turbulence. where A, = 1.5 for E(k) representing the 3-dimensional Molecular viscosity transforms turbulent velocity total energy spectrum and A2 = 0.5 for the l-dimen- shear into heat at the smallest scales of turbulence. The sional variance spectrum of a single velocity compo- rate at which this occurs is known as the turbulent nent (Tennekes & Lumley 1972, Gross et al. 1994) energy dissipation rate E (in m' S-'). (Note that E fre- Eq. (8) has been verified experimentally many times quently is given in different units. Conversion factors since its first convincing demonstration for an ener- are listed in the legend of Table 1.) F is the product of getic tidal flow (Grant et al. 1962). It is one of the most

(velocity shear)' and \I by defin~tion.Velocity shear is important turbulence equations for aquatic ecology the derivative of velocity with respect to distance, because it connects the large scales of turbulence which, expressed in terms of wavenumbers, is equiva- responsible for large-scale mixing with the small scales lent to multiplying by k. Thus, e is given by of turbulence that influence interactions between small plankton. The shear spectrum k2E(k) increases E = 2vjk2~(k)dk (6) as k"%hrough the inertial subrange, reaching a maxi- 0 mum at approximately 0.1-0.2kI; (Lazier & Mann 1989, where E(k) is the 3-dimensional total energy spectrum and Fig. 1). The maximum in the shear spectrum corre- (Tennekes & Lumley 1972). The quantity k2E(k) (in m sponds to the high wavenumber limit of the inertial ss2) is known as the dissipation spectrum or shear spec- subrange, where viscosity begins to dissipate shear trum (Tatterson 1991). energy and the -5/3 slope of E(k)becomes much inore The smallest scale of turbulence and the s.mall size negative. Thus, large eddies at low wavenumbers (high k) limit of the equilibrium range are defined by dominate the turbulent energy spectrum (hence turbu- the Kolmogorov microscale, lent velocities), but small eddies at high wavenumbers dominate the turbulent shear spectrum (hence turbulent shear rates). Turbulence also reduces large-scale grad~ents of (frequently measured in mm; Mann & Lazier 1991, scalars such as temperature, salinity, and nut]-ients Denmdn 1994, Denman & Gargett 1995). r) represents through mixing by successively smaller eddies until the point in a turbulent flow at which fluid inertia is no molecular diffusivity can smooth out the gradients at longer important. At sizes or separations smaller than q, the smallest scales. The theory of isotropic turbulence fluid viscosity dominates and velocity shear is approxi- predicts that the slope of the scalar spectrum Es(k) (in mately the same at all scales, though it varies randomly [scalar unitsI2 m) through the inertial subrange will be in direction and strength (Lazier & Mann 1989). Note the same as the slope of the velocity spectrum E(k),but that Eq. (6) is a factor of 271 greater than the definition it also predicts that Es(k) continues beyond the inertial commonly used by engineers and physical oceanogra- siibrange in water to a higher wavenumber diffusive phers (e.g.Kundu 1990);Eq. (6)is used here because it cutoff (Fig 1).This additional region of the scalar spec- is more common in the ecological literature. With 11 trum is known as the viscous-convective subrange, defined as in Eq. (6),the Kolmogorov wavenumber may and it has a slope proportional to k'(Tennekes & Lum- be defined as kK= 2n/q = (&/v.')'''{which is the same as ley 1972, Kundu 1990). The break in Es(k) occurs at a the definition of k, commonly used by engineers and higher wavenumber than the break in E(k) because physical oceanographers (who frequently leave the fac- molecular diffusivity is not as effective at dissipating tor of 27c out of the relationship between wavenumber scalar gradients as molecular viscosity is at dissipating and size). This distinction between different definitions velocity gradients in water of q is important for aquatic ecologists because r) fre- The smallest size for scalar fluctuations is known as quently is regarded as the actual slze of the smallest the Batchelor microscale, turbulent eddies. Laz~er& hdann (1989) discuss this issue in depth and point out that the definition of q favored by engineers and physical oceanographers is much smaller than any true turbulent eddy. (Mann & Lazier 1991),where Dsis the molecular diffu- The range of wavenumbers such that k, << k << kk, sivity of the scalar (in m2 ss'). In water, the ratio v/Ds is known as the inertial subrange (Fig. 1).It only exists (the Prandtl number for heat and Schmidt number for if the Reynolds number of the turbulence (Re, = everything else) usually is quite large, such that qs c< uRMSVv)is large. The theory of homogeneous, isotropic q. The scalar gradient spectrum defined by k2ES(k) turbulence predicts that the shape of the turbulent reaches a maximum at the break in slope of Es(k) that energy spectrum in the inertial subrange is given by corresponds to the upper limit of the viscous-convec- Table 1 Important turbulence parameters in nature. RMS: root mean square; BBL: benthic boundary layer. Conversion of E units: 100 mm%-' = 1 cm2 S-" = 1 erg g.' S" = 10-1W ,,-3 - 10P W kg'I = 10'4 m' s-3

Parameter Name Defrnilion Environment Typical values Source of values

ii n- 111~IS RMS turbulent velocity I-xu:, n = 1 to 3 Continental shelf BBL 10-~to 10 ' ms-' Heathershaw (1976) \ " 1-1

Shear velocity Continental shelf and IO-~to 10-~m ss' Grant et al. (1984). Sanford & microtidal estuarine BBLs Halka (1993),Gross et al. (1994)

Macrotidal estuarine BBL 10-'to 10.' m S-l Wright et al. (1992).Johnson et al. (1994) Integral length scale Smaller of z or h,,," Grant & Madsen (1986), Abraham (1988) Ozm~dovlength Eq. (4) Stratified interior 10-'to 10~'m ltsweire et al (19931, Denman (1994) Turbulent energy Eqs. (13),(14), (15) Wind-mixed surface layer 5.8 X 10 " W3Z-I W m-.' l' MacKenz~e& Leggett (1993) dissipation rate Near surface, breaking waves lr3to 10-I W m-" Gargett (1989).Johnson et al. (1994). Terray et al. (1996) Energetic tidal channel 10-4 to 10-' W m-" Grant et al. (1968) Stratified intel-ior 10-' to 10-4 W m-" Gargett (1989), Maclntyre (1993) Continental shelf BBL 10-4 to 10 ' W m-3 Gross et al. (1994) Vert~caleddy viscosity, Eqs. (10) to (12) Surface mixed layer IO-~to 1 0-3 mZS' Maclntyre (1993) vertical eddy diffusivity Stratified interior 10-h to 10-' mLss1 ltsweire et al. (1993).Ledwell et al. (1993) BBL 0.4u.z Grant & Madsen (1986). Wright et al. (1992)

tlor~zontaleddy diffusivity Coastal, lx = 100 m 10-' to 10.' m' S-' Okubo (1971) Open ocean, IX = 10 km lol to 10"' S-' Okubo (1971) Kolmogorov microscale For range of E above IO-~to 10-' m Batchelor microscale For range of E above and 10-"0 l or2 m v/DS = 10 to 1000 Viscous sublayer thickness 10vlu. For range of ir. above 10-4 to 10 m Diffusive sublayer thickness SV(v/Ds)-In For range of U. above and 10.' to m v/Ds = 10 to 3000 Boundary layer outer Estuarine and coastal BBLs l00 S Wright et al. (1992) bursting time scale intermittency factor Surface mrxed layer l to2 Baker & Gibson (1987) Stratified inter~or 3 to 7 Baker & Gibson (1987) "where z is distance to the nearest boundary and hb, is boundary layer thickness ''where W IS wind speed in m s ' and z is depth In m Sanford: Turbulentmixing In experimentalecosystems 27 1

tive subrange, at approximately O.lks = 0.1(2n/qs). fusivity. The constant eddy viscosity/diffusivity often is This means that sharp changes in scalar concentration written as proportional to the product of a characteris- can occur across distances similar to the Kolmogorov tic turbulent velocity and the integral length scale of microscale (Fig. l), which may have important conse- the turbulence, or quences for the micro-environment of small plankton.

(Kundu 1990) where U. = (r/p)O"in m S-') is the shear Turbulent mixing velocity (the usual scale velocity for boundary layer turbulence). The constant of proportionality implied in Effective mixing of mass and momentum is one of Eq. (12) is approximately 1, with its exact value the most important consequences of turbulence. Most depending on the details of each situation. However, of this mixing is accomplished by the stirring action of Taylor's theory of turbulent dispersion (e.g. Csanady large, energetic eddies (Okubo 1980, Garrett 1989, 1973, Kundu 1990) demonstrates that assuming a con- Kundu 1990). Since these eddies are dependent on the stant eddy viscosity/diffusivity is valid only when the nature of the large-scale flow, it follows that turbulent length and time scales of interest are larger than the mixing is a property of the flow and not of the fluid. integral length and time scales of the turbulence. The simplest parameterization of turbulent mixing of When this is not the case the eddy viscosity/diffusivity momentum (i.e. turbulent stress) is to assume that tur- may vary with time, with distance away from a bound- bulence results in a much larger effective coefficient of ary (which gives the familiar logarithmic boundary viscosity, the eddy viscosity KM(in m2 S-'). For exam- layer profile; e.g. Grant & Madsen 1986), or with the ple, the vertical shear stress, .s (in kg m-' s2), in a hori- size of a dispersing patch [which gives a characteristic zontally homogeneous, unidirectional flow may be (patch dependence; e.g. Okubo 19711. Constant written: K,,,, and KDare assumed in the remainder of this paper au(~,t) for discussions of scaling, but the limitations of this r(z,t) = pK,,[(z,t)- (10) az assumption should be kept in mind. where r, KAl, and U have been written as functions of the vertical direction z and time t to emphasize that spatial and temporal variabilily of all three is the most Spatial and temporal variability of turbulence general case, and the partial derivative symbol a has been used to emphasize the multi-dimensionality of Landahl & Mollo-Christensen (1986) point out that the problem. The equivalent parameterization of tur- characterizing a variable flow only by its spectra or bulent diffusion of mass is average properties presents a limited description of the true nature of the flow. Temporal and spatial variability are lost in the averaging process. Several important properties of turbulence tend to be temporally and where Fs is the flux of the scalar in the z direction (in spatially variable. Often the flows that generate turbu- scalar mass m'2 S-'), KDis the coefficient of eddy diffu- lence are variable in time and space as well, which can sivity (in mZ S-'), and cs is the concentration of the result in variable mixing on a larger scale. scalar (in scalar mass m-3). Turbulence is intermittent. This intermittency takes For practical purposes it often is assumed that KD= 2 forms, both of which may be related to the probabil- K,,,, which is called the Reynolds analogy (e.g Kundu ity distribution of turbulent quantities. In homoge- 1990). In a well-mixed water column the Reynolds neous, isotropic, steady turbulence, velocity fluctua- analogy is quite reasonable, but it is no longer valid in tions are approximately normally distributed but the presence of stable density stratification (Turner spatial and temporal derivatives of the velocity are not. 1973) Stable stratification decreases turbulent mixing Batchelor (1967) points out that small-scale shear in in general, but mixing of mass decreases more than homogeneous turbulence tends to be intermittent, mixing of momentum such that K, can be significantly characterized by a higher than normal kurtosis (4th smaller than KAl (e.g. Abraham 1988, Lehfeldt & Bloss moment) of its probability distribution that corre- 1988, Chao & Paluszkiewicz 1991). sponds to relatively infrequent bursts of high shear A common and convenient assumption about KM energy. This means that the dissipation rate (the and KD is that they are constant. Under this assump- square of the shear) is intermittent even when there is tion, all of the considerable and relatively familiar no spatial or temporal variability of the turbulence. mathematics of molecular diffusion (Crank 1975) may Dissipation rate also tends to be lognormally distrib- be applied directly to turbulent diffusion as well, sim- uted (Baker & Gibson 1987, Yamazaki & Osborn 1988), ply substituting a much larger value of viscosity or dif- which implies a mean that is greater than the most 272 Mar Ecol Prog Ser 161: 265-293, 1997

probable value and a higher than normal probability of near tbe wall in a smooth turbulent boundary layer. very large events. Similar gradients are present in the wind-mixed sur- The second form of intermittency is associated with face layer (MacKenzie & Leggett 1993), though near- turbulent flows that are not homogeneous or steady. A surface gradients in dissipation may be even streper dimensionless intermittency factor, y, is defined as the during periods of high wind and breaking waves (Gar- fraction of time that the flow at a point is turbulent (e.g. gett 1989, Terray et al. 1996). Localized regions of Townsend 1976. Kundu 1990). At the center of a turbu- higher turbulence intensity near step-like density lent wake y = 1, but it decreases towards the edge of interfaces also have been identified in what might the average envelope of the wake as turbulent eddies otherwise be thought of as continuous stratification become more and more infrequent, until y = 0 outside (MacIntyre et al. 1995). the limit of turbulent activity. This form of variability accentuates the skewness (3rd moment) of the probability distribution of dissipation, causing it to devlate Measurements of natural turbulence from lognormality (Yamazaki & Lueck 1990). Most natural flows are variable in this second sense, including Turbulence in natural water bodies is measured steady shear flows (Townsend 1976, Landahl & Mollo- using 1 of 3 broad classes of techniques. These tech- Christensen 1986), stratified turbulent flows (Yama- niques tend to be limited to different subregions of the zaki & Osborn 1988, Fernando 1991, Gibson 1991),and environment for practical reasons, though some of the complicated, time varying combinations of the two li~ilita.tionsare disappearing as technologies improve. (Dyer & New 1986). First, time series of rapidly sampled, small-scale veloc- Strong spatial gradients of turbulence frequently are ity at a fixed point in a flow are used to determine associated with turbulence generation. For example, mean and turbulent contributions to the total velocity the length scale for turbulence generated by shear at a field. Often these Eulerian measurements are con- boundary increases with distance away from the ducted in the bottom boundary layer (Gross & Nowell boundary, z, while turbulence dissipation rate de- 1983, Grant et al. 1984, Williams et al. 1987) or the sur- creases as z-' (Grant & Madsen 1986). In smooth tur- face mixed layer (Agrawal et al. 1992) with the sensors bulent boundary layer flow, a thin viscous sublayer attached to a rigid, stationary platform. Because most next to the boundary acts essentially in the same turbulence theory deals with length rather than time, capacity as in free turbulence, and a thinner diffusive the time series of turbulent velocity are converted sublayer acts similarly to q, (Dade 1993). Fig. 2a illus- to space series by dividing by the time-averaged veloc- trates the sharp gradients in turbulent d.issipation rate ity, invoking Taylor's 'frozen turbulence' hypothesis (Tennekes & Lumley 1972, Landahl & Mollo-Christensen 1986, Kundu 100 - -~-- -I* - --=5- : \ 1990). Second, nearly instantaneous space series of turbulent velocity or (a) 80 temperature fluctuations are measured with profiling microstructure / instruments (Grant et al. 1968, Its- :l>N 60/ weire & Osborn 1988, Haury et al. 2 40 1990, MacJntyre 1993). More often than not, these measurements are 20 - conducted in the interior of the water 1 column away from the immediate 0--~7- 0.0 0.1 0.2 0.3 vicinity of either boundary. An inter- E V esting variation on this technique has FA ' U been proposed by Galbraith & Kelley (1996),who su.ggest that internal mix- Fig. 2. D~stribut~onof turbulent dissipation rate & in (a) a boundary layer and ing may be estimated by identify~ng (b) near an impeller (a) Near the wall in a smooth turbulent boundar)' layer; from Dade (1993) by permission of the American Society of Limnology and profiles using a Oceanography, Inc Solid llne is modeled, curve, gray area represents scatter of dard CTD Third, some kind of con- data summarized by Pate1 et al. (1985). (b) In a standdrd geometry mixing tank servative tracer 1s injected or placed with an A410 axial irnprller at a Reynolds number of 2 X 105,from Weetman at known locations or depths and its (1992) with kind permission from Kluwer Academic Publishers. Numbers refer time to to the total range of E.Model contours show that E is large near the position of the impeller (not shown) and immediately below at the bottom, but that it estimate mixing directly. Neutrally decreases rapidly with both axial and radial dlstance buoyant dyes are used for both lateral Sanford. Turbulentmixing in experimental ecosystems

dispersion (Okubo 1971) and vertical diffusion studies also has developed in response to modeling and engi- (Ledwell et al. 1993), while isopycnal drifters (Richard- neering needs (Csanady 1973, Fischer et al. 1979) and son 1993) and surface drogues (Davis 1985, List et al. takes the practical approach of assuming some func- 1990) are used primarily to estimate horizontal disper- tional form for K,]and setting controlling parameters sion and transport. empirically. Relationships of the form of Eq. (12) are Several techniques are available for estimating F used frequently (e.g. Middleton et al. 1993). from turbulence measurements. E may be estimated in terms of the large scale turbulence characteristics by Summary

Natural aquatic turbulence is generated at the where A, is a nondimensional constant of order 1 largest scales of motion and dissipated at the smallest (Kundu 1990, Moum 1996).The integral length scale, l, scales. Large-scale velocity gradients and unstable of natural turbulence is sometimes measured (MacIn- buoyancy fluxes are the source of most turbulent tyre 1993), but the assumption that it behaves as in lab- energy. However, velocity and scalar gradients are oratory experiments often yields good results as well. most intense at the smallest scales of turbulent motion. For example, in laboratory experiments on turbulent The large and small scales of turbulence are connected boundary layers, 1 = z and U,qh,s = u., such that Eq. (13) by the well-established theory of isotropic, homoge- becomes neous turbulence, which allows large-scale mixing to be estimated from small-scale parameters (Eq. 16) and small scale dissipation to be estimated from large-scale parameters (Eq. 13) under some conditions. Mixing of where K = 0.4 is von Karman's constant. Thls relation- mass is very similar to mixing of momentum at inter- ship has been found to give reasonable agreement mediate scales, but it is less effective at large scales in with field data (Grant et al. 1984, Gross et al. 1994). the presence of stable stratification and it is less effec- Microstructure investigators usually calculate E as the tive at the smallest scales of turbulence. Turbulence is variance of a single component of shear: variable in both time and space. Dissipation rate is intermittent, with infrequent, large events. The large- scale flows that generate turbulence also vary in time and space. Large gradients in turbulent energy and (SCOR Working Group 69 1988, Yamazaki & Osborn length scales are common, part~cularlynear bound- 1990), where u is a velocity component transverse to aries. the direction of motion z of a n~icrostructureprofiler. Table 1 summarizes the parameters identified in this Finally, a number of investigators have calculated E by section and gives approximate ranges for their values fitting Eq. (8) to observed velocity spectra (Grant et al. in different parts of the natural aquatic environment. It 1984, Agrawal et al. 1992, Gross et al. 1994, Terray et is clear that there is no single parameter that com- al. 1996). pletely characterizes turbulence. It is not yet clear, Several techniques also are available for estimating however, which parameters or con~binationsof para- the effective turbulent diffusion coefficient in nature. meters best characterize turbulent mixing and its When tracers are used, estimates of K, are obtained by effects in experimental ecosystems. This is the subject fitting theoretical curves to observed data (e.g. Kent & of the next section. Pritchard 1959, Ledwell et al. 1993). Another technique for estimating spatially and temporally variable dispersion is through seeding of numerical models with sim- IMPORTANT TURBULENCE SCALES FOR ulated Lagrangian tracers, then following the statisti- ECOSYSTEM STUDIES cal behavior of the ensemble as the numerical flow field evolves (Geyer & Signell 1992). Further, turbu- One approach to evaluating the effects of turbulent lence microstructure investigators frequently estimate mixing in aquatic ecosystems is to express these effects KD based on measurements of energy dissipation, in terms of times, lengths, and velocities, which according to enables straightforward comparison to many ecosystem parameters. This approach is adopted here in an F K,,= 0.2- attempt to condense the numerous natural turbulence NZ parameters discussed in the previous section into a (Osborn 1980, Itsweire et al. 1993). A large body of lit- meaningful and usable set of turbulence parameters erature treating turbulent diffusion in the environment for experimental ecosystem studies. Issues of spatial/ 274 hdar Ecol Prog Ser

temporal variability and benthic-pelagic coupling also are considered.

Large-scale mixing-the mixing time where L, = x(KD/r)"' is the Kierstead-Slobodkin critical patch size (in m; Okubo 1980, Platt 1981). If T,,, > Mixing time is the amount of time that it takes for a Tg, patches develop inside the region and if T, < T,, conservative tracer injected at some point in a region patches disperse. The ratio of the boundary mixing to mix to some degree of uniformity across that region. time (Eq. 17) in a water column of depth h to the set- This may seem like a vague definition, but in fact the tling time, T, = h/ws, (in s) for a particle with fall veloc- precise definition of a mixing time depends on the ity 1% (in m S-') is location of the injection point, the degree of uniformity that is considered 'mlxed', and the boundary conditions of the region of interest. The most frequent expression given for the mixing time in a diffusion- The parameter R,, is a full-depth Rouse number (for a dominated environment is discussion of the Rouse number see, e.g., Muschen- heim 1987). For large R, (7, > T,), settling particles tend to be concentrated near the bottom; for small Rh (T,,< T,), particles tend to be dispersed throughout the (Nixon et al. 1979, Lewis et al. 1984a, MacIntyre water column. This argument is equally valid for buoy- 1993), where T,,,is the mixing time (in S), L is the ant particles, except that accumulation tends to occur size of the region of interest (e.g. depth in m), and near the surface rather than the bottom. Lewis et al. KD is the eddy diffusivity (in m2 S-'). Eq. (17) corre- (1984a, b) also discuss the ratio of the boundary mixing sponds to the time for a tracer injected at one bound- time to the photoadaptation period of phytoplankton, ary of a region to become 97 % uniform within that which, along with the ratio of the mixed layer depth to region, when the boundaries are perfectly reflecting the depth of the euphotic zone, controls the photosyn- (by solution of Eq. 2.17 in Crank 1975). This is a thetic performance of algae in the surface layer. good model for an experimental ecosystem enclo- Finally, the ratio of horizontal mixing time to the dura- sure. If the injection point is located in the interior of tion of larval dispersal should influence the uniformity the region of interest, then the mixing time to the of dispersal within a region of interest (Okubo 1980). same degree of uniformity is controlled by the fur- thest distance to a boundary. For example, if the injection point is in the center of the region then the Mass fluxes and mass transfer coefficients mixing time is given by One of the most important aspects of turbulent mixing in ecology is its influence on fluxes of nutrients and wastes to and from different ecosystem compart- (e.g. MacIntyre 1993). If the boundaries are open, ments. This influence is expressed through flow con- Eq. (18) corresponds to central injection and a Gauss- trol of mass transfer processes, and it is most impor- ian concentration profile with o = L/2 at t = T,, such tant when it limits fluxes relative to biogeochemical that the tracer is 62 % uniform across a region of size L supply or demand. Most often the lirnitlng fluxes are at t= T,,,(Csanady 1973). those that occur across boundaries: the air-sea inter- T, is an excellent choice for the single parameter face (Jaehne et al. 1987), the sediment-water interface that best expresses the influence of large scale mix- (Jorgensen & Revsbech 1985, Santschi et al. 1991, ing in ecology. Many ecological parameters associ- Dade 1993, Glud et al. 1995), the pycnocline (Denman ated w~thlarge scale distribution or dispersal may be & Gargett 1995), surfaces of attached organisms (Koch expressed as ratios of T, to characteristic ecosystem 1994), surfaces of planktonic organisms (Mann 81 times. The most appropriate definition depends on Lazier 1991, Karp-Boss et al. 1996),surfaces of detrital the problem of interest, but generally the boundary aggregates (Alldredge & Cohen 198?), and walls of mixing time (Eq. l?) is best for boundary flux prob- experimental ecosystem enclosures (Oviatt 1994). lems and the central mixing time (Eq. 18) is best for Boundaries restrict turbulent length scales and veloci- internal dispersion problems. The ratio of the central ties and hence restrict the magnitude of the eddy dlf- mixing time (Eq. 18) to the turnover time of a plank- fusivity, such that mixing can become slow enough to ton population, Tg = l/r where r is the growth rate (in Limit fluxes. In general, flux limitation is not an issue S-'), is within the interior of compartments such as the sur- Sanford: Turbulent mixing In experimental ecosystelns 275

face mixed layer and the bottom mixed layer, unless level of turbulent energy inside the benthic chamber is turbulent mixing is very weak. likely to be unrealistically high. Similarly, a realistic Assumption of a constant eddy diffusivity allows all level of turbulent energy in an experimental enclosure of the fluxes of interest to be written using the formal- may result in unrealistically low boundary fluxes. ism of Fick's law: At large scales, P= KD/Az.In this case, both the limiting-layer thickness and the turbulent diffusivity are affected by the flow. The best example of this mode of flow control is mixing across a pycnocline, which dif- where either KD (the turbulent eddy diffusivity in m2 fers depending on the source of turbulent energy S-') or DS (the molecular diffusivity in m2 S-') are used, (Turner 1973, Abraham 1988, Fernando 1991). Internal depending on the scale of the problem, cS IS the con- mixing is generated by veloc~tyshear within the pyc- centration of the scalar quantity of interest (in mass nocline, depending on the Richardson number of the m-"), z is distance in the direction of the maximum gra- flow (Eq. 2). As pointed out previously, internal mixing dient (taken as posit~veupward for simpl~clty,in m), dominates vertical mixing across ocean thermoclines. and AcSrefers to the change in cs across the diffusion- External mixing is generated by turbulence above or limiting layer thickness Az. P is known as the mass below a pycnocline. This form of mixing occurs in transfer coefficient, with units of velocity (m S-'; nature at the base of the surface mixed layer and at the Santschi et al. 1991, Patterson 1992, Dade 1993). top of the bottom mixed layer, but it is virtually the only Eq. (21) provides a convenient way to think about fac- form of mixing possible in an artificial enclosure where tors influencing fluxes; Pis determined by flow condi- there is no large-scale velocity shear to generate inter- tions while Acs is determined by the biological or nal mixing. Internal mixing tends to weaken the den- chemical processes of interest. sity gradient by entraining fluid from outside the pyc- At small scales, = Ds/Az.Since diffusion is entirely nocline into the pycnocline, and it results in a turbulent molecular, flow control of poccurs only through changes diffusivity given by Eq. (16).External mixing tends to in Az; i.e. factors that decrease the thickness of the dif- sharpen the density gradient. If mixing is on one side of fusion-limiting layer increase the mass transfer velocity. the pycnocline only, then the mixed layer entrains the Decreasing Az can occur through increases in flow speed unmixed layer at a rate known as the entrainment or roughness at a solid surface (Dade 1993), through the velocity, which is identical to p (Fernando 1991). If both development of waves at the air-water interface (Jaehne sides of the pycnocline are mixed, then fluid is et al. 1987),through relative velocities Induced by swim- exchanged across the pycnocline in both directions at ming or sinking of larger plankton (Mann & Lazier 1991, the respective, independent entrainment velocities Kiorboe 1993), or in a general sense through anything (Turner 1973).Both internal and external mixing result that increases the Reynolds numbers of organisms (Pat- in mass fluxes across a pycnocline, but the sources of terson 1992, Karp-Boss et al. 1996). In all turbulent flow mixing energy are different, the consequences of mix- cases, Az is proportional to &-'l4 (see Eq. g),where e is the ing are different, and the magnitudes of Pare different. turbulent energy dissipation rate near the outer edge of In many cases, a mass transfer coefficient may be the diffusion-limiting layer converted to a mass transfer rate for comparison to bio- Spat~alvariability in E can lead to problems with seal- geochemical rates of uptake or release. This is particu- ing boundary fluxes in experimental enclosures. When larly convenient in experimental ecosystem enclo- turbulence is generated at a boundary, the dissipation sures. Given a mass transfer coefficient p across a rate is highest near the boundary and decays rapidly boundary with surface area A (in m2) into a volume V away from it (Eq. 14 and Fig. 2a); this is the most com- (in m3),the mass transfer rate, m (in S-'), is given by inon situation in nature, where the surface and bottom boundary layers are important turbulence generation sites. When turbulence is generated away from the boundary and impinges upon it, the dissipation rate is If m is compared to some biological or geochemical low near the boundary and increases away from it rate of uptake or release, r (in S-'), the potential for (Fig. 2b and Brumley & Jirka 1987); this is the most mass transfer limitation may be evaluated readily. For common situation in an exper~mentalecosystem enclo- example, if r represents the maximum nitrate uptake sure. The volume-averaged level of turbulent energy rate by surface layer phytoplankton and m represents needed to achieve the same boundary mass transfer the mass transfer rate of nitrate across the pycnocline, rate is different in these 2 cases. Thus, it is possible to then m/r < 1 indicates that pycnocline fluxes of ammo- stir a benthic flux chamber so as to mimic realistic val- nium may be limiting phytoplankton growth. ues of p at the sediment-water interface (Buchholtz-ten It is important to recognize that similar profiles of Brink et al. 1989, Glud et al. 1995). but the average temperature, salinity, nutnents, etc. may be main- 276 Mar Ecol Prog Ser 1

tained with different rates of mass transfer. For exam- tact due to small-scale turbulent shear. The expression ple, Donaghay 8: Klos (1985) maintained stratified for relative turbulent velocity between 2 particles sep- water columns in the MERL mesocosms at the Univer- arated by a distance, r, that they used was sity of Rhode Island, USA, by chilling the lower layer and relying on solar heating to mainta~na warm upper layer. Mixing was maintained at a constant rate in both which str~ctlyspeaking is valid within the inertial sub- the upper and lower layers. The temperature profile range. Hill et al. (1992) showed that an equation of this that they achieved represented a balance between the form governs particle-particle relative velocities even rate of mixing (which conlrolled m) and the rate of heat at separations smaller than the Kolmogorov microscale loss in the lower layer (essentially the same as r). A (although they quote a factor of 1.37 rather than 1.9), steady-state profile was established for m = r. A similar most probably because particles do not exactly follow profile could have been maintained with less chilling the flow. Extension of Eq. (23) to sub-Kolmogorov and less mixing, or with more chilling and more mix- scales is Important because the organisms most likely ing. The resultant rates of mass transfer across the to be affected by turbulence-enhanced contact are thermocline in these alternative scenarios would have similar to or smaller than q in size (Dower et al. 1997). been quite different, however. In a simllar vein, Boyce Much has been written about the positive influences (1974) demonstrated that similarity in temperature of turbulence on predator-prey contact and the possible profiles inside and outside a thin-wall limnocorral negative influences of turbulence on organism behav- could be achicvcd easily despite gross dissimilarities ior since Kothschild & Osborn's seminai wor~(Sundby between the vertical mixing processes inside and out- & Fossum 1990, Saiz et al. 1992, Alcaraz et al. 1994, side, simply by efficient horizontal heat transfer. Muelbert et al. 1994, Peters & Gross 1994, Denman & A general conclusion from these considerations of Gargett 1995, Landry et al. 1995, Dower et al. 1997). mass transfer is that simulation of both realistic water Some of this research suggests that these small-scale column turbulence and realistic boundary mass fluxes processes may influence directly large-scale abun- is a daunting task in an experimental ecosystem. The dances and distributions (e.g. Sundby & Fossum 1990, primary reason that it is so diffi.cult is that turbulence in Muelbert et al. 1994).However, in a senes of comments nature tends to be generated by shear at the surface on turbulence and predator-prey interactions, Brow- and bottom boundaries or within the pycnocline, while man (1996) and others describe this particular area of mixing in an experimental ecosystem usually is gener- research as theory-rich but data-poor, in need of both ated by artificial internal mechanisms such as paddles, field and laboratory verification. Dower et al. (1997) grids, air bubbling, or pumping. Since mass transfer also caution that more research is needed before links rates depend on the source of mixing energy, it is diffi- between small-scale turbulence and large-scale popu- cult to simulate natural mass fluxes in an artificial lation dynamics can be established firmly. enclosure without distorting the total mixing energy. Small-scale turbulence also influences part~cleag- Natural surface mass fluxes generated by convective gregation and disaggregation processes through its overturning on a windless night may be simulated in a i.nfluence on particle-parti.cle contact and small-scale captured water column, but this is an exception rather shear. Aggregate size and excess density are the pri- than a rule. mary determinants of settling rate (van Leussen 1988, Jumars 1993, Fennessy et al. 1994). Aggregation and disaggregation processes influence settling of phyto- Small-scale effects of turbulence plankton blooms (Kisrboe et al. 1990, Kisrboe 1993), characteristics and vertical distributions of marine Recent research has indicated that t.u.rbulence may snow (Maclntyre et al. 1995), and settling and deposi- have as profound an ecolog~caleffect at small scales as tion of cohesive sediment particles in the bottom it does at large scales, over and above its effects on bound.ary layer (van Leussen 1988, 1997, Wolanski et mass transfer. There are 4 inter-related areas in which al. 1992). van Leussen (1988, 1997) argues that the Kol- turbulence affects small-scale ecosystem processes: mogorov microscale sets an effective upper limit on predator-prey interactions, particle aggregation and aggregate size, demonstrating how turbulence can disaggregation, small-scale patchiness, and species- both promote and limit aggregation. specific growth inhibition. An intriguing aspect of small-scale turbulence is that The influence of small-scale turbulence on plank- it may promote small-scale patchiness rather than uni- tonic pred.ator-prey interactions has received a great formity. Instantaneous gradients of scalars such as deal of attention in recent years. Mu.ch of this attention heat, salt, and nutrients are greatest at scales sim~larto stems from the work of Rothschild & Osborn (1988), q (as discussed previously). Physically th~smay be who proposed an enhanced rate of predator-prey con- attributed to the tendency of small-scale shear, which Sanford: Turbulentmixing in exper~mentalecosystems 277

is no longer truly turbulent, to create elongated con- phytoplankton, with increased clustering during the centration streaks that eventually become narrow periods of calm between intermittent bursts of turbu- enough to be affected by molecular diffusion (Gari-ett lent shear 1989).Microscale patchiness of odor plumes under tur- Variability of larger-scale turbulent mixing is impor- bulent forcing has been observed in the laboratory tant as well. Alternating mixing and stratif.ication is (Moore et al. 1992). Although the mechanism is slightly necessary for ~nitiation of phytoplankton blooms different, Squires & Yamazaki (1995) also have mod- (Legendre 1981, Koseff et al. 1993, Taylor & Stephens eled preferential concentration of particles by small- 1993). Ki~rboe(1993) argued that freq.uent periods of scale turbulence, with possible local concentrations up alternating mixing and stratification give a competitive to 40 times the volume-averaged concentration. advantage to diatoms relative to smaller phytoplank- Small-scale shear similar to that produced by turbu- ton, whereas long perlods of stratification with little lence has been shown to inhibit the growth of certain mixing promote the opposite trend. Lasker (1981) sug- dinoflagellate species (Thomas & Gibson 1992, Gibson gested that periods of stable, non-turbulent conditions & Thomas 1995), presumably due to physiological were needed to avoid over-dilution of larval anchovy stress. Shear thresholds for decreased or inhibited food supplies by turbulent mlxlng. Lewis et al. (1984a, growth are species specific. It appears that relatively b) and Schubert et al. (1995) showed how variable light short exposure to hlgh shear can be just as damaglng exposure of phytoplankton caused b\ large-scale ver- as more continuous exposure. Turbulence also has tical mixing in and out of the euphotic zone can control been shown to alter the structure of bacterioplankton photosynthetic performance. Eckman et al. (1994)indi- communities (Moeseneder & Herndl 1995). The small cated that the tidal variabilities of turbulent bottom scale shear that acts on organisms much smaller than q shear stress and vertical mixing should be important IS proportional to (E/v)'/~,rather than as in Eq. (23) determinants of the settlement success of benthic lar- (Hill et al. 1992). vae in shallow water. The common thread of all of these small-scale effects Difflcult~esarise in attempting to identify mean~ngful of turbulence is that they depend on turbulence dissi- measures of turbulence variability for ecosystem stud- pation rate E raised to some fractional power, in addi- ies. The problem is simplified somewhat by separating tion to depending on properties of the fluid medium or considerations of variability into those that primarily particles. Predator-prey iilteraction and particle aggre- affect small scales and those that primarily dliecl large gation depend on E'" as long as Eq. (23) is valid. Parti- scales. Turbulent shear and dissipation rate, which are cle disaggregation depends on velocity shear relative most important at small scales, are characterized by to aggregate strength, with typical maximum aggre- infrequent large events and intermittency. Reasonable gate sizes similar to q, which in turn depends on E-"~. measures of this kind of turbulence variability in an Velocity shear depends on €'l3 at scales much larger experimental ecosystem might include the range of than q and on E'" at scales much smaller than q.Small turbulent dissipation rates likely to be encountered by scale patchiness depends on the existence of a siynifi- an organism and the characteristic time scale of inter- cant viscous-convective subrange in the scalar energy mittence. Baker & Gibson (1987) advocated use of the spectrum, which in turn depends on E-"' and on the variance of the logarithm of dissipation rate as a mea- ratio of molecular viscosity to molecular diffusivity (the sure of intermittency. In the present context this para- Schmidt number). meter is more like a measure of the range of dissipation rates, but it is a good, parameter to measure because it may be compared to data obtained in natural flows. Spatial and temporal variability of turbulence Temporal variability of large-scale mixing may be characterized by the time history of a large scale tur- Spatial and temporal vdriability of turbulence can bulence parameter such as UR~,S,Tm, or Kh,.Appropri- have important consequences for ecosystem processes. ate measures in experimental ecosystems might At small scales, Gibson & Thomas (1995) reported that include on and off times for mixing and the phase of brief daily exposure to high turbulent shear is enough the mixing cycle relative to other important cycles of to inhibit the growth of dinoflagellates. Hwang et al. external forcing, such as the light-dark cycle. (1994) showed that, though copepods exhibit initial Finally, it must be remembered that turbulence at escape responses to turbulent shear, they eventually large and small scales generally covaries. Thus, high become habituated to the extra stimulus. The length of winds that increase predator-prey contact rates in the calm interval between bursts of turbulent shear near-surface waters also disperse prey patches and determines how long habituation is maintained. potentially lower prey concentrations (Dower et al. Bowen et al. (1993) showed that motile bacteria may be 1997). Similarly, plankton that are advected through capable of temporary clustering in the vicinity of zones of high and low turbulent energy by large eddies 278 Mar Ecol Prog Ser 161: 265-293, 1997

in nature experience considerably greater variation in time, T,,,, and turbulence dissipation rate, E, the former small-scale shear than plankton held in an experimen- representing the effects of large-scale mixing and the tal chamber with a continuously oscillating grid. latter the effects of small-scale shear. T,r, 1s a very useful measure of large-scale mixing effects in experimental ecosystems. In general the boundary mixing Benthic-pelagic coupling time (Eq. 17) is best for boundary flux problems and the central mixing time (Eq. 18) is best for internal dis- It is tempting to consider pelagic and benthic pro- persion problems. Ratios of T,,, to characteristic ecosys- cesses in isolation. For example, SCOR Working Group tem times, such as population turnover time (Eq. 19) or 85 (1990) concentrated separately on free-floating particle settling time (Eq. 20), reveal much about over- open-water enclosures and sublittoral benthic enclo- all distributions and characteristics of associated sures. However, many of the problems that they iden- ecosystem components. There are 2 important caveats, tified as appropriate for investigation in experimental however. First, Tmis loosely defined in the sense that ecosystems are affected directly by benthic-pelagic its definition depends on the choice of a reference coupling. Artifacts resulting from separation of the point within the ecosystem enclosure and the choice of water column and the benthos especially are likely in a level of uniformity that is to be considered mixed. shallow water ecosystems. Oviatt (1994) notes major Second, caution must be used when comparing esti- differences in plankton communities in the MERL mates of T, based on different definitions, since most rnesocosms that resulted from inclusion or exclusion of definitions of T,,, assume a constant eddy diffusivity a realistic benthos; both benthic nutrient remineraliza- that is valid only in a limited sense. E is the controlling tion and pelagic-benthic competition were implicated. physical factor for a wide variety of ecosystem pro- Threlkeld (1994) also presents cogent arguments for cesses, ranging from mass transfer across boundaries pursuing experiments in linked pelagic-benthic sys- to predator-prey interaction to small-scale patchiness. tems, where components of either sub-environment Many of these processes depend on a local value of E can affect components of the other. that may be quite different from the average value, In most experimental ecosystems that do include such that it is just as important to measure the distrib- both pelagic and benthic elements, the benthos is sim- ution of E within an enclosure as it is to determine its ply placed at the bottom of the pelagic tank. This intro- average value. duces a mismatch in benthic and pelaqc turbulence Spatial and temporal variability of turbulent mixing scales, discussed above in the context of benthic mass also may be expressed in terms of T, and E.The time transfer. Benthic organisms also are affected by the history of Tm is an important indicator of large-scale artificial flow environment (Nowell & Jumars 1984, temporal variability. The skewness and kurtosis (the Snelgrove & Butman 1994). For example, feeding 3rd and 4th moments) of the probability distribution of behavior and efficiency (Carey 1983, Muschenheim E are a good measure of the likelihood of rare large 1987, Monismith et al. 1990, Grizzle et al. 1992, events and the degree of intermittency that affect Taghon & Greene 1992, Butman et al. 1994) and larval small-scale processes. settlement (Butman 1987, Pawlik & Butman 1993) are When benthic processes and benthic-pelagic cou- affected by the presence or absence of horizontal flow pling are important, 3 more important turbulence and horizontal particle flux. The relevant velocity scale scales are added. These are the mean and variance of for these processes is the mean shear velocity, U,, and the bottom shear velocity, u., and a typical value of the the relevant length scale near the bottom is the bottom bottom roughness, kb. roughness, k,, (Butman 1986, Muschenheim 1987). Many important processes in experimental ecosys- Thus, experimental ecosystems containing benthos tems are affected by turbulence at all scales. Particle should add 3 more variables for scale comparisons: the cycling is a good example. Large-scale distributions of mean and variance of U. and a typical value of kb. Nat- settling particles are controlled by the mixing time and ural boundary layers presumably are characterized by the settling velocity (Eq. 20). The settling velocity is larger U. means and smaller U. variances than conven- influenced by aggregation and disaggregation pro- tionally mixed experimental ecosystems (except per- cesses, which are controlled by small-scale turbulence. haps for wave-dominated environments; Denny 1988). Resuspension and d.eposition processes may be thought of as mass transfers across the sediment-water interface controlled by parameters similar to those dis- Summary cussed in connection with Eq. (21) and by the time variability of benthic boundary layer flow (Mehta 1988, The 2 most important turbulence parameters for Sanford & Chang 1997). Thus, if particle cycling is to experimental ecosystem research are overall mixing be considered from a system perspective, the implica- Sanford: Turbulent m~xingin experimental ecosystems 279

tions of ignoring or distorting turbulence characteris- (3) Non-interference: The mixing apparatus should not tics at any scale must be considered carefully. block light significantly (when this is an issue), nor should it disturb organisms significantly (Pliestad 1990). IMPLEMENTING AND QUANTIFYING TURBU- (4)Cost: Costs of constructing and maintaining a mix- LENT MIXING IN EXPERIMENTAL ECOSYSTEMS ing system should not be so large as to limit replica- tion or repetition of an experiment. Important features of natural turbulence and impor- (5) Durability: Ecosystem experiments often run for tant mixing scales for experimental ecosystem re- extended periods of time, and environmental condi- search have been identified in the preceding sections. tions frequently are not very hospitable for complex No less important are the practical questions of how to mechanical systems. A good mixing system design implement a mixing scheme and how to gauge its per- will stand up to sustained use over long periods formance. This section explores various aspects of without frequent Interruption for maintenance or implementing and quantifying realistic turbulent mix- repairs. ing in experimental ecosystem enclosures. It is orga- (6) Benignity: Mixing components should not contami- nized into subsections on general considerations and nate or otherwise affect the environmental quality constraints, lessons from chemical engineering, exist- of an ecosysten~enclosure, and they should not ing experimental ecosystem mixing schemes, tech- retain nutrients or contaminants from one experi- niques for measuring turbulent mlxing in enclosures, ment to the next. Heat generated by the mixing and dimensional analysis. apparatus should not significantly change the temperature of the enclosure. (7) Wall shear: The walls of ecosystem enclosures are General considerations and constraints the source of some of the most significant artifacts in experimental ecosystem research (Oviatt 1994). There are a number of mixing considerations for High shear at the bvalls results in little if any mass experimental ecosystems that are more practical than transfer limitation for wall communities. Mixing theoretical. Many of these are little more than common schemes that cause large shear at the walls relative sense, bul they should be enumerated both for com- to the surface, bottom, and interior of an enclosure pleteness and because they impose constraints on the should be avoided. This is especially important if design of a mixing system. The most important are the growth of wall communities cannot be controlled by frequent wall cleaning. (1) Size: There are minimum dimensions for meso- (8) Scope: If an experiment is limited in scope, the cosms based on organism size and behavior (Guan- scale and complexity of the mixing apparatus can guo 1990), light extinction (Menzel & Case 1977), be limited accordingly. For example, experiments trophic complexity (Kuiper et al. 1983), and sam- on benthic recruitment can concentrate on repre- pling requirements. Size also is an issue with senting the benthic environment accurately, as long regard to the state of the turbulence (Osborn & as primary production, nutrient cycling, and trophic Scotti 1996). Targeted natural turbulence dissipa- interactions in the plankton are not a concern (But- tion levels often are quite low (Table 1). If the man 1987, Findlay et al. 1992, Grassle et al. 1992). turbulence generation apparatus is small, the inte- Experiments on attached or tethered organism gral length scale 1 will be small and the turbulence behavior under turbulent conditions can concen- Reynolds number, Re, = UR!,,~1/v = E'~''~~'~'/V,may be trate on flow and turbulence in the vicinity of the too low for true turbulence (< 100; Oldshue & Herbst organism alone (Costello et al. 1990, Johnson & 1990). Sebens 1993, Hwang et al. 1994) The definition of (2)Time scales: The mixing time T,,, has been empha- experimental ecosystem is stretched by inclusion of sized here (Eqs. 17-20), but there are a number of these limited situations, but that 1s not the issue other important experimental ecosystem time here. The point is that simpler can be easier or more scales that must be considered in relation to natural accurate, as long as the limitations of simplification ecosystem time scales. These include flushing time are recognized. relative to generation times for species of interest (an important determinant of ecosystem variability; Lewis & Platt 1982), on-off cycling of mixing rela- Lessons from chemical engineering tive to endogenous rhythms in nature (e.g. the tidal cycle), and on-off cycling of light relative to the nat- Chemical engineers deal routinely with many of the ural die1 cycle. mixing issues raised here. Mixing is an integral 280 Mar Ecol Prog Ser 161. 265-293, 1997

unless otherwise noted) Typical dimensions and flow patterns of standard geometry tanks are indicated in Fig. 3. A standard tank is cylindrical and as wide as it

D-lnpellw Diameter is dccp, with a single impeller at approximately 2/i T.Tank Dlarneter depth that is rotated unidirectionally about a vertical Llquld Hetghl H..T axis. The spin imparted to the flow by the impeller is broken up and converted to vertical stirring by vertical Impeller Blade Wldlh baffles on the walls. Two types of irnpeller are used: a W-114 10 116 D lnpeller Clearance horizontal disk with vertical blades known as a radial C.116 to 112 1 impeller that drives an outward flow, and an open set of pitched blades known as an axial impeller that drives a vertical flow. Three powerful concepts from chemical engineering mixing studies may be transferred to experimental ecosystem studies, not including mechanical design considerations. The first is that the power put into mixing, which is equal to the power dissipated by turbulence at steady state, may be written as a function of LlqUld Helgt the yeolneti-y of the system and the rate of impcller H-T rotation: Impeller Blade Wldlh W-114 10 116 D

where E is the volume averaged dissipation rate, P is kz 1-Tank Diameter applied power (in W = kg m2 s-~),V is tank volume (in (b l m3), Np is the dimensionless, empirically determined Fig. 3. Standard tank geometry for chemical engineering mix- power number, N is impeller rotation rate (in S-'), and ing tanks, from Tatterson (1991) with the permission of the D is impeller diameter (in m). Note that the average McGraw-Hill Companies. (a] Radial impeller and associated value of E on the left-hand side of Eq. (24) does not flow pattern. (b] Axial impeller and associated flow pattern indicate the variability of E within the tank. It typically (see also E distribution in Fig. 2b) varies over almost 2 orders of magnitude, with the highest values in a small region around the impeller process in the chemical, petrochemical, biochemical, (Fig. 2b). Several ecological researchers also have esti- and waste management industries (Oldshue & Herbst mated average E by measuring the power put into mix- 1990, Tatterson 1991). The goals of chemical process ing at steady state (Nixon et al. 1980, Kierrboe et al. mixing differ significantly from the goals of expeli- 1990, Peters & Gross 1994), with mixed success (dis- mental ecosystem mixing, however. In most cases, cussed below). chemical engineers want to maximize the rate of a mix- The second important concept is the use of scale ing-controlled reaction, such that mixing rates, turbu- models for mixing system design and evaluation. lent energies, and Reynolds numbers are all much The power number Np may be shown to be a function higher than is acceptable for experimental ecosystem of the geometry of the tank-mixer system and an research. Perhaps the closest chemical engineering impeller Reynolds number, ReD = ND2/v: analog to an experimental ecosystem is an industrial Np Rel; X nondimensional geometric terms (25) fermentor, where a community of microbes is the prime concern (Feijen & Hoffmeester 1992). In any The exponent a varies with Reynolds number between case, the design principles used by chemical engineers cr= -1 for low Reynolds numbers and a = 0 for high for mixing tanks are a useful touchstone for ecologists. Reynolds numbers. For high Reynolds numbers and Similar conceptual transfers from chemical engineer- similar geometries (e.g. the standard tank geometry), ing have been invoked in other areas of ecology (Penry Np is approximately constant. Eq. (25) allows scale 1989, Patterson 1992). modeling of tank mixing in which the size of the sys- Much of the chemical engineering literature on mix- tem is scaled down and the rotation rate is scaled up to ing deals with impeller designs, flow patterns, and tur- maintain the same Reynolds number. Flow and turbu- bulence characteristics in a 'standard tank geometry' lence characteristics are then identical between a (Oldshue & Herbst 1990, Tatterson 1991; the remain- small-scale model and a full-scale prototype. An obvi- der of this subsection is drawn from these 2 references ous advantage of this approach is that laboratory-scale Sanford: Turbulent mixing in experimental ecosystems 281

Fig. 4. Schematic of 2 mixing schemes in the MERL mesocosms at the Umversity of Rhode Island, USA, from Donaghay & Klos (1985). The vertical plunger on the left was the orlginal rnix- Ing des~gn.It has gradually been replaced by the rotating paddle/ bar design on the right, which was developed to enable a strati- fled water column experiment to be performed. Stratification can be eliminated by placing mixing bars throughout the water column. The direction of paddle rotation is reversed periodically to avold spin-up of the water column In both des~gns,mixing is turned off for 2 to 4 h every 6 h to simulate tidal slack WELL-MIXED MESOCOSM STRATIFIED MESOCOSM models are much easier to construct, measure, and Existing experimental ecosystem mixing schemes modify than full-scale prototypes. The possibilities of scale modeliny in experimental ecosystem research Mixing, like many other aspects of experimental are discussed below in connection with the use of ecosystem design, is something that everyone does dif- dimensional analysis techniques in ecology. ferently. There are, however, several general cate- The third important concept is that mixing in tanks gories into which existing schemes can be placed. can be separated into what chemical engineers refer to These include rotating paddles and oscillating grids in as flow and shear. In more familiar terms, flow is equiv- tanks, flexible-walled in situ enclosures, stirred ben- alent to circulation or stirring and shear is equivalent to thic chambers and flumes, and miscellaneous other turbulent dissipation in the vicinity of the impeller. The schemes including bubbling, pumping, and shaking of design of the impeller controls the ratio between flow a variety of enclosures. A few selected examples are and shear. Large, slowly spinning axial impellers pro- presented here to illustrate the range of designs and to mote flow, while small, rapidly spinning radial or discuss advantages and disadvantages of different unpitched axial lmpellers promote shear. High-flow/ schemes. low-shear mixing is most effective for stirring and sus- Rotating paddle mixers are similar to the standard pension of particles, while low-flow/high-shear mixing chemical engineering mixing scheme shown in Fig. 3. is most effective for promoting small-scale particle They are used in land-based, rigid-wall enclosures. In contact and dispersion. Clearly, neither extreme 1s this design, paddles or mixing bars are rotated about a desirable for experlinental ecosystem studies. High- vertical axis to produce turbulence along with varying flow mixing tends to transfer most of the turbulence levels of circulation. Rotation is periodically stopped production and energy dissipation to the walls. High- and reversed to avoid spinning up the water column in shear mixing tends to create local zones of intense dis- one direction. Examples include the MERL mesocosms sipation with little exchange between different parts of at the University of Rhode Island, USA (Donaghay & the tank. A balance between the two is desirable. The Klos 1985, Klos 1988), the RIKZ mesocosms in Jacoba- right amount of flow will help with large scale disper- haven, The Netherlands (Peeters et al. 1993, Prins et al. sion and will ensure that all of the water in an ecosys- 1994), and the MEERC mesocosms at the University of tem enclosure is carried past the impeller at some Maryland, USA (L. Sanford, S. Suttles, E. Porter & R. point, while the right amount of shear will mimic the Calabrese unpubl.). The MERL systems are illustrated range of dissipation rates likely to be encountered by in Fig. 4. The original mixing scheme in WIERL was a an organism in its natural environment. vertically oscillating plunger, which maintained a well 282 Mar Ecol Prog Ser 161: 265-293.1997

energy is ~ncreasedin compensation (Prins et al. 1994).Disturbance of organisms by the pad- dl.es and ~nitiationof experiments with realistic natural populations do not seem to be major problems in practice (B. Sullivan, MERL, pers. comm.). Oscillating grids have been used by a number of investigators to generate turbulence at a variety of scales and in 2 different modes. A schematic of an oscillating grid mesocosm mix- i.ng system is shown in Fig. 5. Oscillating grids are used most often in rigid-walled land-based tanks ranging in size from laboratory beakers (Kiorboe et al. 1990, Peters & Gross 1994) through microcosms containing tens of liters of water (Estrada et al. 1988, Hwang et al. 1994, Landry et al. 1995) to mesocosms of several m" volume (Howarth et al. 1993). The first mode of grid operation is a short, relatively rapid oscillation centered on a fixed location (Estrada et al. 1987, Ki~rboeet al. 1990, Saiz et al. 1992, Howarth et al. 1993, Hwang et al. 1994, Landry et al. 1995, Brunk et al. 1996). This mode has several advantages. A large por- Fig. 5. Oscillating grid mixing scheme used by Estrada et a1 (1987). tion of the water column is undisturbed, there Two circular pieces of netlon netting of 6 mm mesh size oscillated up are good published measurements of oscillating and down In the upper part of 15 cm diameter culture vessels to stir the lighted surface layer. Other Investigators (e.g. Howarth et al. grid turbulence (Brumley & Jirka 1987, Hill et 1993) have used oscillating grid systems in larger tanks with larger al. 1992, Howarth et al. 1993, Brunk et al. 1996), grid elements and direct measurement of mixing power is possible through the use of force and displace- ment transducers (Kiarboe et al. 1990). The mixed water column with artificially high vertical major disadvantage of this mode of operation is that exchange (Nixon et al. 1980). Rotating paddles were there is an extremely large gradient in turbu.lent dissi- introduced to enable a stratified water column expen- pation rate away from the center of oscillation. Turbu- ment to be conducted (Donaghay & Klos 1985), but lent dissipation rate decays approx~mately as dis- they have become standard for most recent MERL tan~e-~in the vicinity of the grid (Brumley & Jirka experiments (E. Klos, University of Rhode Island, pers. 1987). In addition, there is little net circulation to stir comm.). the water column, such that the various subregions of Rotating paddle mixers can simulate the major fea- the tank may be poorly connected. The second mode of tures of natural water column turbulence. Expenmen- grid operation is a longer, slower oscillation, with the tal ecosystems mixed with rotating paddles are capa- grid passing through most of the water in the tank at ble of sustaining a realistic aquatic ecosystem for least once per cycle (Peters & Gross 1994). This mode extended periods of time Rotating paddles may be ensures more homogeneous turbulence, but it may be used to maintain either a well-mixed water column or more disruptive to delicate organisms and it is more 2 well-mixed layers separated by a pycnocline. San- difficult to sample. Other potential disadvantages of ford et al. (unpubl.) have shown that chemical engi- both modes of operation include grid interference with neering scaling rules (e.g. Eq. 24) are in qualitative the light field and an artificially low energy benthic agreement with the behavior of the rotating paddle environment. mixing systems in the MEERC mesocosms. Because Flexible-wall in situexperimental ecosystems have the systems are accessible, maintenance and wall- been used by aqu.atic ecologists for nearly 40 years cleaning are relatively straightforward. Disadvantages (Banse 1982, SCOR Working Group 85 1990). These of this mixing design include a practical upper limit on enclosures tend to be deep, relatively narrow bags volume (the MERL tanks are the largest at 13 m", constructed of thin, clear plastic sheeting (Menzel & expenses of construction, and an artificially low energy Case 1977. Grice & Reeve 1982). They usually are sup- benthic environment unless the internal mixing ported at the surface by floatation rings, with the walls Sanford: Turbulent mixing in experimental ecosystems 283

kept vertical by weighted shrouds, guy wires, or an --. adjacent structure. Fig. 6 is an illustration of the flexi- - -. . - -. ble-wall in situ enclosures used in the CEPEX field -.--:- program carried out in Saanich Inlet, British Columbia, in the late 1970s (Menzel & Case 1977, Grice & Reeve 1982). Advantages of these systems are that a large volume of jn situ water and most of its associated organisms can be captured with little disturbance, that incident light is more natural than in many other experimental ecosystems, and that temperatures are naturally controlled by the surrounding water Disad- vantages include a somewhat greater difficulty of sampling and the fact that these systems seldom include benthos (but see Riemann et al. 1988, Chrost & Riemann 1994). The most important drawback of flexible-wall enclo- Dtmenstons Small Large Total Length 16 m 29 m sures, however, is that mixing is greatly reduced. For am2 m IOm example, Steele et al. (1977) estimated vertical turbulent diffusivities of approximately 0.1 cm2 S-' in the CEPEX enclosures. This is larger than molecular diffu- 00 sivity; Steele et al. (1977) speculated that a certain Fig 6. Schematic of 2 flexible-wall ~n sjtu enclosures used amount of mixlng was induced by instantaneous tem- in the CEPEX study in Saanich Inlet, BC, Canada, in the perat.ure exchange across the walls, nighttime convec- late 1970% from Grice & Reeve (1982) by permission of tion, and wave forcing at the surface. However, 0.1 cm2 Springer-Verlag, Inc. In most experiments, the enclosures were not mixed other than by naturally induced motion of S-' is at least an order of magnitude smaller than the walls and nighttime cooling, though Eppley et al. (1978) turbulent diffusivity in the natural surface layer. As a and Sonntag & Parsons (1979) describe experiments with result, the CEPEX enclosures were artificially stratified bubbling. The small-diameter enclosures were better mixed with virtually no upward nutrient flux (Takahashi & than the large-dia~llelerenclosures, but both designs were Whitney 1977), and larger phytoplankton settled out signjficantly under-mixed relative to the external water column rapidly after initiation of the experiments (Eppley et al. 1978). Absence of large scale mixing almost certainly meant little turbulent energy at small scales, which Air bubbling is a mixing scheme with precedents in likely affected trophic interactions within the enclo- chemical engineering but very few published applica- sures as well. Brief daily mixing by bubbling was suffi- tions in experimental ecosystems. In chemical process cient to reestablish a more normal plankton (Eppley et mixing, bubbling is most often used in metallurgical al. 1978, Sonntag & Parsons 1979), but the temporal applications. A useful relationship for the average dis- pattern and intensity of mixing were not natural. sipation rate produced by bubbling is Small flexible-wall enclosures narrower than the wavelength of prevailing waves do seem to be better E=-P -QgH mixed (Gust 1977, Takahashi & Whitney 1977).Chrost & pv- v Riemann (1994) also report on experiments In flexible- where Q is the volume flow rate of the gas (in m" S-'), g wall systems stirred by 'wind-driven rmlls', but no further is gravitational acceleration (in m S-'), and H is the details are given. Watanabe et al. (1995) describe a jet- depth of bubbling (in m) (Tatterson 1991). Details of pipe scheme for stirring the upper few meters of moored mixing produced by bubbling depend on the location enclosures, which was sufficient to prevent sedimenta- of bubble injection. In experimental ecosystem appli- tion of the larger phytoplankton. They provide a rea- cations, Eppley et al. (1978) and Sonntag & Parsons sonable description of the resulting circulation, but no (1979) bubbled the CEPEX enclosures to keep larger turbulence measurements appear to have been made. In phytoplankton suspended and to resupply nutrients to addition, thelr scheme requires an external power source the upper part of the water column, respectively. An to run the pumps. The general lack of schemes for im- appropriate duration and frequency of bubbling were plementing controlled mixing in flexible-wall experi- guessed at in both cases, and adjusted as necessary to mental ecosystem enclosures should be addressed, as achieve the desired results. should the lack of data on turbulence characteristics in Recirculation by pumping has been used on occasion these systems. This is especially true in light of some of for mixing purposes (e.g. Kotak & Robinson 1991). the other advantages of these systems. While attractive in its simplicity, pumping is not a very 284 Mar Ecol Prog Ser 161: 265-293, 1997

Fig. 7. Schematic of a soft-bottom sublittoral benthic rnesocosm on the Oslofjord, Norway, from Berge et al. (1986) by permission of Ophelia Publications. (1) Perfo- rated tube for inflow of water; (2) perfo- rated tube for outflo~vof water, (3)flow- meter; (4)sedlment boxes; (5) moveable bridge; (6) dividing partition. By controlling flow rate, water depth, and light, the system can reproduce the basic features of the benthic environment.Realistic distributions of bottom shear stress [Nowell Sc Jumars 1987) require more sophisticated technologies realistic representation of natural turbulence. Pumping be present, however, most of which have been dis- tends to produce flow with low shear in the interior of cussed above. For example, too little flow can have a the experimental ecosystem enclosure and very high profound effect on decomposition and regeneration shear in the pump/hose assembly. If the fluid is rein- processes (Tenore 1987), largely through mass transfer troduced into the tank as a jet, it can contribute to mix- limitation. Similar systems constructed to mimic hard- ing in the enclosure; in this case there are precedents bottom intertidal benthos have added regular surface in the chemical engineering literature (Tatterson 1991) wave forcing to the flow-through (Bakke 1990). A and, interior mixing may be more realistic. caveat to all of these systems is that unrealistically reg- Benthic experimental ecosystem studies may be ular flow patterns can artificially structure the benthos classified as in situ plots, channels, tunnels, or enclo- within an enclosure (Bakke 1990). Attempts to match sures with varying degrees of connection to the sur- in situ boundary layer flow by the use of open channels rounding environment (e.g. Asmus et al. 1992, and see aligned into the flow (Asmus et al. 1992) can be suc- Banse 1982), and land-based facilities with sediments cessful with careful design, but flow disturbance by the and organisms transplanted from the field (e.g. Silver- physical structure may result in entrance condition and berg et al. 1995). A separate classification into soft-bot- container artifacts (Snelgrove et al. 1995). Stirring tom (de Wilde 1990) or hard-bottom (Bakke 1990) away from the boundary can produce realistic sedi- ecosystems may be made as well. In situ benthic stud- ment-water fluxes (Cahoon 1988, Buchholtz-ten Brink ies are not affected as senously by advective changes et al. 1989, Glud et al. 19951, but at a cost of too much as are plankton studies, since many of the organisms of internal energy. Small scale pressure gradients in- interest are fixed to the bottom. This fact, along with duced by stirring an enclosure also may result in the difficulties of transporting undisturbed sediment advective flushing of pore waters in sandy sediments and benthos from the field and the long periods of (Huettel & Gust 1992). adjustment required before experiments can begin (de Man.y of these problems may be addressed through Wilde 1990), have tended to restrict interest in land- careful flume design and construction (Muschenheim based benthic ecosystem studies. However, de Wilde et al. 1986, Nowell & Jumars 1987, Butman et al. 1994, (1990) points out that in situ studies seldom have true Grizzle et al. 1994, G. Taghon, Rutgers University, experimental control over the environment. When this USA, pers. comm.), but frequently such facilities are control, is important, land-based benthic ecosystem quite expensive and complex. An even larger question enclosure studies are a viable alternative. has to do with realistic coupling of pelagic and benthic A reasonable representation of the benthos can be environments in one system. There do not appear to be maintained in a benthic ecosystem enclosure by simple any published experimental ecosystem designs that flow-through (Berge et al. 1986, Bakke 1990) or inter- adequately reproduce both mixing of the water column nal recirculation (Silverberg et al. 1995). Fig. 7 sh.ows and the flow environment of the benthos, although at one such enclosure at Solbergstrand on the east side of least one example of such a design is being tested the Oslofjord, Norway. A number of flow artifacts may (Porter et al. 1997). At this time benthic-pelagic link- Sanford. TUI-bulentmixing in experimental ecosystems 285

age remains an important but unsolved problem in temperature, salinity, composition, and water chem- experimental ecosystem design. istry. The dissolution rate versus speed calibration depends on the size, shape, and Reynolds number regime of the blocks or plates as well. This means that, Techniques for measuring turbulent mixing in practice, gypsum dissolution techniques must be in enclosures calibrated for each application to obtain quantitative results. However, gypsum dissolution is useful as a rel- Quantifying turbulence can be an intimidating ative measure even without calibration data (Oviatt et prospect for an ecologist untrained in physical al. 1977, Nixon et al. 1980). A caveat is that equal gyp- oceanography or fluid mechanics. There are, however, sum dissolution rates in 2 different environments only a number of straightforward techniques for quantify- indicate equal scale velocities in a limited sense. If the ing the important mixing characteristics identified nature of the flow is different but the scale velocity is here. Several of these techniques do not requlre spe- similar (e.g if U in steady flow is approximately the cialized equipment 01- analysis. In addition, recent same as UR,LJSin fluctuating flow), gypsum dissolution instrumentation developments have made direct mea- measurements will indicate a misleading similarity. It surement of turbulence in experimental ecosystem also is important to note that equal gypsum dissolution enclosures less expensive and less complicated than in rates do not indicate equal E; E can be significantly dif- the past. ferent if 1 is significantly different (Eq. 13), in spite of The best method for estimating T,,, is through dye similar values of UR&,S. dispersion techniques, according to its definition Several flow sensors are available for direct mea- (Eq. 17 or 18). Measurements of T, by dye dispersion surement of turbulent velocities in experimental have been reported for several rotating paddle or ecosystems. These include laser doppler velocin~eters plunger mixers (Nixon et al. 1980, Bonner et al. 1992, (LDVs; Hill et al. 1992), hot wire (Gust 1977) and hot Peeters et al. 1993, Sanford et al. unpubl.) and for flex- film (Howarth et al. 1993) probes. small acoustic veloc- ible-wall in situenclosures (Steele et al. 1977). The dye ity sensors (Kraus et al. 1994, Trivett & Snow 1995), and dispersion technique also is used in chemical engi- small electromagnetic velocity sensors (Howarth et al. neering mixing studies (Tatterson 1991) and in physi- 1993). Flush-mounted hot-film probes also are avail- cal oceanography (e.g. Ledwell et al. 1993). A small able for measurement of U. (Gust 1988). Important amount of tracer-labeled neutrally buoyant fluid is requirements for such a sensor are a size much smaller injected either at the surface or at mid-depth and sam- than 1, response time and sampllng rate much faster ples are taken at several locations in the enclosure over than 1/U, and directionality of response. Sensors that time. The mixing time is defined by tracer concentra- do not satisfy these requirements, such as a large tion reaching a specified degree of uniformity through- diameter electromagnetic current meter or a non- out the enclosure. The eddy diffusivity, KD, may be directional hot bead thermistor, are not appropriate for estimated by solving Eq. (l?) or (18),or by fitting a dif- turbulence measurements at small scales. The data fusion model to the time/depth series (Steele et al. logging system also must be capable of accurate, rapid 1977, Bonner et al. 1992). Comparisons between T,, recording of long velocity time series. In the past, these evaluated using different injection points may help to requirements have been beyond the capability of decipher spatial variation of K,,. A very useful exercise many experimental ecosystem facilities and beyond (Tatterson 1991. Peeters et al. 1993, Sanford et al. the expertise of many ecologists. However, recent unpubl.) is measurement of T,,, versus mixer speed improvements in technology (e.g. Kraus et al. 1994) are (e.g. paddle rotation rate). making direct turbulence measurements much simpler In the absence of direct measurements of velocity, and more affordable. gypsum dissolution techniques may be used to esti- Measurement of turbulent velocities in ecosystem mate interior velocity scales (Petticrew & Kalff 1991, enclosures is much the same as in nature. Velocity sen- Howerton & Boyd 1992, Thompson & Glenn 1994, San- sors either are held in a fixed location, measuring time ford et al. unpubl.) and bottom shear velocity scales series of velocity fluct.uations at a point (Gust 1977, (Opdyke et al. 1987, Buchholtz-ten Brink et al. 1989, Howarth et al. 1993, Sanford et al. unpubl.), or they are Santschi et al. 1991). In this technique, carefully pre- traversed rapidly through the turbulent velocity field, pared, dried and preweighed gypsum blocks, spheres, effectively measuring a space series of velocity fluctu- or plates are deployed for a few hours in the flow of ations (Hill et al. 1992, Howarth et al. 1993). interest, then dried and reweighed. The rate of weight One method for calculating E from turbulent velocity loss generally has been found to be proportional to measurements is based on the level of the turbulence some velocity scale raised to a power 51. Care must be energy spectrum in the inertial subrange (Eq. 8). The taken to correct dissolution rates for differences in spectrum is expressed in terms of spatial rather than 286 Mar Ecol Prog Se

temporal variation, which is well suited for spatially bulence-generating grid, which yielded the dissipation traversed velocity measurements. A velocity scale for rate directly. Chemical engineers frequently deter- converting time series to space serles is needed for mine volume-averaged E by measuring the power used fixed point velocity measurements. The mean velocity in mixing a scale model over the same range of is used for this purpose in natural flows, but often there Reynolds numbers as the full-scale mixing tank (Old- is very little mean velocity in enclosures. Tennekes & shue & Herbst 1990, Tatterson 1991). This technique Lumley (1972) offer a solution to this dilemma by sug- has been used for grid stirring of a microcosm by Kiar- gesting that uR, is the appropriate velocity scale for boe et al. (1990). It is difficult to use in many cases, zero-mean flow, but they leave a critical multiplicative however, because the power expended in overcoming constant undefined for lack of data. Terray et al. (1996) mechanical friction often dominates the power ex- indlcate that the value of that constant under near- pended in fluid mixing (e.g.Nixon et al. 1980). surface breaking waves should be approximately the Another technique for estimating the small-scale dis- same as it is for mean flow, leading to the formula tribution of flow and turbulence that is possible in the laboratory but generally not possible in nature is tracking of small particle motion through video (Marrase et al. 1990) or time exposure streak photography (John- son & Sebens 1993).The assumption that the particles where E represents the l-dimensional va.1iance spec- follow the flow accurately allows frame-by-frame esti- trum of the transverse componerlt of velocity (Eq. 8),o mation of the vclocity field. A sophisticated, computer- is radian frequency (S-') and f is cyclic frequency (Hz aided version of this technique, Particle Image Velo- or cycles S-'). Eq. (27) is a reasonable choice for esti- cimetry (PIV), recently has been developed for fluid mating E in ecosystem enclosures. dynamics studies (Gray & Bruce 1995). Another technique for estimating E from measured Estimates of the mass transfer coefficient, P,at the velocity fluctuations involves calculating URMS from surface may be made through careful gas exchange measured data, estimating l, then estimating E from experiments (Nixon et al. 1979, Jaehne et al. 1987). Pat Eq. (13). An advantage of this technique is that uRWls the sediment-water interface may be determined with may be determined from calibrated gypsum dissolu- flush-mounted hot-film probes or gypsum dissolution tion measurements as well as from direct velocity mea- measurements (Buchholtz-ten Brink et al. 1989). These surements (Sanford et al. unpubl.). 1 may be estimated techniques also may be used for measuring P at the from a space series of velocity according to Eq. (5), walls of an enclosure. In most experimental ecosystem from some assumed relationship to the turbulence gen- enclosures, flow at the bottom is too irregular to use eration mechanism (Howarth et al. 1.993), or from data standard boundary layer techniques for determining collected previously under similar conditions (Brumley bottom shear stress (e.g. profiles of average flow veloc- & Jirka 1987). For example, Hill et al. (1992) obtained ity fit to a theoretical log profile; Grant & Madsen 3986, very good estimates of dissipation in grid-generated Wright et al. 1992), but such techniques may be used in turbulence by using Eq. (13), assuming A, = 1 with benthic flumes (Grant et al. 1982, Butman et al. 1994). URM~and 1 calculated from a velocity component measured parallel to the direction of traverse of a LDV. Howarth et al. (1993) also employed this technique to Dimensional analysis obtain reasonable estimates of E by assuming 1 was the same as the spacing of the bars in their turbulence- Dimensional analysis is a method for combining all generating grid. Because many ecosystem processes of the variables describing a problem into fundamental depend on E raised to some fractional power, small dimensionless terms that capture the essence of the uncertainties in the values of 1 and A, are less impor- problem. It is a tool co,mmonly used by physical scien- tant than might otherwise be the case. For example, tists and engineers (Fischer et al. 1979, Tatterson 1991) rearranging Eq. (13) gives that has been adopted by ecologists (Platt 1981, l Legendre & Legendre 2983, Horne & Schneider 1994). There are 2 primary uses of dimensional analysis. The first is to aid in the analysis of complex systems and such that errors of + a factor of 2 in A,/] only lead to data sets. Dimensional analysis can be used in this con- errors of * a factor of 1.26 in €'l3. text to simplify a complex set of governing equations, Other methods for estimating E have been utilized as to formulate testable hypotheses, to design experi- well. Peters & Gross (1994) estimated E in their micro- ments optlmally, to identify scale-dependent ecosys- cosm experiments by measuring the rate of decrease of tem processes, and to present the results of multi- turbulent energy following each passage of their tur- dimensional experiments in as concise a fashion as Sanford: Turbulent mixing in experimental ecosystems 287

possible. This is the mode of use most common in ecol- scaling of both the large- and small-scale turbulence ogy (Lewis et al. 1984a, Miller et al. 1984, Patterson characteristics of the natural ecosystenl. This y~elds 1992, O'Riordan et al. 1993. Horne & Schneider 1994). The second important use of dimensional analysis is to model systems at different scales through preservation of the value of the most important dimensionless quan- In other words, the experimental mixing system must tities, known as maintaining dimensional similarity. be designed to produce an integral length scale that Engineers use this technique routinely for scale model- compensates for the depth distortion between the ing of physical systems (Shapiro 1961, Oldshue & experimental system and the natural system. The light Herbst 1990, Tatterson 1991). The central idea is that extinction depth would have to be adjusted to maintain distortion of one variable (such as size) in a dimension- similarity as well; W. M. Kemp (Univ. of Maryland, less ratio can be compensated by equal and opposite unpubl, data) has shown that this is possible by adjust- distortion of another (such as flow speed). ing the aspect rat10 of the tank, while Peeters et al. It would seem that experimental ecosystem studies (1993) report that diffusers and black tank walls might benefit from the second of these uses of dimen- accomplish much the same thing. sional analysis as much as the first. For example, accurate sinlulation of a 15 m deep water column in a 3 m deep ecosystem enclosure would be quite attractive. Summary There are 2 significant limitations to this concept, however. The first is that realistic ecosystem experiments Designers of experimental ecosystem mixers must may be too complex for description by a manageable consider size, non-interference, cost, durability, benig- number (53) of important dimensionless ratios. How- nity, wall shear, and scope, in addition to the turbulent ever, for relatively simple ecosystem cases scale mod- mixing questions discussed previously. Chemical engi- eling may be feasible. The second limitation is that neenng studies offer several helpful guidelines. First, dimensionless ratios between ecosystem parameters mixing parameters can be expressed in terms of mixer and physical parameters almost always contain terms geometry and mixing rate through dimensional analy- that cannot be distorted because they are set by the sis, and quantified through experimentation. Second, biology or geochemistry of the system (e.g. the growth scale models are a useful and inexpensive way to test rate 1- in Eq. 19). Because of thls, maintaining dimen- different configurations. Third, mixing in enclosures sional similarity to nature requires replicating the nat- can be separated conceptually into large-scale flow ural large-scale mixing time T, and the natural small- and small-scale shear. In general, experimental eco- scale dissipation rate E in the experimental system. system enclosures should have enough flow to prevent Achieving this while distorting physical scale and localized stagnation and enough shear to mimic the appropriately controlling characteristics such as as the range of natural turbulent energy dissipation rates. optical extinction depth is a daunting task. Under cer- Existing experimental ecosystem mixing designs tain circun~stances,however, it may be possible. vary widely. Rotating paddle mixers are the best char- As an example, consider the case of an experimental acterized of the available schemes. They are capable of ecosystem enclosure of depth h,that is to mimic a well- simulating large-scale mixing and water column turbu- mixed natural water column of depth h?> h,.The inte- lence reasonably, they benefit the most from chemical gral length scale of turbulence in the natural system engineering mixing studies, and they are reasonably may be assumed equal to the depth, or l, = h2(this easy to maintain. However, they can be costly to imple- assumption would need to be validated). The integral ment and they do not balance boundary fluxes against length scale of turbulence in the enclosure can be con- intenor mixing very well. Turbulence generated by os- trolled to be some fraction of the depth (at least in con- cillating grid mixers also is reasonably well character- cept) through careful design of the mixing system, ized, although there appear to be few studies of large- such that 1,= f h,where f5 l. An equation relating the scale mixing in oscillating grid tanks. Short, rapid ratio of the mixing times to the ratio of the dissipation oscillations leave much of the water column undis- rates can be derived by combining these expressions turbed, but they result in very large gradients in turbu- for l,and 1, with Eqs. (12), (13), and (17): lent energy near the grid. Passing the grid through the entire water column homogenizes the turbulence better, but interferes with organisms more. Oscillating grids also suffer from a mismatch between boundary fluxes and interior mixing. In situ flexible-wall enclo- Eq. (29) may be solved for the combinations of h2/hl sures offer a number of advantages related to initial and f for which both E, = E, and T,, = Tm2,allowing conditions, volume, light, and temperature. However, 288 Mar Ecol Prog Ser 161. 265-293, 1997

unassisted mixing rates are very low in these enc1.0- ecosystems. If our experimental ecosystems are to sures and small-scale shear presumably is low as well. mimic natural ecosystems, then we must be as con- There are very few published studies of turbulence and cerned about turbulent mixing in our experiments as mixing in flexible-wall enclosures, and there are very we are about light, temperature, salinity, nutrients, etc. few descriptions of assisted mixing schemes. Other Turbulent mixing in experimental ecosystem studies is mixing schemes that have been used in experimental not optional. It is necessary. ecosystem enclosures include bubbling and pumping. This paper has attempted to provide a framework for Benthic mesocosm designs vary even more than consideration of turbulent mixing in experimental water column designs. The best benthic mesocosm ecosystem studies. It has described important charac- designs reproduce both the general flow characteris- teristics of natural turbulence, identified important tur- tics of the natural benthic environment and the details bulence scales for experimental ecosystem studies, of the bottom boundary layer structure. However, and discussed implementation and quantification of these designs tend to be quite complex and expensive turbulent mixing in ecosystem enclosures. The reader to implement. There have been limited attempts to is referred to section summaries for specific conclu- reproduce both mixing of the water column and sions, which will not be repeated here. the flow environment of the benthos in a single, linked A number of issues raised here require further inves- system; more work is needed. tigation. We know little about relationships between There are a number of techniques available for mea- turbulence variability and ecosystem variability. Inter- suring turbulent mixing m experimental ecosystcm actions may occur at al! scales, but what are the mech- enclosures. One of the simplest and most effective for anisms and how important are they? We know little determining large-scale mixing characteristics is dye about microscale environments in turbulent aquatic dispersion, which can be used both for qualitative ecosystems. Sharp gradients and patchy particle distri- determination of mixing uniformity and for quantita- butions have been predicted and in some cases tive determination of a mixing time. Practitioners must observed at microscales, but many of these predictions be careful to use neutrally buoyant dye and to specify have not been verified and their ecological effects the injection location and degree of uniformity consid- have not been evaluated. In a practical sense, more ered mixed, especially with regard to the definition of work is needed on mixing schemes that adequately a mixing time. Gypsum dissolution techniques can be reproduce both mixing of the water column and the quite useful for measuring relative flow intensity, flow environment of the benthos. Flexible-wall in situ though some prior knowledge of the nature of the flow enclosures are an attractive option for many ecosystem is necessary to interpret the results properly. If gypsum experiments, but they are badly undermixed in their dissolution techniques are calibrated under similar usual configuration; this problem can be and should be conditions (i.e. similar ratios of fluctuating flow to addressed. The possibility of scale model experimental steady flow, similar water chemistry, and similar gyp- ecosystem studies based on dimensional similarity sum block morphology), they can be a reasonable should be investigated. More generally, standard pro- method for estimating absolute turbulence intensity tocols are needed for designing mixing systems and and (potentially) dissipation rate. Direct flow measure- measuring turbulence in ecosystem studies. ments are the best method for quantifying turbulent It is unreasonable to expect that every mixing velocity distributions in enclosures, with new, more scheme in every experimental ecosystem will be com- user-friendly technologies easing the task. Estimates of pletely general and optimal. Rather, ecosystem boundary fluxes are possible through dissolution or researchers should weigh the goals of their experi- hot-film measurements at the bottom and gas ex- ments against the costs of implementing a mixing change measurements at the surface. scheme and the likely artifacts of design compromises. Dimensional analysis is a useful tool for both design Turbulent mixing conditions in ecosystem enclosures and analysis of ecosystem experiments. Dimensionally should be characterized before experiments begin, similar scale modeling may be possible under certain and conditions should be monitored during experi- circumstances by taking ad.vantage of some of the un- ments if necessary. When results are reported, the mix- avoidable artifacts of experimental ecosystem en- ing configuration and turbulence characteristics closures and mixing schemes. should be reported as well.

CONCLUSIONS Acknowledgements. I am grateful to many friends and col- leagues for discussions leading to the writing of this paper, to the Applied Ocean Physics and Engineering Department at The basic premise of this paper is that turbulence the Woods Hole Oceanograph~cInstitution for their hospital- and turbulent mixing are integral aspects of aquatic ity during its writing, and to V. Kennedy, E. Porter, C. Oviatt, Sanford: Turbulent mixing in experimental ecosystems 289

A. Sanford, and several anonymous reviewers for their careful Res 36-1083-1101 reviews and helpful suggestions. This research was sup- Butman CA (1986) Larval settlement of soft-sediment inverte- ported by the Multiscale Env~ronmentalEcosystem Research brates: some predictions based on analysls of near-bottom Center (MEERC) at the University of Maryland Center for velocity profiles. In: Nihoul JCJ (ed) Marine interfaces Environmental Science (UMCES) through grant no. R 819640 ecohydrodynamics. Elsevier, Amsterdam, p 487-513 from the U.S. Environmental Protection Agency. UMCES Butman CA (1987) Larval settlement of soft-sediment inverte- publication number 2796. brates. the spatial scales of pattern explained by active habitat selection and the emerging role of hydrodynami- cal processes. Oceanogr Mar Biol Annu Rev 25:113-165 LITERATURE CITED Butman CA, Frechette M, Geyer WR (1994) Flume experiments on food supply to the blue mussel Mytllus edulls L Abraham G (1988) Turbulence and mixing in stratified tidal as a functlon of boundary-layer flow. Limnol Oceanogr 39: flows. In: Dronkers J, van Leussen W (eds) Physical 1755-1768 processes in estuaries. Springer-Verlag, Berlin, p 149-180 Cahoon LB (1988) Use of a whirling cup rotor to stir benthic Agrawal YC, Terray EA, Donelan MA, Hwang PA, Williams chambers Hydrobiologia 160:193-198 AJ 111,Drennan WM, Kahma KK,Kitaigorodskii SA (1992) Cantwell BJ (1981) Organized motion In turbulent flow. Annu Enhanced diss~pation of kinetic energy beneath surface Rev Fluid Mech 13:457-515 waves. Nature 359:219-220 Carey DA (1983) Particle resuspension in the benthic bound- Alcaraz M, Saiz E, Calbet A (1994) Small-scale turbulence ary layer induced by flow around polychaete tubes. Can J and zooplankton metabolism: effects of turbulence on Fish Aquat Sci 40:301-308 heartbeat rates of planktonic crustaceans. Limnol Carpenter SR(1996) Microcosm exper~mentshave limited rel- Oceanogr 39: 1465-1470 evance for community and ecosystem ecology. Ecology 77: Alldredge AL, Cohen Y (1987) Can microscale chemical 677-680 patches persist in the sea? Microelectrode study of marine Chao SY, Paluszkiewicz T (1991) The hydraulics of density snow, fecal pellets. Science 235:689-691 currents over estuarine sills. J Geophys Res 96.7065-7076 Asmus H, Asmus KM, Prins TC, Dankers N, Frances G, Maass Chapman AJ (1974) Heat transfer, 3rd edn. Macmillan Pub- B, Reise K (1992) Benthic-pelagic flux rates on mussel lishing, New York beds: tunnel and tidal flume methodology compared. Chrost RJ, Riemann B (1994) Storm-stimulated enzymatic Helgolander Meeresunters 46:34 1-361 decomposition of organic matter in benthic/pelagic Baker MA, Gibson CH (1987) Sampling turbulence in the coastal mesocosms. Mar Ecol Prog Ser 108:185-192 stratified ocean: statistical consequences of strong inter- Conover RJ, Paranjape MA (1977) Comments on the use of mittency. J Phys Oceanogr 17:1817-1836 a deep tank in planktological research. Helgol Wiss Bakke T (1990) Benthic mesocosms: 11.Basic research in hard- Meeresunters 30:105-117 bottom benthic mesocosms. In: Lalli CM (ed) Enclosed Costello JH, Strickler JR, Marrase C, Trager G, Zeller R, experimental marine ecosystems: a review and re- Freise AJ (1990) Grazing in a turbulent environment- I. commendations, Vol 37. Springer-Verlag, New York, Behavioral response of a calanoid copepod, Centropages p 122-135 hamatus. Proc Natl Acad Sci USA 87:1648-1652 Banse K (1982) Experimental marine ecosystem enclosures in Crank J (1975) The mathematics of diffusion, 2nd edn. a historical perspective. In: Grice GD, Reeve MR (eds) Clarendon Press, Oxford Manne mesocosms. Springer-Verlag, New York, p 11-24 Csanady GT (1973) Turbulent diffusion in the environment. Batchelor GK (1967) The theory of homogeneous turbulence. D Reidel Publishing Company, Dordrecht 5th edn. Cambridge University Press, Cambridge Dade BW (1993) Near-bed turbulence and hydrodynamic Bennett AF, Denman KL (1989) Large-scale patchiness due to control of dlffusional mass transfer at the sea floor. Limnol an annual plankton cycle. J Geophys Res 94:823-829 Oceanogr 38:52-69 Berge JA. Schaanning M, Bakke T, Sandoy KA, Skeie GM, Daehler CC, Strong DR (1996) Can you bottle nature? The Ambrose WG Jr (1986) A soft-bottom sublittoral mesocosm roles of microcosms in ecological research. Ecology 77: by the Oslofjord: description, performance and examples 663-664 of application. Ophelia 26:37-54 Davis RE (1985) Drifter observations of coastal surface cur- Bonner JS, Hunt CD, Paul JF, B~ermanVJ Jr (1992) Transport rents during CODE: the statistical and dynamical views. of low-level radioactive soil at deep-ocean disposal site. J Geophys Res 90:4756-4772 J Environ Eng 118:101-119 Denman KL (1994) Scale-determining biological-physical Bowen JD, Stolzenbach KD, Chisholm SW (1993) Simulating interactions in oceanic food webs. In: Giller PS, Hildrew bacterial clustering around phytoplankton cells in a turbu- AG, Raffaelli DG (eds) Aquatic ecology: scale, pattern and lent ocean. Limnol Oceanogr 38.36-51 process. Blackwell Scientific Publications, Oxford, Boyce FM (1974) Mixing withln experimental enclosures: a p 377-399 cautionary note on the Limnocorral. J Fish Res Bd Can 31: Denman KL. Gargett AE (1995) Biological-physical interac- 1400-1405 tions in the upper ocean: the role of vertical and small Brocvman HI (1996) Predator-prey interactions in the sea: scale transport processes. Annu Rev Fluid Mech 27: commentaries on the role of turbulence. Mar Ecol Prog Ser 225-255 139:301-302 Denny MW (1988) Biology and the mechanics of the wave- Brurnley BH, Jirka GH (1987) Near-surface turbulence in a swept environment. Princeton University Press. Princeton. grid-stirred tank. J Fluid Mech 183:235-263 N J Brunk B, Weber-Shirk M, Jirka G, Lion LW (1996) Modeling de Wilde PAWJ (1990) Benthic mesocosms: I.Basic research natural hydrodynamic systems with a differential-turbu- in soft-bottom benthic mesocosms. In: Lalll CM (ed) lence column. J Hydra Eng 122:373-380 Enclosed experimental marine ecosystems: a review and Buchholtz-ten Brink MR, Gust G. Chavis D (1989) Calibration recommendations, Vol 37 Springer-Verlag, New York, and performance of a stirred benthic chamber. Deep Sea p 109-121 290 Mar Ecol Prog Ser 161. 265-293, 1997

Donaghay PL, Klos E (1985) Physical, chemical and biological Grant WD, Madsen OS (1986) The continental-shelf bottom responses to simulated wind and tidal mixing in experi- boundary layer. Annu Rev Fluid Mech 18:265-305 mental marine ecosystems. Mar Ecol Prog Ser 26:35-45 Grant WD, Williams AJ 111. Glenn SM (1984) Bottom Dower JF, Miller TJ, Leggett WC (1997) The role of stress estimates and their prediction on the Northern microscale turbulence in the feeding ecology of larval fish. California Continental Shelf during CODE-I the impor- Adv Mar Biol 31.169-220 tance of wave-current ~nteraction.J Phys Oceanogr 14: Dyer KR, New AL (1986) Intermittency in estuarine mixing. 506-527 In: Wolfe DA (ed) Estuarine variability. Harcourt Brace Grassle JP, Butman CA. Mills SW (1992) Act~vehabitat selec- Jovanovich, Orlando, FL, p 321-339 tion by Capitella sp. I. larvae. 11. Multiple-choice experi- Eckman JE, Werner FE, Gross TF (1994) Modelling some ments in still water and flume flows. J Mar Res 50:717-743 effects of behavior on larval settlement in a turbulent Gray C, Bruce T (1995) The application of particle image boundary layer. Deep Sea Res 41:185-208 velocimetry (PIV) to offshore engineering. In: Proc 5th Int Eppley RW, Loeller P, Wallace JGT (1978) Stirring influences Offshore and Polar Engineering Conf, The Hague the phytoplankton species composltlon within enclosed (The Netherlands), 11-16 June 1995, Vol 3. International columns of coastal sea water. J Exp Mar Biol Ecol 32: Society of Offshore and Polar Engineers, Golden, CO, 219-239 p 701-708 Estrada M, Alcaraz M, Marrase C (1987) Effects of turbulence Grice GD, Reeve MR (1982) Introduction and description of on the composition of phytoplankton assemblages in experimental ecosystems. In: Grice GD, Reeve MR (eds) marine microcosms. Mar Ecol Prog Ser 38:267-281 Marine mesocosms. Springer-Verlag, New York, p 1-9 Estrada M, Marrase C, Alcaraz M (1988) Phytoplankton Grizzle RE, Langan R, Howell H (1992) Growth responses of response to intermittent stirring and nutrient addition in suspension-feeding bivalve molluscs to changes in water marine microcosms Mar Erol Prog Ser 48:225-234 flow: differences between siphonate and nonsiphonate Feijen J, Hoffmeester JJ (1992) Gradients in production scdle taxa. J Exp Mar Biol Ecol 162:213-238 bioreactors In. King R (ed) Fluid mechan~csand its appli- Gnzzle RE, Langan R, Howell H (1994) Growth responses of cations. 10: Fluid mechanics of mixing: modelling, opera- Crassostrea virginlca, ~Mercer~ariamercenaria and Mytilus tions and experimental techniques. Kluwer Academic edulis to changes In water flow: a test of the 'inhalant Publishers, Dordrecht, p 65-72 pumping speed' hypothesis. J Shellfish Res 13:315 Fennessy MJ, Dyer KR, Huntley DA (1994) Size and settling Gross TF, Nowell ARM (1983) Mean flow and turbulence scal- velocity distributions of flocs in the Tamar Estuary during ing in a tidal boundary layer. Cont Shelf Res 2:109-126 a tidal cycle. Neth J Aquat Ecol 28:275-282 Gross TF, Williams AJ, Terray EA (1994) Bottom boundary Fernando HJS (1991) Turbulent mixing in stratified fluids. layer spectral dissipation estimates in the presence of Annu Rev Fluid Mech 23:455-493 wave motions. Cont Shelf Res 14:1239-1256 Findlay RH, Kim SL, Butman CA (1992) Colonization of Guanguo L (1990) Different types of ecosystem experiments freshly deposited barite and silica sediments by marine In: Lalli CM (ed) Enclosed experimental marine ecosys- microorganisms in a laboratory flume flow. Mar Ecol Prog tems: a review and recorrunendations, V01 37 Spnnger- Ser 90:73-88 Verlag, New York, p 7-19 Fischer HB, List EJ, Koh RCY, Imberger J, Brooks NH (1979) Gust G (1977) Turbulence and waves inside flexible-wall sys- Mixing in inland and coastal waters. Academic Press, Inc, tems designed for biological studies. Mar Biol42:47-53 New York Gust G (1988) Skin friction probes for field applications. Galbraith PS. Kelley DE (1996) Identifying overturns in CTD J Geophys Res 93:14121-14132 profiles. J Atmos Oceanic Technol 13:688-702 Haury LR, Yamazaki H, Itsweire EC (1990) Effects of turbu- Gargett AE (1989) Ocean turbulence Annu Rev Fluid Mech lent shear flow on zooplankton distribution Deep Sea Res 21:419-451 37:447-461 Garrett C (1989) A mixing length interpretation of fluctua- Heathershaw AD (1976) Measurements of turbulence in the tions in passive scalar concentration in homogeneous tur- Irish Sea benthic boundary layer. In: McCave IN (ed)The bulence. J Geophys Res 94:9710-9712 benthic boundary layer. Plenum Press, New York, p 11-32 Geyer WR, Signell RP (1992) A reassessment of the role of Hill PS, Nowell ARM. Jumars PA (1992) Encounter rate by tidal dispersion in estuaries and bays. Estuaries 15:97-108 turbulent shear of particles similar in diameter to the Kol- Geyer WR, Smith JD (1987) Shear instability in a highly strat- mogorov scale. J marRes 50:643-668 ified estuary. J Phys Oceanogr 17:1668-1679 Hopfinger EJ (1987) Turbulence in stratified fluids: a review. Gibson CH (1991) Turbulence, mixlng, and heat flux in the J Geophys Res 92:5287-5303 ocean maln thermocline. J Geophys Res 96:20403-20420 Horne JK, Schneider DC (1994) Analysis of scale-dependent Gibson CH, Thomas WH (1995) Effects of turbulence inter- processes with d~mensionlessratios. O~kos70:201-211 mittency on growth inhibition of a red tide dinoflagellate. Howarth RW. Butler T, Lunde K, Swaney D, Chu CR (1993) Gonyaulax. J Geophys Res 100:2484 1-24846 Turbulence and planktonic nitrogen fixation: a mesocosm Glud RN, Gundersen JK, Revsbech NP. Jsrgensen BB, Huet- experiment. Limnol Oceanogr 38: 1696-17 11 tel M (1995) Calibration and performance of the stirred Howerton RD, Boyd CE (1992) Measurement of water circula- flux chamber from the benthic lander Elinor. Deep Sea Res tion in pondi with gypsum blocks. Aquacult Eng 11. 42:1029-1042 141-155 Grant HL, Hughes BA, Vogel WM, Moillet A (1968)The spec- Huettel M, Gust G (1992) Solute release mechanisms from trum of temperature fluctuation in turbulent flow. J Flu~d confined sedlment cores in stirred benthic chambers and Mech 34.423-442 flume flows. Mar Ecol Prog Ser 82:187-197 Grant HL, Stewart RW, Moilhet A (1962) Turbulence spectra Hwang JS, Costello JH. Strickler JR (1994) Copepod grazing from a tidal channel. J Fluid Mech 12:241-263 in turbulent flow: elevated foraging behavior and habitua- Grant WD, Boyer LF, Sanford LP (1982) The effects of biotur- tion of escape responses. J Plankton Res 16:421-431 bation on the initiation of motion of intertidal sands. J Mar Itsweire EC, Osborn TR (1988) Microstructure and vertical Res 40:659-677 velocity shear distribution in Monterey Bay. In: Nihoul Sanford: Turbulent mixing in experimental ecosystems 291

JCJ, Jamart BM (eds) Small-scale turbulence and mixing ecosystems. In: Lalli CM (ed) Enclosed exper~~nental in the ocean. Elsevier. Amsterdam. p 213-228 marine ecosystems: a review and recommendations, ltsweire EC, Koseff JR, Briggs DA, Ferziger JH (1993) Turbu- Vol 37. Springer-Verlag, New York, p 20-60 lence in stratified shear flows: implications for interpreting Lazier JRN. Mann KH (1989)Turbulence and the diffusive lay- shear-induced mixing in the ocean. J Phys Oceanogr 23: ers around small organisms. Deep Sea Res 36:1721-1733 1508-1522 Ledwell JR, Watson AJ, Law CS (1993) Evidence for slow mix- Jaehne B, Muennich KO, Boesinger R,Dutzi A, Huber W, Lib- ing across the pycnocline from an open-ocean tracer- ner P (1987) On the parameters influenc~ngair-water gas release experiment. Natur~364.701-703 exchange. J Geophys Res 92:1937-1949 Legendre L (1981) Hydrodynamic control of marine phyto- Johnson AS, Sebens KP (1993) Consequences of a flattened plankton production: the paradox of stability. In: Nihoul morphology. effects of flow on feeding rates of the sclerac- JCJ (ed) Ecohydrodynarnics Elsevier Scientific, Amster- tinian col-a1 Meandnna meandntes. Mar Ecol Prog Ser 99. dam. p 191-208 99-114 Legendre L, Legendre P (1983) Numerical ecology. Elsevier Johnson GC, Lueck RG, Sanford TB (1994) Stress on the Scientific, Amsterdam Mediterranean outflow plume. Part 2. Turbulent dissipa- Lehfeldt R, Bloss S (1988) Algebraic turbulence model for tion and shear measurements. J Phys Oceanogr 24: stratified t~dalflows In Dronkers J, van Leussen W (eds) 2084-2092 Physical processes in estuaries. Springer-Verlag, Berlin, Jsrgensen BB, Revsbech NP (1985) Diffusive boundary layers p 278-294 and the oxygen uptake of sediments and detritus Limnol Lewis MR, Cullen JJ, Platt T (1984a) Relationships between Oceanogr 30:lll-122 vertlcal mixing and photoadaptataion of phytoplankton: Jumars PA (1993) Concepts in biological oceanography: an similarity criteria. Mar Ecol Prog Ser 151141-149 interdlsciplinary primer. Oxford University Press, New Lewis MR, Horne EPW, Cullen JJ, Oakey NS, Platt T (1984b) York turbulent motions may control phytoplankton photosyn- Karp-Boss L, Boss E, Jumars PA (1996) Nutrient fluxes to thesis in the upper ocean. Nature 31 1:49-50 planktonic osmotrophs in the presence of fluid motion. Lewis MR, Platt T (1982) Scales of variability in estuarine Oceanogr Mar Biol Annu Rev 34:71-107 ecosystems. In: Icennedy VS (ed) Estuarine compansons. Kent RE. Pritchard DW (1959)A test of mixing length theories Academic Press, New York, p 3-20 in a coastal plain estuary. J Mar Res 18:62-72 List EJ, Gartrell G, Winant CD (1990) Diffusion and dispersion Kisrboe T (1993)Turbulence, phytoplankton cell size, and the in coastal waters. J Hydra Eng 116:1158-1179 structure of pelagic food webs. Adv Mar Biol 29:l-72 Maclntyre S (1993) Vertical mixing in a shallow, eutrophic ffisrboe T, Andersen KP, Dam HG (1990) Coagulat~oneffi- lake: possible consequences for the light clunate of phyto- ciency and aggregate formation in marine phytoplankton. plankton. Limnol Oceanogr 38:798-817 Mar Biol 107:235-245 Maclntyre S, Alldredge AL, Gotshalk CC (1995) Accumula- Klos E (1988) An experimental estuarine salinity gradient In: tlon of marine snow at density d~scontinuitlesin the water Proc Oceans 88 Conf. lnstitute of Electrical and Electron- column. Limnol Oceanogr 40:449-468 ics Engineers, Piscataway, NJ, p 1529-1535 MacKenzie BR. Leggett WC (1993) Wind-based models for Koch EW (1994) Hydrodynamics, diffusion-boundary layers estimating the dissipation rates of turbulent energy in and photosynthesis of the seagrass Thalassia testudinum aquatic environments: empincal comparisons. Mar Ecol and Cymodocea nodosa. Mar Biol 118:767-776 Prog Ser 94:207-216 Koseff JR, Holen JK, Monismith SG, Cloern JE (1993) Cou- Mann KH, Lazier JRN (1991) Dynamics of marine ecosystems: pled effects of vertical mixing and benthic grazlng on biological-physical interactions in the oceans. Blackwell phytoplankton populations in shallow, turbid estuaries. J Scientific Publications, Cambridge, MA Mar Res 51:843-868 Marrase C, Costello JH, Granata T, Strickler JR (1990) Graz- Kotak BG, Robinson, GGC (1991) Artificially-induced water ing in a turbulent environment: energy dissipation, turbulence and the physical and b~ologicalfeatures within encounter rates, and efficacy of feeding currents In Cen- small enclosures. Arch Hydrob~ol122:335-349 tropages hamatus. Proc Natl Acad Sci USA 87:1653-1657 Kraus NC. Lohrmann A, Cabrera R (1994)New acoustic meter Mehta AJ (1988) Laboratory studies on cohesive sediment for measunng 3-d laboratory flows. J Hydra Eng 120: deposition and erosion. In: Dronker J, van Leussen W (eds) 406-412 Phys~calprocesses in estuaries. Springer-Verlag, Berlin, Kuiper J. Brockmann UH, van het Groenewoud H, Hoorns- p 427-445 man G, Hammer KD (1983) Influences of bag dimensions Menzel DW, Case J (1977) Concept and design: controlled on the development of enclosed plankton communities ecosystem pollution experiment. Bull Mar Sci 27:l-7 during POSER. Mar Ecol Prog Ser 14:9-17 Middleton JH, Griffin DA, Moore AM (1993)Oceanic clrcula- Kundu PK (1990) Fluid mechanics. Academic Press, Inc. San tion and turbulence in the coastal zone. Cont Shelf Res 13: Diego 143-168 Landahl MT, Mollo-Christensen E (1986)Turbulence and ran- Miller DC, Jumars PA, Nowell ARM (1984) Effects of sedi- dom processes in fluid mechanics. Cambridge University ment transport on deposit feeding: scaling arguments. Press, Cambridge Limnol Oceanogr 29: 1202- 1217 Landry F, Miller TJ, Leggett WC (1995) The effects of small- Moeseneder MM, Herndl GJ (1995) lnfluence of turbulence scale turbulence on the ingestion rate of fathead minnow on bacterial production in the sea. Limnol Oceanogr 40: (Pimephales promelas) larvae. Can J Fish Aquat Sci 52: 1466-1473 1714-1719 Monismith SG, Koseff JR, Thompson JK, O'Riordan CA. Nepf Lasker JK (1981) Factors contributing to variable recruitment HM (1990) A study of model bivalve siphonal currents. of the northern anchovy (Engraulismordax) in the Califor- Limnol Oceanogr 35:680-696 nia Current: contrasting years. 1975 through 1978. Rapp Moore PA, Zimmer-Faust RK, Bement SL, Weissburg MJ, Par- PV Reun Comm Int Explor Mer 178:375-388 rish JM. Gerhardt GA (1992) Measurement of microscale Lasserre P (1990) Marine microcosms: small-scale controlled patchiness in a turbulent aquatic odor plume using a semi- 292 Mar Ecol Prog Ser 161. 265-293, 1997

conductor-based microprobe B101 Bull (Woods Hole) 183 Peetc,rs JCH, Arts F, Escaravage V, Haas HA, de Jong Jr.\ 138 142 \an Loon R, Moest l!, van der Put A (1993)Studies on light Moum JN (1996) Energy-contain~ngsrdles of turbulence in climate., mlxlng and reproducib~lltyof ecosystem variables the ocean J Geophys Res 101 14095-14109 in mciocosm- consequences for the design In. Peeters Muelbert JH Lewls MR Kelley DE (1994) The importance of JCH, Joordens JCA, Smaal AC, Nienhuls PH (eds) The small-scdle turbulence In the feeding of herr~nglarvae impact of marine eutrophicatlon on phytoplankton and J Plankton Res 16 927-944 benthic suspenslon feeders. results of a mesocosm pilot Muschenheim DK (1987) The dynamics of near-bed seston study. D~enstGetljde wateren, Middelburg, Netherlands, flux and suspension-feedlng benthos J Mar Res 45 Report DGW-93039 / NIOO/CEMO-654, p 7-23 473-496 Penry D (1989) Tests of kinematic models for deposit-feeders' Muschenhelm DK Grant J, Mills EL (1986)Flumes for benthic guts. patterns of sediment processing by Parastichopus ecolog~sts theory, construction and practlce Mar Ecol californicus (Stimpson) (Holothuroidea) and Amphicte~s Prog Ser 28 185-196 scaphobranch~ata Moore (Polychaeta). J Exp Mar Biol Nlxon SW Ovlatt CA BucMey BA (1979)Turbulent mixing in Ecol 128.127-1.46 marine microcosms-some relative measures and ecolog- Peters F, Gross T (1994) Increased grazing rates of ~calconsequences In Jacoff FS (ed) Advances In marine microplankton in response to small-scale turbulence Mar environmental research-proceedings of a symposium Ecol Prog Ser 115 299-307 US EPA Environmental Research Lab Narragansett RI, Peters H, Gregg MC, Sanford TB (1994) The diurnal cycle of p 382-409 the upper equatonal ocean, turbulence, fine-scale shear, Nixon SW, Alonso D Pilson MEQ Buckley BA (1980) Turbu- and mean shear. J Geophys Res 99:7?07-7723 lent mlxlng in aquatlc microcosms In Giesy JP (ed) Pettlcrew EL, Kalff J (1991) Callbration of a gypsum source for Microcosms In ccolog~cal research DOE Svmposium freshxvater flow measurements. Can J Fish Aquat Sci 48

Series, Augusta, (74, p 818-849 1244-1249 Nowell ARM Jumars PA (1984) Flow envlronments of aquatlc Platt T (1981) Think~ngin terms of scale: introduction to benthos Annu Rev Ecol Syst 15 303-328 dlmens~onalanalysis. In: Platt T, Mann KH, Ulanowicz RE Nowell ARM Jumars PA (1987) Flumes theoretical and (eds) Mathematical models In biological oceanography expenmental considerations for simulat~on of benthic UNESCO Press, Pans, p 112-121 envlronments Oceanogr marB101 Annu Rev 25 91-112 Porter ET, Newell RIE, Sanford LP (1997) The effect of Olestad V (1990) Speciflc appllcatlon of meso- and macro- bivalves and water flow on benthic-pelagic coupling in cosms for solv~ngproblems in flshenes research In Lalli shallow coastal ecosystems. In: Abstracts of the ASLO CM (ed) Enclosed expenmental manne ecosystems a Aquatic Sclences meeting, Santa Fe, NM, February, 1997. revlew and recommendat~ons Vol 37 Spnnger-Verlag Lewis International, Inc, Halifax, NS, p 271-272 New York, p 136-154 Prins TC, Escaravage V, Pouwer AJ, Haas HA (1994) Descr~p- Okubo A (1971) Oceanic diffusion diagrams Deep Sea Res tion of mesocosms, methods and comparison wlth North 18 789-802 Sea conditions. In: Smaal AC, Peeters JCH, Haas HA, Okubo A (1980) D~ffusionand ecological problems mathe- Help CHR (eds) The Impact of manne eutrophication on matlcal models Spnnger-Verlag New York phytoplankton and benth~csuspenslon feeders. Progress Oldshue JY, Herbst NR (1990) A gulde to fluid mixing Mlxing report I: results of mesocosm expenments wth reduced Equipment Company Rochester, NY P-load and Increased grazing pressure Ministry of Trans- Opdyke BN, Gust G Ledwell JR (1987) Mass transfer from port, Publlc Works and Water Management, Directorate- smooth alabaster surfaces In turbulent flows Geophys Res General of Public Works and Water Management, Lett 14 1131-1134 National Institute for Coastal and Marine Manage- 0 Rlordan CA Monlsmith SG, Koseff JR (1993) A study of ment/RIKZ, Mlddelburg, Netherlands, Report RIKZ - concentration boundary layer format~onof a bed of model 94.035 / NIOO/CEMO - 1994 2, p 10-40 blvalves Llmnol Oceanogr 38 1712-1729 Richardson LF (1922) Weather prediction by numer~cal Osborn TR (1980) Est~matesof the local rate of vert~cald~ffu- process Cambridge Iniversity Press, Cambridge sion from dissipation measurements J Phys Oceanogr 10 Richardson PL (1993) Tracking ocean eddies Am Sci 81 83-89 261-271 Osborn T, Scotti A (1996) Effect of turbulence on predator- R~emannB, Nielsen TG, Morsted SJ. Koefoed Bjornsen P, prey contact rates where do we go from herc7 hlar Ecol Pock-Steen J (1988) Regulation of phytoplankton biomass Prog Ser 139 302-304 in estuarine enclosures. Mar Ecol Prog Ser 48:205-215 Oviatt C (1994) Biological considerations In manne enclosure Rothschlld BJ, Osborn TR (1988) Small-scale turbulence and expenments challenges and revelations Oceanography plankton contact rates. J Plankton Res 10.465-474 7 45-51 Saiz E, Alcaraz M, Paffenhofer GA (1992) Effects of small- Oviatt CA Perez KT, Nlxon SW (1977) Multlvanate analysis scale turbulence on feed~ngrate and gross-growth effi- of expenmental manne ecosystems Helgol W~ssMeeres- clency of three Acartja species (Copepoda. Calanolda) unters 30 30-46 J Plankton Res 14:1085-1097 Pate1 VC Rod1 W Scheuerer G (1985) Turbulence models for Sanford LP, Chang ML (1997) The bottom boundary condition near-wall and low Reynolds number flows a revlew Am for sediment deposltlon. J Coast Res S1 25.3-17 Inst Aeronaut Astronaut J 23 1308-1319 Sanford LP, Halka JP (1993) Assessing the paradigm of mutu- Patterson MR (1992) A mass transfer explanation of metabolic ally exclus~veeroslon and deposlt~onof mud, with exam- scallng relations in some aquatlc Invertebrates and algae ples from upper Chesapeake Bay. Mar Geol 114:37-57 Sclence 255 1421-1423 Santschi PH, Anderson RF, Fleisher MB, Bowles CV (1991) Pawllk JR Butman CA (1993) Settlement of a manne tube Measurements of diffusive sublayer thicknesses in the worm as a function of current velocity interacting effects ocean by alabaster dissolution, and their imphcations for of hydrodynamics and behav~or Limnol Oceanogr 38 the measurements of benthlc fluxes. J Geophys Res 96 1730-1739 10641-10657 Sanford: Turbulent mixing in experimental ecosystems 293

Schubert H,Matthijs HCP, lMur LR, Schiewer U (1995) Bloom- Estimates of k~neticenergy d~ssipationunder breaking ing of cyanobacteria in turbulent water with steep light waves. J Phys Oceanogr 26:792-807 gradients: the effect of intermittent light and dark periods Thomas WH, Gibson CH (1992) Effects of quantified small- on the oxygen evolution capacity of Synechocystjs sp. scale turbulence on the dinoflagellate, Gymnodinium san- PCC 6803. FEMS Microbial Ecol 18:237-245 guineum (splendens): contrasts with Gonyaulax (Lingulo- SCOR Working Group 69 (1988) Small-scale turbulence and diniun~)polyedra, and the fishery implicat~on.Deep Sea mixing In the ocean: a glossary. In: Nihoul JCJ, Jamart BM Res 39:1429-1437 (eds) Small-scale turbulence and mixing In the ocean Thompson TL, Glenn EP (1994) Plaster standards to measure Elsev~er,Amsterdam, p 3-10 water motlon. L~mnolOceanogr 39:1768-1779 SCOR Working Group 85 (1990) Introduction. In: Lalli CM Threlkeld ST (1994) Benthic-pelagic interactions in shallow (ed) Enclosed experimental marine ecosystems: a review water columns: an experimental~st'sperspective. Hydro- and recommendations. Springer-Verlag, New York, p 1-6 biologia 279276~293-300 Shapiro AH (1961) Shape and flow. Doubleday and Company, Townsend AA (1976) The structure of turbulent shear flow, Inc, Garden City, NY 2nd edn. Cambridge University Press, Cambridge Shimeta J, Jumars PA (1991) Physical mechanisms and rates Tnvett DA, Snow JW (1995) Combined veloc~ty-density-vor- of particle capture by suspension-feeders. Oceanogr Mar ticity sensor: fully three-dimensional acoustic flow sensor Biol Annu Rev 29:191-257 measures small-scale velocities, physical measurements Silverberg N. Gagnon JM, Lee K (1995) A benthic mesocosm simultaneously. Sea Technol 36:27-32 facility for maintaining soft-bottom sediments. Neth J Sea Turner JS (1973) Buoyancy effects in fluids. Cambridge Uni- Res 34:289-302 versity Press, Cambridge Smith IR (1975) Turbulence in lakes and rivers. Freshwater van Leussen W (1988) Aggregation of particles, settling velo- Biolog~cal Association, Ambleside, Cumbna, Sci Pub1 city of mud flocs: a review. In: Dronkers J, van Leussen W no. 29 (eds) Physical process in estuaries. Springer-Verlag, Snelgrove PVR, Butman CA (1994) Animal-sediment relation- Berlin, p 347-403 ships revisited: cause versus effect. Oceanogr Mar Biol van Leussen W (1997) The Kolmogorov microscale as a 11m1t- Annu Rev 32:lll-117 ing value for the floc sizes of suspended fine-grained sed- Snelgrove PVR, Butman CA, Grassle JF (1995) Potential flow iment~in estuaries. In: Burt N, Parker R, Watts J (eds) artifacts associated with benthic experimental gear: deep- Cohesive sediments. John Wiley and Sons, New York, sea mudbox examples. J Mar Res 53:821-845 p 45-62 Sonntag NC. Parsons TR (1979) Mixing an enclosed, 1300 Watanabe d,Kohata K. Kilnura T, Takamatsu T, Yamaguchi cubic meter water column: effects on the planktonic food S, loriya T (1995) Generation of a Chattonella ant~qua web. J Plankton Res 1:85-102 bloom by impos~nga shallow nutncline in a mesocosm. Squires KD. Yamazaki H (1995) Preferential concentration of Limnol Oceanogr 40:1447-1460 marine particles in isotropic turbulence. Deep Sea Res I Weetman RJ (1992) Development ot transitional flow 42:1989-2004 impeller. In: King R (ed) Fluid mechanics and its applica- Steele JH, Farmer DM, Henderson EW (1977) Circulation and tions, 10: Fluid mechanics of mixing: modelling, opera- temperature structure in large marine enclosures. J Fish tlons and experimental techniques. Kluwer Academic Res Bd Can 34:1095-1104 Publishers, Dordrecht, p 19-26 Sundby S, Fossum P (1990) Feed~ngconditions of Arcto-Nor- Weinstock J (1992) Vertical diffusivity and overturning length wegian cod larvae compared with the Rothschild-Osborn in stably strat~f~edturbulence. J Geophys Res 97: theory on small-scale turbulence and plankton contact 12653-12658 rates. J Plankton Res 12:1153-1162 Williams AJ 111, Tochko JS, Koehler RL, Grant WD, Gross TF, Taghon GL. Greene RR (1992) Utilization of deposited and Dunn CVR (1987) Measurement of turbulence in the suspended particulate matter by benthic 'interface' feed- oceanic bottom boundary layer with an acoustic current ers. L~mnolOceanogr 37 1370-1391 meter array. J Atmos Oceanic Technol 4.312-327 Takahash~M, Whitney FA (1977) Temperature, salin~tyand Wolanslu E, Gibbs RJ, Mazda Y, Mehta A, King B (1992)The light penetration structures: controlled ecosystem pollu- role of turbulence in the settling of mud flocs. J Coast Res tion experiment. Bull Mar Sci 273-16 8:35-46 Tatterson GB (1991) Fluid mixing and gas dispersion in agl- Wright LD, Boon JD, Xu JP. Kim SC (1992)The bottom bound- tated tanks. McGraw-Hill, Inc. New York ary layer of the Bay Stem Plains environment of lower Taylor AH, Stephens JA (1993) Diurnal variations of convec- Chesapeake Bay Estuarine. Coast Shelf Sci 35:17-36 tive mixing and the spring bloom of phytoplankton. Deep Yamazaki H, Lueck R (1990) Why oceanic dissipation rates Sea Res 40:389-408 are not lognormal. J Phys Oceanogr 20 1907-1918 Tennekes H. Lumley JL (1972) A first course In turbulence. Yamazalu H, Osborn TR (1988) Review of oceanic turbulence MIT Press. Cambridge, MA implications for biodynamics. In: Rothschild BJ (ed) Tenore KR (1987) Nitrogen in benthlc food chains. In: Black- Toward a theory on biological-physical interactions in burn TH. Sorensen J (eds) Nitrogen cycling in coastal the world ocean. Kluwer Academic Publishers, Dordrecht, marine environments. Wiley. New York, p 191-206 p 215-234 Terray EA, Donelan MA, Agrawal YC, Drennan WM, Kahma Yamazaki H, Osborn T (19901 Dissipation estimates for strati- KK, Williams AJ 111, Hwang PA, Kitaigorodski~SA (1996) fled turbulence. J Geophys Res 95:9739-9744

Editorial responsibility: Otto Kinne (Editor), Submitted: January 6, 1997; Accepted: Septenlber 23, 19.97 Oldendorf/Luhe, Germany Proofs received from author(s): December 22, 1997