Juhani Salmi Ja Tomi Tapper

Studies on turbulence in lakes Juhani Salmi ja Tomi Tapper WETS 150

Introduction

The fluctuations in the motion indicate the presence of turbulence. The most rapid fluctuations have a period of about a second and the smallest turbulent motion with scales of a few millimetres. Turbulent motions of these small scales are usually assumed three-dimensional and statistically similar in all directions. For scales as large as or larger than the depth of water, the motions lose homogeneity and become two-dimensional eddies. (Mann & Lazier 1991)

The energy in the turbulent eddies is extracted from larger-scale motions via many different instability mechanisms. The most common instability is the breaking of surface waves. The breaking converts the regular and predictable motion of the wave into random turbulent motion. The energy in turbulent motion is continually being transferred from large scales of motion to small scales in energy cascade. This process does not change the total amount of energy in the turbulence nor does it convert the kinetic energy to another form of energy. (Mann & Lazier 1991)

With the decrease in the size of turbulent eddies comes an increase in the velocity gradient across the eddies. The forces due to viscosity are quantified by calculating the Reynolds number (Re=ud/v), which is the ratio of the inertial force to the viscous force acting on the body of an animal or fluid element. The inertial force is necessary to accelerate the body to the velocity it now possesses or to stop the body travelling at a constant speed under its own inertia. (Mann & Lazier 1991)

Across distances greater than a few millimetres the eddies of the turbulence mix the water much more effectively than molecular motion. The eddy-caused diffusion works the same way as molecular motion except that it is the same for all properties. This means that heat, salt and nitrate will have the same eddy diffusion constant. (Mann & Lazier 1991)

Methods and materials

In most cases, the direct measurement of turbulence is difficult to process. This problem is avoided by using approximation via measurements of velocity fluctuations. The velocity is usually determined indirectly by using the Acoustic Doppler Current Profiler (ADCP) and Conductivity Temperature Depth- probe (CTD). In addition, one-point current meters can be used to get the necessary data to do approximations. (Huttula 2009 [Referenced 4.4.2009])

ADCP is based on three transducers sending the sound pulse, which travels through the water in different, but known directions. As the sound energy leaves and arrives, it is shifted in frequency by the relative velocity of the water. As that sound energy is returned by scatters in the water the sound may also be shifted in frequency if there is relative velocity of water to scatter. Trigonometry, averaging and some critical assumptions are used to calculate the velocity of the group of echoing scatters in a volume of water. (NortekUsa 2009 [Referenced 4.4.2009]) Figure 1. Acoustic Doppler Current Profiler

The CTD- probe gathers information about the conductivity and temperature in different depths. Other features can be added to the probe. CTD is based on either optical or/and gas exchange technology. (Ysi 2009 [Referenced 4.4.2009])

Figure 2. Conductivity Temperature Depth- probe.

Microstructure sensors (MSS) can be used for direct turbulence measurements. MSS profilers are multi-parameter probes for the measurement of microstructure and turbulence in marine and limnic waters. They are equipped with a high-resolution microstructure and standard hydrographic sensors. (Isw-Wasser 2009 [Referenced 4.4.2009])

The technology to measure turbulence is based on the cross-stream components of turbulent velocity producing a lifting force at the water foil. The piezoceramic beam senses the lift force and the output of the piezoceramic element is a voltage proportional to the instantaneous cross-stream component of the velocity field. (Huttula 2009 [Referenced 4.4.2009])

Figure 3. Microstructure Sensors profiler. The Portable Flux Profiler is used to directly measure turbulent fluxes and other turbulent parameters. It uses a three-axis laser Doppler anemometer to measure water velocities in all three directions and measures conductivity, temperature and depth at the micro-scale (1mm). (Centre for Water Research 2009 [Referenced 4.4.2009])

Figure 4. Portable Flux Profiler.

Effects on the biota

The effects of turbulence vary among different organisms. Large creatures such as fish are little influenced by turbulence but it might be a matter of life and death to small organisms. In this chapter, impacts of turbulence on major groups of aquatic organisms are considered.

Phytoplankton

Turbulence has a great impact on phytoplankton because most phytoplankton is lacking or only has weak locomotory capabilities. These organisms are carried by turbulence around the mixing layer and may end up in better or worse light climate or nutrient supply (MacIntyre 1998). The phytoplankton cells may be carried too deep where there is not enough light for photosynthesis or too near the surface where ultraviolet light may harm them. Nevertheless, not all phytoplankton is just passively floating in the water: diatoms are rather heavy so they resist turbulent uplifting, some species (e.g. some cyanobacteria) have gas-filled vacuoles to keep them from sinking, some (e.g. dinoflagellates) have flagella with which they can swim against the turbulent water.

Turbulence moves not only the phytoplankton but nutrients and other solutes as well. These can be lifted from the aphotic zone or from the sediments to the euphotic zone where they are available to the phytoplankton (MacIntyre 1998). It is also possible that phytoplankton cells travel with turbulence to take up nutrients from the more nutrient-rich aphotic zone to use them when they are returned to the light.

Turbulence may affect the diffusivity between phytoplankton cells and the water. Larger phytoplankton cells in particular (>20 μm in diameter) benefit from turbulence in their nutrient uptake 50 per cent or more compared to stagnant water. Smaller cells can benefit if they take up large slowly diffusing molecules. Nutrient uptake may be hindered if the cells' movement is rotational and unparallel to the direction of shear. Phytoplankton may also have adapted their shape to maximize nutrient diffusion from turbulent water (Karp–Boss et al. 1996). For example, Tabellaria diatoms form comb- or zigzag-shaped colonies, which enhance their nutrient uptake. Zooplankton

Although zooplankton has usually better swimming abilities than phytoplankton, they too are affected by turbulence. Especially mid-sized zooplankton can benefit from turbulence as it enhances their probability to find and encounter prey. On the other hand, turbulence shortens the time for the predator to capture the prey (Kiørboe & Saiz 1995). It is likely that each zooplankton predator has a turbulence optimum where its hunting strategy works most efficiently (Mackas et al. 1993). Turbulence and zooplankton density are difficult to observe simultaneously but it is possible in some circumstances with an echo sounder (Ross et al. 2007). Movements of large schools of zooplankton can even create turbulence (Kunze et al. 2006).

Macrophytes

Effects of turbulence on macrophytes have been studied mostly in rivers where macrophyte biomass has been observed to decline with increasing current velocities (Chambers et al. 1991). Lower end of studied velocity ranges (0.01–1.0 m/s) should be applicable to lakes as well. Where turbulence is strong, macrophytes may not be able to root, or the substrate might be too coarse for them to grow (Kalff 2001). Macrophytes affect turbulence as well. Water velocity can decline in and behind macrophyte stands by as much as 50 per cent (Pluntke & Kozerski 2003).

Fish may be affected by turbulence in their egg and larval life stages. Turbulence has greatest impact on fish eggs in marine environment where pelagic eggs are easily carried by water currents. In fresh water, benthic eggs of fishes may be buried in sediment set in motion by turbulence. On larval fish, turbulence has effects similar to zooplankton i.e. they can enhance their feeding success in moderately turbulent water (Kiørboe & Saiz 1995). Strong turbulence on the other hand can displace the larvae to a less suitable habitat (MacKenzie & Leggett 1991). Adult fish often exploit turbulence in order to use less energy for swimming or maintaining position, e.g. by staying behind a current-breaking object or by swimming in the wake of another fish (Liao et al. 2003).

Results

Recent studies from three research groups

Jörg Imberger

Main interests of Imberger’s group are the motion and mixing in lakes, estuaries and coastal seas in response to both natural forces such as tides, meteorological surface fluxes, river inflows and outflows as well as to anthropogenic forces such as effluent buoyant jets, bubble plumes and mechanical mixers and the effect of such motions and mixings on ecological systems residing in the water bodies. The application of this combined knowledge to the sustainable management of such water bodies. (Centre for Water Research 2009 [Referenced 4.4.2009]) Imberger’s group uses mainly the MSS profiler for turbulence measurements but also the Portable Flux Profiler.

Table 1. Recent studies from Imberger’s research group. Lemckert, C.J., Imberger, J. 1998, Turbulent benthic boundary layer mixing events in fresh water lakes in Physical Processes in Lakes and Oceans. American Geophysical Union, Washington, D.C. Lemckert, C.J., Antenucci, J.P., Saggio, A.A., Imberger, J. 2004, Physical properties of turbulent benthic boundary layers generated by internal waves. Journal of Hydraulic Engineering, 130, 1, pp. 58-69. Etemad Shahidi, A., Imberger, J. 2002, Anatomy of turbulence in a narrow and strongly stratified estuary. Journal of Geophysical Research (Oceans), 107, C7, pp. 7.1-7.16. Dallimore, C.J., Imberger, J., Ishikawa, T. 2001, Entrainment and turbulence in saline underflow in Lake Ogawara. Journal of Hydraulic Engineering, 127, 1, pp. 937-948 Luketina, D.A., Imberger, J. 2001, Determining turbulent kinetic energy dissipation from Batchelor curve fitting. Journal of Atmospheric and Oceanic Technology, 18, 1, pp. 100-113. Saggio, A., Imberger, J. 2001, Mixing and turbulent fluxes in the metalimnion of a stratified lake. Limnology and Oceanography, 46, 2, pp. 392-409. Antenucci, J., Imberger, J., Saggio, A. 2000, Seasonal evolution of the basin-scale internal wave field in a large stratified lake. Limnology and Oceanography, 45, 7, pp. 1621-1638 Gomez-Giraldo, A, Imberger, J, Antenucci, JP, Yeates, PS 2008, Wind-shear-generated high-frequency internal waves as precursors to mixing in a stratified lake. LIMNOLOGY AND OCEANOGRAPHY, 53, pp. 354-367.

Alfred Wüest

Wüest has leaded since 1989 the Aquatic Physics Group at EAWAG. The group studies microstructure-observed small-scale turbulence, benthic boundary and stratified interior mixing, turbulence modelling, internal wave analysis and the relation of physical processes to bio- geochemical cycling in lakes. (Eawag 2009 [Referenced 4.4.2009]) Wüest’s group uses ADCP and CTD- probes for measuring the turbulence.

Table 2. Recent studies from Wüest’s research group. Lorke, A., B. Müller, M. Märki and A. Wüest (2003). Breathing sediments: The control of diffusive transport across the sediment-water interface by periodic boundary-layer turbulence. Limnol. Oceanogr. 48(6), 2077-2085. Jonas, T., A. Wüest, W. Eugster, and A. Stips (2003). Observations of a quasi shear-free lacustrine convective boundary layer: stratification and its implications on turbulence. J. Geophys. Res., 108 (C10), 3328, doi:10.1029/2002JC001440. Lorke A., and A. Wüest (2005). Application of coherent ADCP for turbulence measurements in the bottom boundary layer. J. Atmospheric Oceanic Technology 22, 1821-1828. Wüest A., T. M. Ravens, O. Kocsis, M. Schurter M. Sturm and N. Granin (2005). Cold Intrusions in Lake Baikal - Direct Observational Evidence for Deep Water Renewal. Limnology and Oceanography 50(1), 184-196. Lorke, A., F. Peeters, and A. Wüest (2005). Shear-induced convective mixing in bottom boundary layers on slopes. Limnol. Oceanogr. 50(5), 1612-1619. Schmid, M., M. Halbwachs and A. Wüest (2006). Simulation of CO2 concentrations, temperature, and stratification in Lake Nyos for different degassing scenarios. Geochem. Geophys. Geosyst., 7, Q06019, doi:10.1029/2005GC001164.

Sally MacIntyre

MacIntyre’s studies focus on the hydrodynamic controls on production internal waves, turbulent eddies, the filamentous intrusions due to streams, ocean currents, the vortices induced by flow around kelp blades and corals. These all have a role in the supply of nutrients to autotrophs, dissolved organic carbon to heterotrophs, and particulates to filter feeders and zooplankton. Internal waves and turbulence moderate the light supply to phytoplankton. The ongoing field experiments in temperate, tropical, and arctic lakes are determining the role of wind forcing and internal waves in turbulence production, nutrient transport and system productivity. Similar studies are beginning in kelp forests and coral reefs. (University of California, Santa Barbara 2009. [Referenced 4.4.2009]) MacIntyre’s group studies the turbulence mainly by using the MSS profiler.

Table 3. Recent studies from MacIntyre’s research group. MacIntyre, S., and J.R. Romero. 2000. Predicting upwelling, boundary mixing, and nutrient fluxes in lakes. Verh. Internat. Verein. Limnol. 27:246-250. MacIntyre, S., and R. Jellison. 2001. Nutrient fluxes from upwelling and enhanced turbulence at the top of the pycnocline in Mono Lake, CA. Hydrobiologia. 466: 13-29. MacIntyre, S., J. R. Romero, and G.W. Kling. 2002. Spatial-Temporal Variability in Mixed Layer Deepening and Lateral Advection in an Embayment of Lake Victoria, East Africa. Limnology and Oceanography 47: 656-671. Wurtsbaugh, W., J. Cole, D. McKnight, P. Brezonik, S. MacIntyre, and K. Potter. 2003. Emerging Research Questions for Limnology: The Study of Inland Waters. Boulder, CO. Am. Soc. Limnol. Oceanogr. 45 p Banerjee, S, and S. MacIntyre. 2004. The air-water interface: turbulence and scalar exchange. pp. 181-237 in John Grue, Philip L. F. Liu, and Geir K. Pedersen eds. Advances in Coastal and Ocean Engineering. World Scientific. MacIntyre, S., J.O. Sickman, S.A. Goldthwait, and G.W. Kling. 2006. Physical pathways of nutrient supply in a small, ultra-oligotrophic arctic lake during summer stratification. Limnol. Oceanogr. 51: 1107-1124. Caceres, C.E., S.R. Hall, M.A. Duffy, A.J. Tessier, C. Helmle, and S. MacIntyre. 2006. Physical structure of lakes constrains epidemics in Daphnia populations. Ecology 87: 1438-1444. Evans, M.A., S. MacIntyre, G.W. Kling. (in submission). Internal wave effects on primary productivity: experiments, theory and modeling. Limnol. Oceanogr. McPhee-Shaw, E.E., S. MacIntyre, and W.J. Shaw. (in review). Internal waves and mixing in Mono Lake, California. J. Geophys. Res. Literature

Centre For Water Research 2009. [Referenced 4.4.2009]. Available http://www.cwr.uwa.edu.au/services/field.php?mode=list. Centre For Water Research 2009. [Referenced 4.4.2009]. Available http://www.cwr.uwa.edu.au/cwr/people.php?id=359. Chambers P.A., Prepas E.E., Hamilton H.R. & Bothwell M.L. 1991. Current velocity and its effect on aquatic macrophytes in flowing waters. Ecol. Appl. 1: 249–257. Eawag 2009. [Referenced 4.4.2009]. Available http://www.eawag.ch/research_e/apec/people/wuest_e.html. Huttula T. 2009. Wets150 lecture notes. [Referenced 4.4.2009]. Available http://users.jyu.fi/~thuttula/WETS150/. Isw-Wasser 2009. [Referenced 4.4.2009]. Available http://www.isw-wasser.com/product1.htm. Kalff, J. 2001. Limnology: inland water ecosystems. Prentice-Hall, Upper Saddle River NJ, 592 p. Karp–Boss L., Boss E. & Jumars P.A. 1996. Nutrient fluxes to planktonic osmotrophs in the presence of fluid motion. Oceanogr. Mar. Biol. Ann. Rev. 34: 71–107. Kiørboe T. & Saiz E. 1995. Planktivorous feeding in calm and turbulent environments, with emphasis on copepods. Mar. Ecol. Prog. Ser. 122: 135–145. Kunze E., Dower J.F., Beveridge I., Dewey R. & Bartlett K.P. 2006. Observations of biologically generated turbulence in a coastal inlet. Science 313: 1768–1770. Liao J.C., Beal D.N., Lauder G.V. & Triantafyllou M.S. 2003. Fish exploiting vortices decrease muscle activity. Science 302: 1566–1569. MacIntyre S. 1998. Turbulent mixing and resource supply to phytoplankton. In Imberger J. (editor) Coastal and estuarine studies: Physical processes in lakes and oceans, 561–590. Mackas D.L., Sefton H., Miller C.B. & Raich A. 1993. Vertical habitat partitioning by large calanoid copepods in the oceanic subarctic Pacific during Spring. Prog. Oceanogr. 32: 259–294. MacKenzie B.R. & Leggett W.C. 1991. Quantifying the contribution of small-scale turbulence to the encounter rates between larval fish and their zooplankton prey: effects of wind and tide. Mar. Ecol. Prog. Ser. 73: 149–160. Mann K.H. & Lazier J.R.N. 1991. Dynamics of marine ecosystems, Biological-Physical Interactions in the Oceans. USA: Blackwell Scientific Publications, Inc. NortekUsa 2009. [Referenced 4.4.2009]. Available http://www.nortekusa.com/principles/Velocimeters.html. Pluntke T. & Kozerski H-P. 2003. Particle trapping on leaves and on the bottom in simulated submerged plant stands. Hydrobiologia 506: 575–581. Ross T., Gaboury I. & Lueck R. 2007. Simultaneous acoustic observations of turbulence and zooplankton in the ocean. Deep-Sea Res.Pt I 54: 143–153. University of California, Santa Barbara 2009. [Referenced 4.4.2009]. Available http://www.lifesci.ucsb.edu/eemb/faculty/macintyre/research/research.html. Ysi 2009. [Referenced 4.4.2009]. Available https://www.ysi.com/DocumentServer/DocumentServer? docID=YSI_T601.