A shell shape that reduces drag: laboratory demonstration of a hydrodynamic mechanism and an exploration of its effectiveness in nature

MARKDENNY Biological Sciences Department, Stanford University, Hopkins Marine Station, Pacific Grove, CA 93950, U.S.A. Received October 3, 1988

DENNY,M. 1989. A limpet shell shape that reduces drag: laboratory demonstration of a hydrodynamic mechanism and an exploration of its effectiveness in nature. Can. J. Zool. 67: 2098 - 2 106. As the velocity of flow increases, smooth, symmetrical objects such as spheres and cylinders exhibit an abrupt transition from a laminar to a turbulent boundary layer. As a consequence, these shapes experience a substantial reduction in fluid- dynamic drag at velocities above the transition. The possibility was explored that this form of drag reduction operates in ben- thic marine organisms, and a single individual limpet has been found that exhibits the phenomenon in a laboratory flume. When the limpet's anterior end is oriented upstream, the shell shows a sudden 40% reduction in drag at a water velocity of 1.6 m/s, a velocity that is commonly encountered on wave-swept shores. It is unlikely, however, that this drag-reduction mechanism operates effectively under field conditions because flow is often from a direction inappropriate for drag reduction and the presence of upstream objects can abolish the effect. Furthermore, drag is much less likely to act as an agent of distur- bance than is lift, so any reduction in drag is unlikely to enhance survivorship. The likelihood that drag reduction via an abrupt boundary-layer transition is ineffective under natural conditions may help to explain why many benthic organisms do not have "typical" low-drag shapes.

DENNY,M. 1989. A limpet shell shape that reduces drag: laboratory demonstration of a hydrodynamic mechanism and an exploration of its effectiveness in nature. Can. J. Zool. 67 : 2098-2106. A mesure qu'augmente la vitesse du courant, les objets lisses et symktriques, tels les sphkres et les cylindres, passent brusquement d'une couche limitrophe laminaire A une couche limitrophe turbulente. I1 en rksulte que ces formes subissent une rkduction substantielle de la trainee en phase liquide aux vitesses qui ddpassent la vitesse de transition. Afin de voir si cette forme de reduction de la trainke se manifeste chez des organismes marins benthiques, j'ai examine le comportement d'une patelle dans un ruisseau artificiel. Lorsque l'extremitk antkrieure de la patelle est orientke face au courant, la coquille subit une brusque rkduction de 40% de la trainke lorsque la vitesse de l'eau est de 1,6 m/s, vitesse qui prevaut souvent sur les rives balaykes par les vagues. I1 semble cependant peu probable que ce mkcanisme de rkduction de la trainee soit trks efficace en nature, car le courant vient souvent d'une direction qui ne favorise pas la reduction de la trainee et la presence d'objets en aval peut abolir l'effet. En outre, la poussee est un phknomkne beaucoup plus susceptible d'agir sur les organismes que la trainee et une rkduction de la trainke risque donc peu de favoriser la survie. La rkduction de la trainee par transition brusque de la couche limitrophe est donc peu efficace en nature et cela explique sans doute pourquoi plusieurs organismes marins n'ont pas une forme "typique" d'objet A faible trainke. [Traduit par la revue] For personal use only.

Introduction often broken in storms (e.g ., Tunnicliffe 198 1; Vosburgh Drag, a fluid-dynamic force acting in the direction of flow, 1982). Similarly, Branchand Marsh (1978) examined the drag can be of practical importance. For instance, it is the force that characteristics of a variety of limpet and found that an airplane, train, or automobile must overcome in moving some of the species that inhabited the most severe flow envi- through air, or that a submarine must overcome in moving ronments have the highest size-specific drags. through water. Drag is the force which topples offshore oil Several explanations have been put forward to account for rigs during storms. Because of its practical importance for the apparent dearth of drag-reducing shapes among benthic man-made objects, drag has been well studied (Hoerner 1965). marine organisms. For instance, if an organism is sufficiently One result of these studies is a list of attributes one expects of flexible, its high-drag shape may be converted to a low-drag shapes designed to minimize drag. In general, these shapes shape as the organism deforms in response to flow (Vogel have the smooth-surfaced, "streamlined" appearance one 1981, 1984). In other cases, the lack of correlation between associates with airplanes, expensive cars, and submarines. drag and shape may be because some mechanisms used for Can. J. Zool. Downloaded from www.nrcresearchpress.com by Stanford University on 05/04/12 It has often been proposed that the shapes of benthic marine drag reduction in man-made objects simply do not work effec- plants and exposed to flowing fluids are in part a tively in the flow environments encountered by benthic organ- response to drag (e.g., Hubbard 1974; Koehl 1977, 1984; isms. For example, on wave-swept shores the direction of Warburton 1976; Branch and Marsh 1978; Branch 1981; water flow often cannot be predicted (Denny 1985), a factor Vogel 1981, 1984). Although this proposal is intriguing and which renders many streamlined shapes useless in terms of there are a few cases in which it has been demonstrated that reducing drag (Vogel 198 1; Denny 1988). This study exam- the shape of a benthic organism is likely to be a response to ines a second mechanism of drag reduction that has proven drag (e.g., Branch 1981; Warburton 1976; Hubbard 1974), useful in man-made objects (induction of an abrupt boundary- the adaptive relationship between drag and shape is not always layer transition) and addresses the question of whether it will apparent. If drag has generally been an important factor in work for benthic plants and animals. determining the shape of benthic plants and animals, why do When a solid object and its surrounding fluid move relative so few marine organisms living in rapid flows have typical to each other, a velocity gradient in the fluid (the boundary low-drag shapes? For example, many hermatypic corals have layer) is established at the object's surface. At low velocities, platelike or cylindrical shapes and rugose surfaces, attributes flow in this gradient is laminar, but as the velocity increases that are associated with large drag forces, and these corals are a point is reached at which flow in the boundary layer becomes

Printed in Canada I ImprimC au Canada DENNY 2099

turbulent. The velocity at which this transition occurs is number of these organisms is thus approximately lo4- lo6, affected by (among other things) the size of the object mea- spanning the range in which boundary-layer transition typi- sured as a characteristic length, L, and the kinematic viscosity cally occurs. Furthermore, the conical shape of is of the fluid, v. These parameters are usually grouped into a more regular than that of most benthic organisms, and their dimensionless index of the pattern of fluid flow, the Reynolds surfaces can be relatively smooth. Because of these factors, if number, Re = ~Llv,where u is the mainstream velocity of the drag reduction via an abrupt boundary-layer transition is pos- fluid relative to the object. For smooth-surfaced objects such sible in benthic marine organisms, limpets are ideal candidates as cylinders and spheres far from a solid surface, the for its application. Three questions are asked: (1) Is drag boundary-layer transition occurs abruptly at a Re of approxi- reduction via an abrupt boundary-layer transition possible for mately 3 - 5 x lo5. For an object 10 cm in characteristic limpets? (2) If possible, is this mechanism likely to work under length, this translates to a velocity of about 5 m/s in water at natural flow conditions? (3) Is this drag reduction mechanism 10°C or 75 m/s in air at 20°C. likely to be an important factor determining the shape of The transition from a laminar to a turbulent boundary layer limpet shells? can be accompanied by a drastic decrease in drag for a range of velocities above the transition (Hoerner 1965) because fluid traveling past an object in a turbulent boundary layer can fol- Methods low the shape of the object farther downstream before separat- There are three major hydrodynamic forces acting on limpets: ing to form a wake than can fluid in a laminar boundary layer. drag, lift, and the acceleration reaction. This downstream displacement of the point of separation Drag reduces the size of the wake, and thereby reduces drag Drag measurements were conducted on the shells of 33 limpets (Schlichting 1979). The magnitude of the decrease in drag, representing 14 species from South Africa and the west coast of and the Reynolds number at which the boundary-layer transi- North America (Table 1). A bolt was glued to the inside of each shell tion takes place, are affected by the object's morphology. For extending perpendicularly to the plane of the aperture and passing as instance, the rougher the surface, the lower the velocity at nearly as possible through the centroid of the aperture. Each shell was which transition takes place (Vogel 1981 ; Hoerner 1965). then attached by the bolt to a force platform similar to that of Denny Practical use has been made of this effect. For instance, the (1982) (Fig. 1A) and inserted into the working section of a flume "roughness" caused by dimples lowers the transition velocity (Denny 1988). Mainstream velocity in the flume was varied from of a golf ball to less than that of a well-hit drive (Shapiro < 1.0 to >3.5 m/s in approximately 0.25 m/s increments (as mea- 1961). The consequent decrease in drag allows for longer sured by a Pitot-static tube centered in the working section), and the force caused by each velocity was recorded. Force measurements flight of the ball. were corrected for the relatively small shear force acting on the There are reasons to believe that this mechanism of drag exposed area of the force platform itself. In all cases measurements reduction will not work for benthic marine organisms (Vogel were made for three shell orientations: anterior upstream, posterior 1981 ; Denny 1988). (1) Most benthic plants and animals have upstream, right side upstream. One limpet that showed anomalous rough or ribbed surfaces. The presence of a rugose surface, in drag behavior was tested in additional orientations with its anterior

For personal use only. addition to triggering the transition to a turbulent boundary end rotated 10 -50" from directly upstream. From these force mea- layer, also decreases the magnitude of the change in drag at surements, the drag coefficient, Cd, corresponding to each velocity transition. For objects with roughness elements exceeding and orientation was calculated: 1/50 their characteristic length, the decrease in drag accom- panying boundary-layer transition is barely noticeable (Hoer- ner 1965; Sarpkaya and Isaacson 198 1). (2) If an organism has where Fd is the measured drag, pis the density of the fluid (in this an irregular shape, the irregularities may act in the same case fresh water, p = 1000 kg/m3), and A, is the area of the shell fashion as roughness elements to decrease the magnitude of projected in the direction of flow. A, was measured using a digitiz- ing pad to trace a calibrated photograph of the shell taken from the drag reduction. (3) The substratum around the organism also appropriate angle. The length of the shell in the direction of flow was has a boundary layer, and for the high velocities commonly measured, allowing water velocity to be expressed in terms of a Rey- found in nearshore benthic environments the boundary layer is nolds number. The projected area of the shell in each case was less intensely turbulent (Nowell and Jumars 1984; Denny 1988). than 10% of the flume cross section (100 cm2), and therefore cor- Turbulence generated upstream of an organism in the substra- rections for horizontal buoyancy were deemed unnecessary (see tum's boundary layer may strongly influence the flow patterns Webb 1975, Appendix 1). Can. J. Zool. Downloaded from www.nrcresearchpress.com by Stanford University on 05/04/12 around the object. If this externally imposed turbulence dis- Lifr rupts the orderly separation of flow, the reduction in drag As a comparison for drag, lift, the force perpendicular both to the associated with transition cannot occur. Because most benthic direction of flow and to the substratum, was measured for the same plants and animals have rugose surfaces, irregular shapes, or set of 33 limpet shells. In each case the shell was attached by its bolt both, and because (by definition) they are found on the sub- to a lift transducer similar to that of Denny (1982) (Fig. 1B). Because stratum where they can be affected by turbulence generated in this transducer requires that the shell be free to move perpendicularly the substratum's boundary layer, it seems unlikely that drag to the substratum for a force to be recorded, it was necessary to reduction of the sort that operates for golf balls will work for mount the shell with a small (generally ~0.5mm) gap between its benthic organisms. base and the wall of the flume. In a live limpet this gap would be In this study I explore this conclusion through an examina- minimized and the presence of the limpet's body would prevent any flow under the shell. Under these natural circumstances it is likely tion of the hydrodynamic forces acting on limpets. These that the pressure in the 's visceral mass is an average of the small (ca. 1 - 10 cm shell length) gastropods characteristically varying pressures present around the lip of the shell and therefore inhabit the intertidal and shallow subtidal zones of wave-swept remains near that of the local hydrostatic pressure. However, in these shores where water velocities of 1 - 10 m/s are common experiments the presence of a gap at the lip of the shell and the (Denny 1985, 1987, 1988; Denny et al. 1985). The Reynolds absence of the limpet's body allow water to flow under the shell. This CAN. J. ZOOL. VOL. 67, 1989

TABLE1. Species examined Turbulence levels in the flume The turbulence intensity in the flume working section was quanti- No. fied through an examination of the boundary-layer profile. According Species examined to theory (Schlichting 1979), the time-averaged velocity, ii, at a dis- tance D from the wall of the flume is a function of the shear velocity, Patella argenvillei u*: Patella barbara Patella concolor Patella granatina where k is von Karman's constant (0.4) and S is a parameter related Patella granularis to the roughness of the wall. The shear velocity can be experimentally Patella longicosta determined by measuring ii at various distances from the wall and Patella miniata plotting ln(D) vs. ii. Rearranging eq. 6 we see that Helcion petunculus digitalis Lottia gigantea Lottia limatula Thus, the slope of the curve ln(D) vs. ii is (klu,), from which u, can Lottia pelta be determined. Mcclintockia scabraa The shear velocity, u,, is a measure of the intensity of tubulence mitra in the flow; u, = (m)'I2, where u' and w' are the instantaneous deviations from the time-averaged horizontal and vertical velocities, "Previously known as scabra (Kozloff respectively, and the bar denotes the temporal mean (Schlichting 1987). 1979). Thus, u,, is a measure of the velocity typical of the correla- tion between horizontal and vertical fluctuations. Because in turbu- lence flow w' may be small when u' is large (and vice versa), u'w' flow can affect the subshell pressure and thereby change the mea- is likely to be smaller than g2or g2.Therefore u, is generally sured lift. To account for this potential confounding factor, the pres- somewhat smaller than the root mean square (rms) turbulent fluctua- sure under the shell was measured relative to the local hydrostatic tions present in the flow. pressure in the flume's working section. These measurements were made with a manometer (Fig. 1B) and were conducted simultane- Tenacity ously with the measurement of apparent lift. The measured lift forces The tenacity of 44 Lottia pelta was measured in situ at Hopkins were adjusted in the subsequent calculation of the lift coefficient to Marine Station, Pacific Grove, California. In the field a small hook reflect the force that would have been measured if the pressure under fashioned from a paper clip was glued to the shell of each individual the shell had remained at ambient hydrostatic pressure. The lift near its center using epoxy putty, and the putty was allowed to set for coefficient, C,, is calculated analogously to the drag coefficient: 24 h. For tests of the tensile force required to dislodge a limpet, a string was attached to the hook and a force was applied in a direction perpendicular to the substratum with a recording spring scale similar to that of Jones and Demetropoulos (1968). For tests of the shear where F, is the corrected lift force and A, is the aperture area of the force required to dislodge a limpet, the string was looped around the shell, measured from photographs as described above. base of the putty at a level approximately equal to the centroid of the For personal use only. Acceleration reaction projected area of the shell and the dislodging force was applied The third major hydrodynamic force acting on limpets is the parallel to the plane of the-aperture. In a few cases a hook was glued acceleration reaction, Fa: approximately halfway between the center of the shell and the mar- gin, and force was applied-to the hook in a direction 45" to the plane of the shell aperture. Application of force at this oblique angle allows where Cm is the inertia coefficient, V is the volume of fluid dis- one to explore the possibility that the simultaneous application of both placed by the limpet, and a is the acceleration of the water relative tensile and shear forces can reduce the animal's tenacity. In all cases to the animal. If we assume that a limpet shell is roughly conical, with the limpet was given sufficient time after the string was attached and basal radius R and height H, the ratio of displaced volume to A, is before the force was applied to "hunker down" and achieve its maxi- nR/3 metres and the ratio of displaced volume to A, is H/3 metres. mal tenacity. Tenacity was calculated in all cases as the recorded Therefore, to a first approximation dislodgment force divided by the aperture area. Aperture area is cal- culated from the length and width of the shell by assuming the aper- ture to be an ellipse (a reasonable assumption for L. pelta; see Fig. 7). Temperature (both air and rock substratum) at the time of and these tests was 12.8- 14°C. Can. J. Zool. Downloaded from www.nrcresearchpress.com by Stanford University on 05/04/12 Results In other words, only if the magnitude of Ra or Ha is comparable to u2, and Cm is comparable to Cd or C,, is the acceleration reaction Detaired drag and lift results are reported elsewhere (M. W. similar in magnitude to lift or drag. Denny, T. L. Daniel, and G. M . Branch, in preparation); only This study concentrates on one particular limpet species, Lottia those related to boundary-layer transition are discussed here. pelta, previously known as Collisella pelta (Lindberg 1986). Data One individual L. pelta showed an abrupt decrease in drag reported by Denny et al. (1985) suggest that for Lottia pelta, Cm/Cd coefficient of approximately 40% at a Reynolds number of is approximately 3.7 and Cm/Clis approximately 3.6. Both H and R 5 x lo4 (Fig. 2A), corresponding to a water velocity of are approximately 0.01 m. The maximum velocities and accelerations reported by Denny et al. (1985) were 14 m/s and 400 m/s2, respec- approximately 1.6 mls. The drag coefficient remained low to tively. Even under these stressful circumstances the acceleration a velocity of at least 3.8 mls, the highest velocity used in these reaction is only 16% of drag and 5 % of lift. Because the acceleration tests. Lottia pelta is commonly found on exposed shores where reaction is likely to be so small compared with lift and drag in these velocities in the range of 1 - 5 mls occur with nearly every organisms, I have not included it in the analysis presented here. breaking wave (Denny 1985, 1988). DENNY

limpet shell B lift \ 1

bridge plifier

FIG. 1. Transducers for measuring drag and lift. (A) The drag transducer. A limpet shell is attached by a bolt to a force platform lying flush with the surface of the flume's working section. The platform is supported by two steel beams, the bending of which is proportional to drag. This bending is transduced to a voltage signal through the use of foil strain gauges glued to the beams. The transducer housing is sealed so that no water moves in or out of the working section through the gap around the force platform. (B) The lift transducer. The transducer is similar to the drag transducer but the orientation of the beams is rotated through 90". The difference in pressure between the upstream fluid in the working section and the fluid beneath the limpet shell (which communicates with the sealed transducer housing via the hole through which the mounting bolt extends) is sensed by a manometer.

At velocities in the range over which the abrupt decrease in The lift coefficient versus Reynolds number curves for drag occurred, the drag periodically jumped between two L. pelta are shown in Fig. 5. No variation in lift correspond- values. The fraction of time spent in the high-drag state ing to the sudden decrease in drag was observed in the three decreased as the water velocity was increased (Fig. 2B). L. pelta tested, including the individual showing the abrupt The decreased drag in this individual occurred only when decrease in drag (Fig. 5A), nor was any abrupt change in lift the limpet was oriented with its anterior end upstream. The observed in the other species tested. curve of Cd VS.Re for limpets oriented posterior upstream is For mainstream velocities in the range at which the typically similar to that of the limpet oriented anterior boundary-layer transition was observed, u, in the flume is upstream (M. W. Denny, T. L. Denny, and G. M. Branch, 6 -6.5 % of the mean mainstream velocity (Fig. 6), implying in preparation), and this is true for the other L. pelta tested that the rms turbulent fluctuations in velocity (either parallel For personal use only. (Fig. 3). Comparison between the two orientations for the to or normal to the substratum) are at least 6% of the average anomalous limpet (Fig. 2A) clearly shows that the change in mainstream velocity and can be somewhat larger. drag at Re = 5 x lo4 when it is oriented anterior upstream On average, L. pelta at Hopkins Marine Station were more is a reduction in drag at higher water velocities rather than an tenacious in shear (average tenacity = 1.67 x lo5 N/m2, unusually high drag at low velocities. The effect was repro- SD = 0.60 x lo5 N/m2, n = 19) than in tension (average ducible both when increasing and decreasing the water veloc- tenacity = 1.12 x lo5 N/m2, SD = 0.43 x lo5 N/m2, n = ity, and removing and replacing the limpet on the force 16) when compared by means of a t-test (P < 0.0005). Previ- platform did not affect the results. These results are inter- ous studies (Grenon and Walker 1981 ; Miller 1984) found that preted as being due to an abrupt transition from a laminar to limpets were less tenacious in shear than in tension when a turbulent boundary layer over the shell, and demonstrate that tested on smooth substrata in the laboratory. The high shear this transition can act as a drag-reduction mechanism. tenacity of L. pelta in this case is probably attributable to a A similar reduction in drag was observed when the limpet large frictional resistance to shearing caused by the rugose was yawed so that its anterior end was 10-40" away from substratum on which this species was found in the field. When

Can. J. Zool. Downloaded from www.nrcresearchpress.com by Stanford University on 05/04/12 directly upstream, but the transition to a reduced drag coeffi- force was applied at 45" to the plane of the aperture, the aver- cient occurred at increasingly higher velocities as the angle age tenacity (1.10 x lo5 N/m2, SD = 0.46 x lo5 N/m2, was increased (Fig. 4). When the anterior end of the shell was n = 9) was not significantly different from that measured in at an angle of 250" to the direction of flow, a distinct transi- pure tension when compared by means of a t-test (P > 0.05). tion to a decreased drag coefficient was not observed. Experiments revealed that it was not difficult to disrupt the drag-reducing effect of the anomalous limpet shell by placing Discussion small objects upstream. Even a single small "Lego" block The occurrence in a single individual limpet of an abrupt 8 mm square by 5 mm high (44% of the height of the limpet) decrease in drag due to a boundary-layer transition demon- placed 4 cm upstream totally abolished the drag-reducing strates that this phenomenon is indeed possible for biological effect with the animal oriented anterior directly upstream. objects attached to a solid substratum. This demonstration, Neither of the two other L. pelta tested (Fig. 3), nor any of however, raises four questions. the other species tested, exhibited any abrupt decrease in drag (1) Why does ,the transition occur at a Reynolds number an within the range of velocities used in these experiments. order of magnitude lower than that reported for smooth- CAN. J. ZOOL. VOL. 67, 1989

A anterior upstream anterior upstream posterior upstream posterior upstream 0.9,- A side upstream

A side upstream 0.8 r

Log Reynolds Number

Log Reynolds Number FIG. 3. Drag coefficient versus Reynolds number curves for two other Lottia pelta. Note the absence of an abrupt decrease in drag and the fact that drag when the shell is oriented with its anterior upstream (0)is nearly identical to drag when oriented posterior upstream (a).

boundary layer \ A

- 1.50 1.60 1.70 1.80

Mainstream Velocity (m/s) For personal use only. FIG.2. An abrupt boundary-layer transition in a single individual Lottia pelta. (A) The drag coefficient as a function of Reynolds num- " ber. When the limpet shell is oriented with its anterior end upstream 0 10 2 0 3 0 4 0 (0)a 40%reduction in drag coefficient is encountered at a Reynolds number of approximately 5 x lo4. The effect is not seen when the Degrees of Yaw shell is oriented with its posterior upstream (D) or with its side FIG.4. The velocity at which the boundary-layer transition occurs upstream (A). (B) In the velocity range over which the boundary- in the anomalous Lottia pelta increases as the anterior end of the shell layer transition occurs the drag coefficient switches abruptly between is yawed away from being directly upstream. The vertical lines the high-drag, laminar boundary layer state and the low-drag, turbu- represent the range of velocities over which the transition occurs. At lent boundary layer state. The higher the velocity, the less the time angles above 40" no distinct transition was observed. The curve is a spent in the high-drag state. third order polynomial, least-squares fit to the midpoints of the transi- tion ranges. surfaced objects far from the substratum (Hoerner 1965)? Note that this lower transition velocity could be construed as a turbulent boundary layer (Prandtl and Tietjens 1934; Hoerner Can. J. Zool. Downloaded from www.nrcresearchpress.com by Stanford University on 05/04/12 adaptive: if transition occurred at the "standard' ' Reynolds 1965; Schlichting 1979), and most measurements of boun- number of 3 - 5 x lo5, it would occur at a velocity of 9 - dary-layer transition have been conducted in flumes or wind 15 m/s for the anomalous L. pelta. These are extremely high tunnels inwhich care has been taken to minimize mainstream velocities and would require a wave approximately 4 - 11 m turbulence. In this respect the "standard" transition Re of high at breaking to be realized on a natural shore (Denny 3 - 5 x lo5 represents an upper bound. Flow in the flume 1988). The lower transition velocity noted here (1.6 m/s, cor- in which this study was conducted was quite turbulent, with responding to the maximum velocity associated with a break- u, approximately 6 % of the mainstream velocity. Turbulence ing wave only 0.13 m high) is a much more common of this intensity may well serve to lower the transition velocity occurrence on wave-swept shores. to well below that which would be otherwise expected. For There are two probable reasons for the low transition veloc- example, Hoerner (1965) notes a decrease in the transition ity: (i) the limpet shell is not smooth (Fig. 7), and the ribs and velocity for a sphere from 4 x lo5 without mainstream turbu- other surface rugosities could serve to induce transition at a lence to 1.5 X lo5 for an rms velocity fluctuation equal to lower than expected Re in the same way that dimples lower the 4% of mainstream velocity. The magnitude of drag reduction transition velocity of a golf ball, and (ii) ambient turbulence for the sphere was not affected by the intensity of mainstream in the mainstream flow can drastically lower the transition to turbulence. DENNY

anterior upstream posterior up stream

A side upstream

Log Reynolds Number FIG.5. Lift coefficient versus Reynolds number curves for Lottia pelta. No abrupt change in lift coefficient is observed analogous to Contour Interval = I. 1 I mm the change in drag noted in Fig. 2. The anomalous limpet shell is that of A; it is quite similar to that for other L. pelta (B and C). Apex Elevation = 1 1 .4 mm FIG. 7. A contour map of the anomalous Lottia pelta shell. Mainstream Velocity

shell length for the anomalous limpet fall well within the range of other limpets tested (Table 2). There is no apparent gross

For personal use only. difference in ribbing or other surface architecture between this shell and those of other L. pelta tested. Apparently, the precise combination of overall shell shape and fine-scale surface mor- phology allows the abrupt boundary-layer transition exhibited by this individual, and the absence of this precise combination in other individuals disrupts the effect. An attempt was made to visualize the flow around the limpet with dye streams, and thereby to obtain information regarding which small-scale aspects of shape control the boundary-layer transition. Unfortunately, the intense turbulence in the main- stream flow dispersed the dye too quickly to allow effective flow visualization. In light of the discussion that follows regarding the biological significance (or lack thereof) of this drag-reduction mechanism, more heroic attempts to determine Can. J. Zool. Downloaded from www.nrcresearchpress.com by Stanford University on 05/04/12 the shape factors controlling transition were not pursued. (3) Although this mechanism of drag reduction is possible in

Average Water Velocity (m/s) laboratory flows, is it probable that it works in the field? Three factors are likely to reduce the effectiveness of this mechanism FIG.6. Boundary-layer profiles in the working section of the flume under natural conditions. (i) Denny (1985) has demonstrated at mainstream velocities spaning that in which transition occurs. At that the direction from which maximum forces are applied is a mainstream velocity of 1.16 mls, ln(D) = 5.67 (i)- 1 1.05 (r2 = unpredictable in the surf zone where L. pelta is commonly 0.983). Thus u, = 7.1 cmls, 6.1 % of mainstream velocity. At a found. The reduction in drag afforded by the abrupt boundary- mainstream velocity of 1.74 mls, ln(D) = 3.42 (ii) - 10.60 (r2 = layer transition in the anomalous L. pelta was evident only 0.986). Thus u, = 11.7 cmls, 6.7% of mainstream velocity. when the anterior end of the limpet was within approximately 40" of the direction of flow. Therefore, approximately 78 % (2) What about this particular shell shape renders it con- of the maximal velocities (those that presumably would place ducive to an abrupt boundary-layer transition? No answer is the limpet at maximal risk of dislodgment) would arrive from immediately apparent. The ratios length :width, length: height, a direction for which this drag reduction mechanism does not widtkheight, and distance from upstream lip to apex : total work. (ii) The drag reduction effect can be abolished by the CAN. J. ZOOL. VOL. 67, 1989

TABLE2. Aspect ratios for the limpet shells examined

L/H L/W A/L - The anomalous L. pelta Anterior upstream 2.959 1.227 0.329 Posterior upstream 2.959 1.227 0.671 Right side upstream 2.41 0.815 0.5 Range for the other 32 limpets examined Anterior upstream 1.590-5.405 1.057- 1.395 0.190-0.506 Posterior upstream 1.590-5.405 1.057 - 1.395 0.494-0.810 Right side upstream 1.504-5.076 0.7 17 -0.946 0.5

NOTE:Three aspect ratios were measured: (i) shell length, L (maximum length along the anterior -posterior axis) divided by shell height, H (the perpendicular distance from the plane of the aperture to the apex); (ii) shell length divided by shell width, W (maximum lateral dimension of the shell); (iii) distance, A, from the upstream edge of the shell to a line perpendicular to the plane of the aperture and passing through the shell's apex, divided by shell length.

presence of upstream objects. The mechanism of this effect is From eqs. 1 and 2 it is evident that lift and drag are both uncertain, but it is possible that turbulence in the wake of the directly proportional to the square of imposed water velocity. upstream object, when added to that already present in the Consequently, the occurrence of a large drag force is (in mainstream and in the substratum's boundary layer, disrupts theory) perfectly correlated with the imposition of a large lift the orderly separation of flow. There are two lines of evidence force. Assume for the moment that the ability of a limpet to supporting this possibility. First, imposition of externally resist a lift force is not affected by the magnitude of drag, in generated turbulence has been shown to have a drastic effect other words, that lift and drag act independently in dislodging on the transition to a turbulent boundary layer on flat plates an animal. In this case, only if the likelihood of being dis- (Schlichting 1979), suggesting that mainstream turbulence lodged by drag is larger than the likelihood of being simultane- could have a strong (although not precisely predictable) effect ously dislodged by lift, will drag act as the effective cause of on the flow pattern around a limpet shell. Second, studies of disturbance. The validity of the assumption that drag and lift heat-transfer coefficients (which often behave similarly to the act independently is examined below. drag coefficient) have shown that externally generated turbu- Through a comparison of eqs. 1 and 2 it can be seen that for lence minimizes the effect of shape on boundary-layer flow a given water velocity the ratio of lift to drag is (Ab/Ap) (Mitchell 1976). An analogous effect in the case of the limpet (Cl/Cd). The average ratio of Ab/Ap for the three L. pelta used shell could negate the drag-reducing effects of this particular in this study is 3.43 (anterior or posterior upstream) and 2.86 shell shape. Note, however, that the experiments with heat- (side upstream), and the ratio of CJCd (averaged over the For personal use only. transfer coefficients were carried out at Reynolds numbers Re range shown in Figs. 2 and 3 and with exception of the well below transition for the shapes used (Re < lo5), so that anomalously low values for the single limpet) is 0.51 for a it is uncertain whether the general conclusion presented by limpet oriented anterior upstream, 0.44 for a limpet oriented Mitchell (1976) is applicable to limpets in the field. (iii) If it anterior downstream, and 0.40 for a limpet oriented sideways. is indeed an increased turbulence intensity that disrupts drag Thus, on average, the ratio of lift to drag is 1.75 (limpet reduction, it is possible that higher levels of mainstream turbu- oriented anterior upstream), 1.5 1 (posterior upstream), and lence alone could have such an effect. Turbulence levels in the 1.13 (side upstream). Furthermore, L. pelta is less tenacious surf zone can be considerably higher than those present during in tension (as imposed by a lift force) than in shear (as imposed the flume experiments. Data cited by Svendsen (1987) suggest by drag). The observed tenacity distributions can be coupled that rms turbulent fluctuations in the surf zone are typically with the measured force coefficients to estimate the probability 5 - 15% of the maximum mainstream velocity and can thus be that a stationary individual chosen at random will be dislodged nearly three times those present in the flume experiments. In by a certain water velocity (Fig. 8). In all cases the animal is light of these factors, it is likely that in the natural environment at much greater risk of being dislodged by lift than drag. Only

Can. J. Zool. Downloaded from www.nrcresearchpress.com by Stanford University on 05/04/12 a limpet will seldom encounter a situation where drag reduc- if a limpet has a tensile tenacity near the largest measured and tion of the sort shown here is effective. simultaneously has a shear tenacity near the lowest measured, (4) Although this mechanism of drag reduction works only will it ever be dislodged by drag rather than lift. Under these under a limited (and presumably rare) combination of orienta- circumstances it seems unlikely that even the relatively high tions and flow conditions, it nonetheless represents a substan- drag typical of limpets acts as an agent of disturbance. As a tial reduction in drag when it operates, and therefore it could consequence, a reduction in drag cannot enhance survivor- potentially enhance survivorship. Because the shape of the ship, implying that drag is not an important factor in the anomalous L. pelta is not substantially different from others of evolution of shell shape. This may help to explain why a drag- the same species, it would seem that the ability to reduce drag reducing shape was found in only 1 of the 33 limpets exam- would be at a negligible cost to the animal. Is, then, this ined, but this conclusion must remain tentative without data on mechanism of drag reduction likely to be a factor in determin- the heritability of shell shape and the survivorship of limpets ing the shape of limpet shells? A thorough answer to this ques- as a function of wave exposure. tion is not possible, given the available evidence, but an The tenacity of limpets is lower when they are crawling than important aspect can be explored by comparing the relative when stationary. For example, Miller (1974) found that, on likelihood that drag and lift act as agents of disturbance in average, the tensile tenacity of crawling limpets is 36 % of that L. pelta. for the same animal when stationary. Assuming that this ratio DENNY

Lift Drag n - anterior upstream

posterior upstrea

A side upstream

Limpet Stationary 10 20 3 0 4 0 50 6 0 70 I Moving 6 12 18 2 4 3 0 3 6 4 2

Water Velocity (m/s) FIG.8. The probability that an individual Lottia pelta chosen at random from the population at Hopkins Marine Station will be dislodged by a given water velocity. Solid lines denote probabilities of dislodgment by lift; dotted lines denote probability of dislodgment by drag. For any given water velocity, the probability that the limpet will be dislodged by lift is much higher than that by drag. Limpets are less tenacious when moving than when stationary, and therefore require a lower velocity to be dislodged.

lift ment. To test for the presence of such an effect, nine L. pelta were dislodged by a force applied at 45" to the plane of the aperture, simultaneously imposing equal tensile and shearing forces. As previously noted, the overall tenacity measured in these tests was virtually identical to that measured in pure ten- sion. If we assume that this equality holds for all dislodgment forces applied at angles between 45 and 90" to the plane of the For personal use only. aperture, the net hydrodynamic force required to dislodge the animal can be separated into its tensile and shearing compo- nents. For instance, on average when L. pelta is oriented with its anterior upstream (the position in which drag reduction is possible), lift is 1.75 times drag and the net force on the organ- ism is applied at an angle of 60.3" to the plane of the aperture (Fig. 9). In this case, the tensile component of the dislodgment force is 86.6% of the force that would have to be applied by lift alone to dislodge the organism. In other words, the action FIG.9. Without the drag reduction afforded by an abrupt boundary- of drag (as simulated by this experiment) has been to reduce layer transition, the net hydrodynamic force acting on a Lottia pelta by approximately 13.4 % the lift force required to dislodge the oriented anterior upstream acts at an angle of 60.3" to the horizontal organism. If drag were reduced by 40% owing to an abrupt (solid arrows) and lift is 86.6% of the overall force. If drag were boundary-layer transition, the net force on the organism would reduced by 40%, the net force would act at an angle of 71. 1" to the Can. J. Zool. Downloaded from www.nrcresearchpress.com by Stanford University on 05/04/12 act at an angle of 71. 1" to the plane of the aperture, and the horizontal (dashed arrows) and lift would be 94.6% of the overall tensile component of the dislodgment force would be 94.6 % force. of that which would have to be applied by lift alone, an 8% increase in the-apparent resistance to tensile stress. Note that of crawling to stationary tenacities holds true for L. pelta, the this is the maximum increase in tensile tenacity afforded by a probability can be calculated that a crawling individual will be reduction in drag; it will be realized only in those rare circum- dislodged by a certain water velocity (Fig. 8). In this case, the stances discussed above when drag reduction works at all. The limpet will be dislodged at a lower water velocity than when overall effect of drag on lift will be much smaller. Therefore, stationary, but the dominance of lift over drag remains to a close approximation, the assumption that lift acts indepen- unchanged. dently of drag as the primary hydrodynamic agent of distur- The conclusion that lift rather than drag acts as the effective bance is valid. fluid-dynamic cause of disturbance could be affected if there Arnold and Weihs (1978) discuss an example in which lift were a strong interaction between drag and the ability to resist and drag strongly interact in determining the flow velocity lift. If, for instance, the tensile tenacity of a limpet is substan- required to dislodge a benthic organism, in their case, the tially reduced by a relatively small shearing force, a reduction velocity required to move a plaice downstream. Their analysis in drag could effectively reduce the probability of dislodg- and conclusions differ from those presented here because the 2 106 CAN. J. ZOOL. VOL. 67, 1989 mechanism of adhesion in the plaice is different from that in 1985. Wave forces on intertidal organisms: a case study. Lim- limpets. Arnold and Weihs assume that the plaice is held in nol. Oceanogr. 30(6): 117 1 - 1187. place only by friction with the substratum, and that the fric- 1987. Life in the maelstrom: The biomechanics of wave- tional resistance is directly proportional to the net downward swept rocky shores. Trends Ecol. Evol. 2(3): 6 1 - 66. 1988. Biology and the mechanics of the wave-swept environ- force acting on the animal. As lift increases, the net downward ment. Princeton University Press, Princeton, NJ. force (weight - lift) decreases, and the resistance to drag DENNY,M. W., DANIEL,T. L., and KOEHL,M. A. R. 1985. Mechan- decreases. In contrast, limpets resist lift through a combina- ical limits to size in wave-swept organisms. Ecol. Monogr. 55: 69 - tion of Stefan adhesion and pressure-difference adhesion, both 102. acting via the pedal mucus (Denny 1988). In this situation, GRENON,J.-F., and WALKER,G. 1981. The tenacity of the limpet, drag has no effect on the tensile tenacity. The physical basis Patella vulgata L. : an experimental approach. J. Exp. Mar. Biol. for the slight interaction noted above is not known, but it may Ecol. 54: 277 -308. be due to a peeling component of force introduced when the HOERNER,S. 1965. Fluid-dynamic drag. Hoerner Fluid Dynamics, limpets were stressed at 45" to the substratum, similar to the Brick Town, NJ. effect noted by Grenon and Walker (1981). HUBBARD,J. A. E. B. 1974. Scleractinian coral behavior in a This study illustrates a danger inherent in any attempt to calibrated current experiment: an index to their distribution pattern. Proc. Int. Coral Reef Symp. 2nd, 2: 107 - 126. apply information gained from laboratory experiments to the JONES,W. E., and DEMETROPOULOS,A. 1968. Exposure to wave study of plants and animals in the field. Flume experiments action: measurement of an important ecological parameter on the clearly show that a substantial reduction in drag via an abrupt shores of Anglesey. J. Exp. Mar. Biol. Ecol. 2: 46 - 63. boundary-layer transition is possible for benthic marine organ- KOEHL,M. A. R. 1977. Effects of sea anemones on the flow forces isms. A closer examination, however, reveals that the they encounter. J. Exp. Biol. 69: 87 - 105. mechanism is unlikely to be effective under nearshore field 1984. How do benthic organisms withstand moving water? conditions. It therefore seems safe to conclude that for all Am. Zool. 24: 57-70. practical purposes this mechanism of drag reduction is not KOZLOFF,E. 1987. Invertebrates of the Pacific Northwest. University available to limpets and is perhaps unavailable to other near- of Washington Press, Seattle. shore benthic marine organisms as well, a conclusion which LINDBERG,D. R. 1986. Name changes in the "Acmaeidae". Veliger, 29(2): 142 - 148. may help to explain why so few of these organisms have typi- MILLER,S. L. 1974. Adaptive design of locomotion and foot form in cal low-drag shapes. Although it appears unlikely that drag prosobranch gastropods. J. Exp. Mar. Biol. Ecol. 14: 99- 156. reduction via an abrupt boundary-layer transition is biologi- MITCHELL,J. W. 1976. Heat transfer from spheres and other animal cally important in the nearshore flow regime, this does not forms. Biophys. J. 16: 561 -569. preclude it from being important in habitats where the flow is NOWELL,A. R. M., and JUMARS,P. A. 1984. Flow environments of more conducive to the effect. For example, the demonstration aquatic benthos. Annu. Rev. Ecol. Syst. 15: 303 -328. here that this mechanism of drag reduction is indeed possible PRANDTL,L., and TIETJENS,0. G. 1934. Applied hydro- and aero- may be important to the study of organisms living in smooth- mechanics. Dover Publications, New York. bottomed streams or rivers. SARPKAYA,T., and ISAACSON,M. 1981. Mechanics of wave forces on offshore structures. Van Nostrand-Reinhold Co., New York. For personal use only. SCHLICHTING,H. 1979. Boundary layer theory. 7th ed. McGraw-Hill, Acknowledgements New York. I thank T. Farrell, T. Daniel, A. DeTomaso, and J. King- SHAPIRO,A. H. 196 1. Shape and flow. Doubleday, Garden City, NY. solver for their technical assistance and constructive advice. SVENDSEN,I. A. 1987. Analysis of surf zone turbulence. J. Geophys. Res. 92: 5115-5124. This study was funded by National Science Foundation Grant TUNNICLIFFE,V. 1981. Breakage and propagation of the stony coral OCE 83-14591. Acropora cervicornis. Proc. Natl. Acad. Sci. U.S.A. 78: 2427 - 243 1. ARNOLD,G. P., and WEIHS,D. 1978. The hydrodynamics of rheotaxis VOGEL,S. 1981. Life in moving fluids. Willard Grant Press, Boston, in the plaice (Pleuronectes platessa L.). J. Exp. Biol. 75: 147 - MA. 162. 1984. Drag and flexibility in sessile organisms. Am. Zool. BRANCH,G. M. 1981. The biology of limpets: physical factors, 24: 37-44. energy flow and ecological interactions. Oceanogr. Mar. Biol. VOSBURGH, F. 1982. Acropora reticulata: structure, mechanics and Annu. Rev. 19: 235 -380. ecology of a reef coral. Proc. R. Soc. Lond. 214: 481 -499.

Can. J. Zool. Downloaded from www.nrcresearchpress.com by Stanford University on 05/04/12 BRANCH,G. M., and MARSH,A. C. 1978. Tenacity and shell shape WARBURTON,K. 1976. Shell form, behavior and tolerance of water in six Patella species: adaptive features. J. Exp. Mar. Biol. Ecol. motion in the limpet Patina pellucidu (L.) (:Proso- 34: 111 - 130. branchia) J. Exp. Mar. Biol. Ecol. 23: 307 -328. DENNY,M. W. 1982. Forces on intertidal organisms due to breaking WEBB,P. W. 1975. Hydrodynamics and energetics of fish propulsion. waves: design and application of a telemetry system. Limnol. Bull. Fish. Res. Board Can. No. 190. Oceanogr. 27(1): 178 - 183.