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passive and active flow control by swimming fishes and mammals

passive and active flow control by swimming fishes and mammals

Annu. Rev. Fluid. Mech.

Annu. Rev. Fluid. Mech. 2006.38:193-224. Downloaded from arjournals.annualreviews.orgby WEST CHESTER UNIVERSITY on 12/20/05. For personal use only.Figure 10Velocity transects through vortices in the wake of a steadily swimming eel to show theseparation through time of the two vortex cores. The location of the center of the first vortexis indicated by the vertical dotted line, and zero velocity by horizontal dotted lines at eachtime. Sample flow fields at the times indicated by the arrows are shown on the right. Thecenter of the first vortex core is indicated by a cross, and the center of the second by a circle.Idealized profiles through a single and two same-sign Rankine vortices are shown above andbelow the transect plots, respectively. Transect plots show fluid velocity at seven pointsthrough time along the line connecting the two vortex centers as indicated on the vorticityand vector plots to the right. (Modified from Tytell & Lauder 2004.)The front half of the body of swimming eels produces very low vorticity, consistentwith observed kinematic patterns in which steadily swimming eels at low to moderatespeeds of 0.5 to 1.5 Ls −1 possess relatively little lateral body motion in this region(Gillis 1996, 1998; Tytell 2004a; Tytell & Lauder 2004). Indeed, the view that eellocomotion involves large sideways movement of nearly the entire body even at slow206 Fish·Lauder

Annu. Rev. Fluid. Mech. 2006.38:193-224. Downloaded from arjournals.annualreviews.orgby WEST CHESTER UNIVERSITY on 12/20/05. For personal use only.swimming speeds is one of the most enduring inaccuracies in the literature of aquaticswimming. Many workers accept the kinematic patterns shown for eels by Gray (1933)in his classic paper as a canonical representation of eel swimming. But, as discussedby Lauder & Tytell (2004), Gray’s eels were small individuals that were most likelyaccelerating. Accelerating eels do exhibit much larger anterior side movements (Tytell2004b). But eels swimming in a controlled steady rectilinear manner do not displaythis pattern, and instead exhibit an amplitude envelope that is remarkably similar tothat of other fishes (Lauder 2005): very low amplitude motion in the front half of thebody, and rapidly increasing amplitude in the last one third of the body.However, during linear accelerations by eels the thrust signature of downstreammomentum in the wake that is absent during steady swimming appears (Figure 11).Tytell (2004b) studied carefully controlled linear accelerations ranging from −1.4 to1.3 Ls −2 and showed that axial fluid momentum appearing in the eel wake is significantlycorrelated with the magnitude of body acceleration. Thus, axial momentumin aquatic vortex wakes can reflect thrust, demonstrating the necessity of carefullycontrolling animal body movement and kinematic patterns when attempting to drawconclusions about the hydrodynamic structure of the wake.The maximum spatial amplification and optimal creation of thrust-producing jetvortices lies in a narrow range of nondimensional frequencies referred to as theStrouhal number (St) (Triantafyllou et al. 1991). Peak swimming efficiencies forcetaceans and fish occur at St = 0.2–0.4 (Figure 12; Rohr & Fish 2004, Triantafyllou&Triantafyllou 1995). Animal propeller efficiencies have been estimated at 0.77 to0.98 (Fish 1998b, Fish & Rohr 1999, Webb 1975).Figure 11Vortex wake of anaccelerating eel.Acceleration is toward theleft at 0.6 Ls −2 by an eelstarting from steadyswimming at 1.42 Ls −1 .Note the strongdownstream jet flowsbetween vortex cores(labeled 1), similar indirection and relativemagnitude to steadyswimming in fish withdistinct tail propellers.(Modified from Tytell2004b.)3.3. Structure of Fish FinsThe fins of all fishes are stiffened with internal supporting elements, fin rays,that serve as sites of muscle attachment and support for the thin collagenous finwww.annualreviews.org • Fish and Mammal Locomotion 207

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