Fish larvae exploit edge vortices along their dorsal and ventral fin folds to propel themselves

Abstract

Larvae of bony fish swim in the intermediate Reynolds number (Re) regime, using body-and caudal-fin undulation to propel themselves. They share a median fin fold that transforms into separate median fins as they grow into juveniles. The fin fold was suggested to be an adaption for locomotion in the intermediate Reynolds regime, but its fluid-dynamic role is still enigmatic. Using three-dimensional fluid-dynamic computations, we quantified the swimming trajectory from body-shape changes during cyclic swimming of larval fish. We predicted unsteady vortices around the upper and lower edges of the fin fold, and identified similar vortices around real larvae with particle image velocimetry. We show that thrust contributions on the body peak adjacent to the upper and lower edges of the fin fold where large left-right pressure differences occur in concert with the periodical generation and shedding of edge vortices. The fin fold enhances effective flow separation and drag-based thrust. Along the body, net thrust is generated in multiple zones posterior to the centre of mass. Counterfactual simulations exploring the effect of having a fin fold across a range of Reynolds numbers show that the fin fold helps larvae achieve high swimming speeds, yet requires high power. We conclude that propulsion in larval fish partly relies on unsteady high-intensity vortices along the upper and lower edges of the fin fold, providing a functional explanation for the omnipresence of the fin fold in bony-fish larvae.

On the diverse roles of fluid dynamic drag in animal swimming and flying

“…Physically, the quadratic drag that resists the lateral motion of a cross-section of an elongated swimmer comes from the strong separations at the edges of the undulating body (figure 4). How this lateral drag force can produce unexpected thrust has been pointed out recently in the case of fish larvae that exploit edge vortices along their dorsal and ventral fins folds to propel themselves [70]. Hydrodynamic thrust generation and power consumption in future bioinspired undulatory swimmers will thus be the outcome of a strongly coupled fluid-structure interaction problem where local dissipation is a key issue.…”

“…The first term f ma is the reactive contribution due to the acceleration of the surrounding fluid by the undulating body or appendage, as it was derived using a potential flow assumption by Lighthill's elongated body theory [52,69]. But, the second term f d represents a resistive force associated with the dynamic stalls at each swimming cycle that result from the large transversal local velocities and the finite geometry of the fish section, as illustrated for instance in figure 4 from a recent simulation of the flow around a model fish (figures from [70]). Although a resistive model to describe the locomotion of long and narrow animals was developed by Taylor in the 1950s [71], ever since Lighthill's works [52,69], the reactive term has been the usual expression used to describe thrust production for high Reynolds number swimmers, marking a clear difference between the basic mechanisms for locomotion at low and high Reynolds numbers: the former being resistive and the latter reactive.…”

On the energetics and stability of a minimal fish school

“…Johansen et al [12] estimated 26 that trailing fish in a school (striped surfperch Embiotoca lateralis) benefited from over 27 25% reduction in oxygen consumption, based on correlations between swimming speeds, 28 pectoral fin beat frequency, and oxygen consumption of solitary fish. Marras et al [13] 29 also inferred reduced costs of swimming from measurements of tail-beat frequency of 30 grey mullet Liza aurata alone and in schools, combined with relationships between 31 tail-beat frequency and activity metabolism. Interestingly, they found that all members 32 of the school received energetic benefit regardless of their spatial position relative to 33 neighbors.…”

“…A physical description of the local interactions between nearest neighbors, 70 which are crucial in determining the whole group dynamics, still needs deeper insight. 71 We therefore study the minimal subsystem of fish school, consisting in two fish 72 swimming together, using a three-dimensional computational approach developed by Li 73 et al [29][30][31]. We investigate the consequences of spatial organization and kinematic 74 synchronization on the energy expenditure of the two-fish school (see Fig.…”

“…We developed an in-house three-dimensional overset grid numerical approach based on 342 finite-volume method and programmed in FORTRAN 90 to simulate cyclic swimming of 343 fish [29][30][31]40]. The approach comprises surface models of the changing fish shape around the fish with sufficient resolution (supportive information on grid resolution and 347 size tests can be found in supplementary materials).…”