An inertial mechanism behind dynamic station holding by fish swinging in a vortex street

Abstract

Many aquatic and aerial animal species are known to utilise their surrounding flow field and/or the induced flow field of a neighbour to reduce their physical exertion, however, the mechanism by which such benefits are obtained has remained elusive. In this work, we investigate the swimming dynamics of rainbow trout in the wake of a thrust-producing oscillating hydrofoil. Despite the higher flow velocities in the inner region of the vortex street, some fish maintain position in this region, while exhibiting an altered swimming gait. Estimates of energy expenditure indicate a reduction in the propulsive cost when compared to regular swimming. By examining the accelerations of the fish, an explanation of the mechanism by which energy is harvested from the vortices is proposed. Similar to dynamic soaring employed by albatross, the mechanism can be linked to the non-equilibrium hydrodynamic forces produced when fish encounter the cross-flow velocity generated by the vortex street.

Figure 1

Fish exhibit two distinct swimming gaits: (a) regular swimming outside the wake in the uniform flow field and (b) swinging between vortices. Sequential positions of the fish centreline advected downstream with the mean flow velocity are imposed on the ink visualisation of the reverse Kármán street, obtained in separate experimental series. Profiles of the mean streamwise flow velocity are shown below the images. In the top left corner, the contour of the fish body is shown with the part of the centreline associated with muscle marked blue.

Figure 2

Proportion of time spent in different swimming modes, averaged between the three individual fish which exhibit the swinging behaviour: blue—regular swimming outside the wake, red—altered gait in hydrofoil wake, green—swimming regimes which can not be uniquely identified. In the absence of the vortex street, hence with zero blade oscillation frequency, fish only swim regularly.

Figure 3

Frequency spectra of the curvature of fish body in different swimming regimes. Blue—regular swimming outside the wake, red—altered gait in the hydrofoil wake. Each marker corresponds to an individual fish. The vertical dashed line indicates foil oscillation frequencies. A clear peak at the hydrofoil oscillation frequency is evident in the altered gait cases, corresponding to the fish tuning their body shapes to the vortices.

Figure 4

Power expenditure by fish in different swimming modes divided by that in the absence of the vortex street: blue circles—regular swimming outside the wake, red triangles—altered gait in hydrofoil wake. Pairs corresponding to the same fish are joined by grey lines and shifted horizontally to improve clarity. A consistent reduction of the energy expenditure can be observed for all three fish at the foil frequencies of 1.4 Hz, 1.6 Hz and 2.0 Hz.

Figure 5

Phase-averaged trajectory of an individual fish in the space of cross-stream/streamwise accelerations in different swimming modes: blue—regular swimming outside the wake in the uniform flow field, red—swinging in the wake, green—swimming regimes which can not be uniquely identified. The non-averaged trajectory in the swinging regime is shown by the pale red line. Observe the well-defined figure of eight in swinging mode, when the fish ’pushes off’ the cross-stream flow to produce positive streamwise acceleration. The figure shows phase trajectory of fish #1 recorded for 22 s. The foil oscillation frequency is 2 Hz.

Figure 6

Forces acting on the fish in the flow composed of the uniform component and the component added by vortices. The vector sum of lift and drag forces has a positive streamwise component assisting fish propulsion. The cross-stream component of the hydrodynamic force leads to fish following an undulatory trajectory with the acceleration shown in Fig. 5.

Figure 7

Fish muscle curvature at different phases of the fish streamwise position with respect to vortices. Blue—regular swimming outside the wake, red—swinging in the wake. Clear dependence of the curvature on the position in the vortex street suggests fish adjust the body shape to improve efficiency of interaction with the cross-flow. The figure shows data acquired from fish #1 swinging in the hydrofoil wake with an oscillation frequency of 2 Hz.

Figure 8

Histogram of extracted fish muscle curvature phase versus non-dimensional distance to vortex. $\lambda$ denotes the distance between vortices, while the distance of the fish centre of volume to the next upstream vortex is $x_v$. The extracted phase can been seen to vary close to linearly with distance to vortex. The figure shows data acquired from fish #1 swinging with a foil oscillation frequency of 2 Hz.