Figure 1

A fish’s wake consists of vortex rings originating from the tail beats with a velocity component (thick arrows) that compensates for the fish’s displacement. Vector $\mathbf{k}$ describes the orientation of a vortex. A second, rotationally symmetric, fish with body $\mathcal{B}$ is tracking the wake structure. The continuous distribution of hydrodynamic poles $g(z)$ located on the axis of the fish body between $\alpha$ and $\beta$ (lower picture) ensures that the flow through its surface $\partial \mathcal{B}$ is zero.Reuse & Permissions

Figure 2

Pressure-difference distributions $\partial p/\partial x$ along the (trunk) lateral line due to a vortex ring as a function of position along the body relative to the body length. (a) and (b) During wake tracking vortices with different orientations $\gamma$ moving in $z$ direction with respect to the fish occur. Any such vortex generates an excitation pattern specific to its orientation angle $\gamma$. Patterns corresponding to orientations that differ by $\gamma =\pi /2$ are orthogonal functions so that the orientation of a vortex ring can be determined by projecting the stimulus pattern onto a given basis function. Fish can thus determine the direction they must follow to track their target. (c) Vortices at different distances from the fish generate excitation patterns that only differ in amplitude. The same holds true for changes in $\Gamma$, $R$, and $U$. (d) For a fixed fish in experiments, a vortex ring with $\gamma \in \{0,\pi \}$ and $\delta =0$ generates excitation patterns that are either four-phasic or two-phasic depending on the vortex propagation speed $\tilde{U}$. In contrast to cases (a) and (b), there is no one-to-one relation between $\gamma$ and stimulus. Hence a theory of vortex ring detection cannot be based solely on the experimentally verifiable case (d).Reuse & Permissions

Figure 3

Neuronal response ensuing from a canal neuromast (experimental results). The dots represent time-dependent spike rates of a canal neuromast measured when a vortex with $\gamma \in \{0,\pi \}$ and $\delta =0$ passed a fixed fish, averaged over ten time runs. As the vortex has approximately constant velocity, the recorded time-dependent data match the nervous excitation pattern along the lateral line at one moment of time. Canal neuromasts react to the pressure difference $\Delta p\approx (\partial p/\partial x)\Delta x$ between two adjacent pores shown in Fig. 2. The solid graph is a fit to theory; because of negative hair-cell polarity it is in the present case a mirror image of the black solid line in Fig. 2d.Reuse & Permissions