A model of the lateral line of fish for vortex sensing

In this paper, the lateral line trunk canal (LLTC) of a fish is modeled to investigate how it is affected by an external flow field. Potential flow theory is adopted to model the flow field around a fish's body in the presence of a Karman vortex street. Karman and reverse Karman streets represent the flow patterns behind a bluff body and a traveling fish, respectively. An analytical solution is obtained for a flat body, while a fish-like body is modeled using a Joukowski transformation and the corresponding equations are solved numerically. The pressure distribution on the body surface is then computed employing Bernoulli's equation. For a known external flow, the flow inside the LLTC is driven by the pressure gradient between a pair of consecutive pores, which can be solved analytically. Governing dimensionless parameters are obtained from this analytical solution, and the effects of these numbers on the amplitude or features of the velocity distribution inside the canal are studied. The results show that the main characteristics of a vortex street including the magnitude of vortices, their translational speed, their spacing, their distance from the fish's body and the angle of the vortex street axis can all be recovered by measuring the velocity distribution along the canal and its changes with time. To this end, the proposed LLTC model could explain how a fish identifies the characteristics of a Karman vortex street shed by a nearby object or a traveling fish. It is also demonstrated that while this model captures the ac (alternating current) component of the external velocity signal, the dc (direct current) component of the signal is filtered out. Based on the results of our model, the role of the LLTC in a fish's schooling and its evolutionary impact on fish sensing are discussed.