A vortex sheet-based hydrodynamic model of fish swimming*

Hydrodynamic models of fish can help elucidate a range of swimming phenomena, such as schooling and rheotaxis. Particularly enticing is the vortex dipole model, which offers an elegant representation of the flow physics at a modest computational cost. The model assumes the flow to be incompressible, irrotational, and inviscid, while the fish is treated as a dipole consisting of a pair of point vortices of equal and opposite strength. Despite its technical value and promise, this modeling paradigm does not fully capture major characteristics of the flow field around a swimming fish, featuring a high velocity region in the wake and the emergence and advection of local vorticities. To address these limitations, we explore an alternative hydrodynamic model, in which we explicitly take into consideration the wake generated by fish. Specifically, the time-averaged flow surrounding the fish is modeled as a pair of vortex sheets with spatially decaying strength, separated by a finite distance. The parameters of each vortex sheet and the distance between the sheets are determined by calibrating on a numerical simulation of a fish swimming in a channel. We demonstrate the feasibility of the proposed modeling scheme in the study of hydrodynamic interactions between multiple fish.