Dipole- and vortex sheet-based models of fish swimming

Abstract

Elucidating the hydrodynamics of fish swimming is critical to identifying the processes underlying fish orientation and schooling. Due to their mathematical tractability, models based on potential flow are preferred in the study of bidirectional interactions of fish with their surroundings. Dipole-based models that assimilate fish to pairs of vortices are particularly enticing, but yet to be thoroughly validated. Here, we embark on a computational fluid dynamics (CFD) campaign informed by experimental data to validate the accuracy of dipole-based models. The locomotory patterns of a fish undergoing carangiform swimming are reconstructed from existing experimental data, which are used as inputs to CFD simulations of a fish swimming in a channel flow. We demonstrate that dipole-based models are accurate in capturing key features of the fluid flow, but cannot predict the elongated flow streamlines around the fish that are evident in CFD. To address this issue, we propose an alternative model that replaces each vortex in the pair with a sheet along the fish length. Using a pair of vortex sheets that span approximately 80% of the fish body length with a separation distance of approximately 50% of the body width, the model is successful in predicting the fluid flow around the swimming fish for a range of background flow speeds and channel widths. The proposed model shows improved accuracy at the cost of a mildly increased computational effort, thereby constituting an ideal basis for research on fish hydrodynamics.

Keywords: CFD; Dipole; Hydrodynamics; Locomotion; Potential flow.