Hydrodynamic model of fish orientation in a channel flow

Abstract

For over a century, scientists have sought to understand how fish orient against an incoming flow, even without visual and flow cues. Here, we elucidate a potential hydrodynamic mechanism of rheotaxis through the study of the bidirectional coupling between fish and the surrounding fluid. By modeling a fish as a vortex dipole in an infinite channel with an imposed background flow, we establish a planar dynamical system for the cross-stream coordinate and orientation. The system dynamics captures the existence of a critical flow speed for fish to successfully orient while performing cross-stream, periodic sweeping movements. Model predictions are examined in the context of experimental observations in the literature on the rheotactic behavior of fish deprived of visual and lateral line cues. The crucial role of bidirectional hydrodynamic interactions unveiled by this model points at an overlooked limitation of existing experimental paradigms to study rheotaxis in the laboratory.

Stability of schooling patterns of a fish pair swimming against a flow

“…Each fish is modelled as a vortex dipole (Tchieu et al., 2012), a representation that has previously been used in several studies of fish schooling (Filella et al., 2018; Gazzola et al., 2016), and has been validated with experimental observations (Porfiri et al., 2021) as well as numerical simulations (Porfiri et al., 2022; Zhang, Peterson, & Porfiri, 2023). The mean flow field generated by the swimming fish is modelled using potential flow, wherein the potential field due to the self-propelling motion of each fish is given by where .…”

“…wind vane) mechanisms play in rheotaxis and how are these influenced by fish factors (e.g. body shape) and flow dynamics?’ In this vein, Porfiri, Zhang, and Peterson (2022) recently developed a hydrodynamic model for a fish swimming in a channel flow, providing the first analytical justification of rheotaxis by purely hydrodynamic mechanisms in the absence of any sensory feedback. Their model is the first to analyse rheotaxis as a bidirectional fluid–structure interaction problem, in which the fish modifies the surrounding flow field and the flow field, in turn, affects fish swimming.…”

“…This work seeks to understand the implications of the passive hydrodynamic pathway discovered in Porfiri et al. (2022) on fish schooling.…”

“…First, we develop a mathematical model of the positions and orientations of both the fish by considering all the passive hydrodynamic interactions in the system. The behaviour of each fish is modelled as a vortex dipole in a two-dimensional flow under the finite-dipole paradigm of Tchieu, Kanso, and Newton (2012), which has been extensively used in the past to study the hydrodynamics of swimming animals (Filella et al., 2018; Gazzola, Tchieu, Alexeev, de Brauer, & Koumoutsakos, 2016; Kanso & Tsang, 2014; Porfiri, Karakaya, Sattanapalle, & Peterson, 2021; Porfiri et al., 2022). Instead of considering a fish to be a passive body that does not affect the flow, we model their effect on the background flow in the presence of the channel walls (Porfiri et al., 2022).…”

“…The behaviour of each fish is modelled as a vortex dipole in a two-dimensional flow under the finite-dipole paradigm of Tchieu, Kanso, and Newton (2012), which has been extensively used in the past to study the hydrodynamics of swimming animals (Filella et al., 2018; Gazzola, Tchieu, Alexeev, de Brauer, & Koumoutsakos, 2016; Kanso & Tsang, 2014; Porfiri, Karakaya, Sattanapalle, & Peterson, 2021; Porfiri et al., 2022). Instead of considering a fish to be a passive body that does not affect the flow, we model their effect on the background flow in the presence of the channel walls (Porfiri et al., 2022). This results in a five-dimensional dynamical system for the fish pair in the channel flow, characterized by bidirectional couplings between the two fish and the fluid flow.…”