A hydrodynamic analytical model of fish tilt angle: Implications regarding acoustic target strength modelling

We implement a simple hydrodynamical model to study the behavioural swimming tilt angle of open swimbladder fish. For this purpose we analysed the force stability which act upon a fish swimming horizontally at a constant velocity. Furthermore, the open swimbladder compression at depth is modelled by Boyle's law. With these, our model gives us an analytical solution relating depth with body tilt angle and velocity. An interesting result that surges from steady horizontal swimming is that the body tilt decreases with velocity almost like v−1. Moreover, we provide an expression for the tilting as function of depth that asymptotically yields the maximum tilt angle. Additionally, by introducing the assumption of constant swimming power we can relate the swimming velocity to the tilting. We also show that the hydrodynamical influence of a temperature gradient produced by a thermocline does not seem to affect fish tilting significantly. Finally, we obtain reasonable results by comparing our hydrodynamics solutions with acoustic observations and simulations obtained from of Target Strength simulations of Argentine anchovy (Engraulis anchoita).