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

Abstract

We implement a simple hydrodynamical model to study behavioural swimming tilt angle of open swimmbladder fish. For this purpose we study the stability of forces acting on a fish swimming horizontally with constant velocity. Additionally, the open swimbladder compression with the depth is modelled by Boyle's law. With these, our model gives an analytical solution relating the depth with the body tilt angle and the velocity. An interesting result for steady horizontal swimming is that the body tilt decreases with velocity almost like $v^{-1}$. Moreover, we give an expression for the maximum tilt angle. Then, by introducing the assumption of constant swimming power we relate the swimming velocity with the tilting. Furthermore, we show that the hydrodynamical influence of a temperature gradient produced by a thermocline seems to be negligible for the fish tilting. These results are considerably helpful for more realistic modelling of the \emph{acoustic target strength} of fish. Finally, we tested our results by comparing the hydrodynamics solutions with others obtained from acoustic observations and simulations of target strength for Argentine anchovy.