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

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