Numerical investigation of small fish accelerating impulsively to terminal speed

Abstract

The present paper discusses acceleration in the swimming of a small three-dimensional fish with two motions, carangiform and anguilliform. Flow fields generated by fish deformations are investigated numerically by the constrained interpolation profile method in combination with an immersed boundary method. The three-dimensional vortical structure visualized using a second invariant and the pressure field around the fish body show that a fish with anguilliform motion accelerates more rapidly than one with carangiform motion because of a larger thrust due to the strong transverse vortex in the wake of the fish and a large pressure variation around the fish body. It is also found that the time variations of inline swimming speed of a small fish and the fluid force acting on it can be estimated using a free-fall model, and the fluid force can be expressed by a linear function of the fish speed. This function consists of a thrust part that is independent of fish speed and a viscous drag part that is proportional to fish speed. Thus, time histories of swimming speed, swimming distance, and fluid force can be predicted by simple functions from rest to terminal speed.