Some Hydrodynamical Aspects of Fish Schooling

Abstract

Hydrodynamical interactions between fish swimming close to each other in synchronization at equal velocities are examined. An inviscid flow model is employed to show that by proper positioning fish in a tightly packed school can utilize part of the energy shed by their neighbors. A two-dimensional model is suggested for each horizontal layer in the school, and the velocity field is calculated by means of the complex potential of the wakes of the various members of the school. Three different effects are examined quantitatively. The decrease in relative velocity for given absolute fish velocity due to induced wake flows. The changes in net thrust forces obtained for given propulsive motions, due to the proximity of other fish in the same horizontal layer. Effect of wakes of neighboring fish on the lift required for horizontal swimming of fish with negative buoyancy. The optimal configuration is found to be an array of two dimensional diamonds resulting in reductions of the swimming effort of up to a factor of 5.