Swimming of a deformable slab in a viscous incompressible fluid with inertia

Abstract

The swimming of a deformable planar slab in a viscous incompressible fluid is studied on the basis of the Navier-Stokes equations. A continuum of plane wave displacements, symmetric on both sides of the slab and characterized by a polarization angle, allows optimization of the swimming efficiency with respect to polarization. The mean swimming velocity and mean rate of dissipation are calculated to second order in the amplitude of the stroke. The optimum efficiency depends on the ratio of viscosity and mass density of the fluid. For high viscosity a stroke is found with significantly higher efficiency than Taylor's solution for a swimming sheet. For low viscosity the efficiency is optimal for a nearly irrotational flow pattern.