  Swimming of a sphere in a viscous incompressible fluid is studied on the
basis of the Navier-Stokes equations for wave-type distortions of the spherical
shape. At sizable values of the dimensionless scale number the mean swimming
velocity is the result of a delicate balance between the net time-averaged flow
generated directly by the surface distortions and the flow generated by the
mean Reynolds force density. Depending on the stroke, this can lead to a
surprising dependence of the mean swimming velocity on the kinematic viscosity
of the fluid. The net flow pattern is calculated as a function of kinematic
viscosity for axisymmetric strokes of the swimming sphere. The calculation
covers the full range of scale number, from the friction-dominated Stokes
regime in the limit of vanishing scale number to the inertia-dominated regime
at large scale number. The model therefore provides paradigmatic insight into
the fluid dynamics of swimming or flying of a wide range of organisms.
