Formation of Vortex Streets

Abstract

It is shown that, for vortex trails in a nonviscous fluid, the mean longitudinal spacing a and mean transverse spacing h are invariant. It follows from this and other known facts, that the periodicity of a vortex trail is unstable, not the ratio h/a. In a viscous fluid, a is invariant but h increases. This fact explains various known experimental observations. A rough explanation is given for the order of magnitude of the Strouhal number S, based on the inertia opposed by the wake to transverse oscillations. Finally, using the theory of logarithmic potential, it is shown that, even in a nonviscous fluid, the concentration of vorticity is limited to circles whose diameter is about a/4.