Local instability characteristics and frequency determination of self-excited wake flows

As suggested by the strong effect resonances and feedback mechanisms can exert upon vortices shed from blunt bodies, it is proposed that the discrete frequency, self-excited vortex shedding process itself is governed by a resonance-like mechanism. With the assumption that to a first approximation the shedding frequency is determined by the behaviour in the linear regime, the resonance hypothesis is found to lead to a bifurcation condition (direct resonance condition) of the local instability eigenvalue. In a corresponding initial value formulation the same condition separates a subcritical region of locally absolute instability from a supercritical region of locally convective instability. The critical basic wake profile corresponding to the bifurcation condition is found to be near the end of the potential core. The pertinent frequency is close to experimentally found values if, in the absence of numerically determined (physically unstable) solutions of the steady Navier-Stokes equations, the steady basic wake flow is modelled realistically. For asymmetrical steady wakes a limiting asymmetry seems to exist beyond which no time-harmonic resonance could be determined. This provides a link to mixing layers where apparently only convective instabilities are possible.