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The Foppl model for the incompressible flow about the circle is considered. The major feature of this model is the understanding of the convective mechanism that gives rise to the onset of the instability in the flow past the circle. Through this model the real flow is approximated by means of a potential field with two singular points, counter-rotating vortices, placed symmetrically behind the circle. This field configuration is topologically analogous to the actual steady field for Reynolds numbers below the critical value corresponding to the onset of the first instability. The intrinsic instability of the Foppl field to small perturbations may be described by a second-order linear dynamical system. In this paper the instability behaviour of the Foppl field during transient motions is studied. It is shown that a reduction of the instability growth rate may be induced by a positive acceleration of the asymptotic stream or by a pulsating asymptotic stream. In this last case the effect is directly displayed by a reduction of the temporal growth rate of the perturbation with respect to that belonging to the steady state. In the first case the reductive effect is appreciated through a modified form of Shen's criterion. The relevance of these results to experimental observations of the real flow is discussed.

Nonsteady stability of the flow around the circle in the Föppl model