NONSTEADY STABILITY OF THE FLOW AROUND THE CIRCLE IN THE FOPPL MODEL

The Foppl model for the incompressible now about the circle is conside red. The major feature of this model is the understanding of the conve ctive mechanism that gives rise to the onset of the instability in the now past the circle. Through this model the real flow is approximated by means of a potential held with two singular points, counter-rotati ng vortices, placed symmetrically behind the circle. This field config uration is topologically analogous to the actual steady field for Reyn olds numbers below the critical value corresponding to the onset of th e first instability. The intrinsic instability of the Foppl field to s mall perturbations may be described by a second-order Linear dynamical system. In this paper the instability behaviour of the Foppl held dur ing transient motions is studied. It is shown that a reduction of the instability growth rate may be induced by a positive acceleration of t he 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 th rough a modified form of Shen's criterion. The relevance of these resu lts to experimental observations of the real flow is discussed.