NONLINEAR CONVECTIVE ABSOLUTE INSTABILITIES IN PARALLEL 2-DIMENSIONALWAKES/

The linear versus nonlinear convective/absolute instability of a famil y of plane wake profiles at low Reynolds number is investigated by num erically comparing the linearized and the fully nonlinear impulse resp onses. Through an analysis of the linear flow response obtained by dir ect numerical simulation (DNS), the linear temporal and spatiotemporal instability properties are retrieved, in excellent agreement with the properties obtained by Monkewitz [Phys. Fluids 31, 3000 (1994)] from the study of the associated viscous dispersion relation. Nonlinear ter ms are then shown to limit the amplitude to a saturation level within the response wave packet, while leaving the trailing and leading edges unaffected. For this family of open shear flows, the velocities of th e fronts, formed between the trailing or leading edge and the central saturated region, are thus selected according to the linear Dee and La nger criterion [Phys. Rev. Lett. 50, 383 (1983)], whereas the front so lutions are fully nonlinear. This property may be of importance in jus tifying the use of linear instability properties to predict the onset and the frequency of the von Karman vortex street, as determined by Ha mmond and Redekopp [J. Fluid Mech. 331, 231 (1997)]. (C) 1998 American Institute of Physics. [S1070-6631(98)01710-3].