RESONANTLY INTERACTING MODES IN WAKE-SHEAR LAYERS

The resonant interaction between the sinuous and varicose modes of a w ake is studied for a family of velocity profiles with symmetry-breakin g perturbations. The leading-order nonlinear interaction, which vanish es identically for symmetric wake profiles, increases dramatically as a small velocity ratio is imposed across the wake. Coefficients of the coupled amplitude equations describing the interaction in flows with asymmetric mean profiles are evaluated numerically for finite Reynolds numbers. The dynamical system defined by these equations is analyzed for temporally-forced, spatially-evolving modes for a velocity ratio w here the flow is convectively unstable. The leading-order model is sho wn to be inadequate to describe the dynamical interactions for at leas t a limited range of velocity ratios.