ON VORTEX WAVE INTERACTIONS .1. NONSYMMETRICAL INPUT AND CROSS-FLOW IN BOUNDARY-LAYERS

The paper studies certain effects of non-symmetry on vortex/wave inter actions, for inviscid inflexional waves interacting nonlinearly with t he vortex component of the mean how in boundary-layer transition at la rge Reynolds number. Two types of nonsymmetry are investigated, namely for unequal input wave amplitudes and for small cross-flows. These le ad to coupled integro-differential equations for spatial development o f the wave amplitudes, which are examined in an essentially equivalent differential form for various degrees of the non-symmetry present. Ea ch type of nonsymmetry can have a significant influence on the nonline ar interaction properties. Special emphasis is given to bounded soluti ons, and numerous interesting new flow responses are found analyticall y and computationally. The theory provides a basis for tackling enhanc ed non-symmetry in the input or stronger cross-flows.