Smith, FT; Brown, SN; (1996) On vortex/wave interactions. Part 1. Non-symmetrical input and cross-flow in boundary layers. Journal of Fluid Mechanics , 307 101 - 133. 10.1017/S0022112096000067.

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Abstract

The paper studies certain effects of non-symmetry on vortex/wave interactions, for inviscid inflexional waves interacting nonlinearly with the vortex component of the mean flow in boundary-layer transition at large Reynolds number. Two types of non-symmetry are investigated, namely for unequal input wave amplitudes and for small cross-flows. These lead to coupled integro-differential equations for spatial development of the wave amplitudes, which are examined in an essentially equivalent differential form for various degrees of the non-symmetry present. Each type of non-symmetry can have a significant influence on the nonlinear interaction properties. Special emphasis is given to bounded solutions, and numerous interesting new flow responses are found analytically and computationally. The theory provides a basis for tackling enhanced non-symmetry in the input or stronger cross-flows.

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