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Nonlinear evolution of Rayleigh waves in an initial value context: non‐symmetric input and cross‐flow
Author(s) -
Allen T.,
Brown S. N.,
Smith F. T.
Publication year - 1998
Publication title -
mathematika
Language(s) - English
Resource type - Journals
SCImago Journal Rank - 0.955
H-Index - 29
eISSN - 2041-7942
pISSN - 0025-5793
DOI - 10.1112/s0025579300014170
Subject(s) - mathematics , nonlinear system , flow (mathematics) , context (archaeology) , rayleigh scattering , mechanics , mathematical analysis , geometry , physics , optics , geology , paleontology , quantum mechanics
In recent papers the present authors considered the effects of small cross‐flow on the evolution of two unequal oblique waves. In these studies the relative size of the crossflow meant that a diffusion (or buffer) layer was required around the critical layer to smooth out the algebraic growth in the mean‐flow distortion generated by the nonlinear critical‐layer interactions. The present analysis increases the cross‐flow to an order of magnitude such that the buffer and critical layers coalesce. In this instance the nonlinear critical layer contains viscous as well as nonequilibrium effects. The resulting amplitude equations are solved for perturbations initiated at a fixed station in the flow.