Near-planar TS waves and longitudinal vortices in channel flow: Nonlinear Interaction and Focussing

P. Hall, F. T. Smith

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The nonlinear interaction between planar or near-planar Tollmien-Schlichting waves and longitudinal vortices, induced or input, is considered theoretically for channel flows at high Reynolds numbers. Several kinds of nonlinear interaction, dependent on the input amplitudes and wavenumbers or on previously occurring interactions, are found and inter-related. The first, Type 1, was studied the most here and it usually produced spanwise focusing of both the wave and the vortex motion, within a finite scaled time, along with enhancement of both their amplitudes. This pointed to the nonlinear interaction Type 2 where new interactive effects come into force to drive the wave and the vortex nonlinearly. Types 3, 4 corresponded to still higher amplitudes, with 3 being related to 2, while 4 was connected with a larger-scale interaction 5 studied in an allied paper. Both 3, 4 are subsets of the full three-dimensional triple-deck-lie interaction, 6. The strongest nonlinear interactions are those of 4, 5, 6 since they alter the mean-flow profile substantially, i.e., by an 0(1) relative amount. All the types of nonlinear interaction however can result in the formation of focussed responses in the sense of spanwise concentrations and/or amplifications of vorticity and wave amplitude. (A)

Original languageEnglish
Title of host publicationInstability and Transition
Place of PublicationNew York USA
ISBN (Electronic)978-1-4612-3432-6
ISBN (Print)978-0-387-97324-1
Publication statusPublished - 1 Jan 1990

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