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Wave‐Mean Flow Interactions in Thermally Stratified Poiseuille Flow
Author(s) -
Denier James P.,
Stott Jillian A. K.
Publication year - 1999
Publication title -
studies in applied mathematics
Language(s) - English
Resource type - Journals
SCImago Journal Rank - 1.164
H-Index - 46
eISSN - 1467-9590
pISSN - 0022-2526
DOI - 10.1111/1467-9590.00106
Subject(s) - hagen–poiseuille equation , amplitude , mean flow , stratified flow , flow (mathematics) , reynolds number , mechanics , wavenumber , wavelength , monochromatic color , mathematics , physics , nonlinear system , potential flow , mathematical analysis , optics , quantum mechanics , turbulence
We consider nonlinear wave motions in thermally stratified Poiseuille flow. Attention is focused on short wavelength wave modes for which the neutral Reynolds number scales as the square of the wave number. The nonlinear evolution of a single monochromatic wave is governed by a first harmonic/mean‐flow interaction theory in which the wave‐induced mean flow is comparable in size to the wave component of the flow. An integrodifferential equation is derived which governs the normal variation of the wave amplitude. This equation admits finite‐amplitude solutions which bifurcate supercritically from the linear neutral point(s).