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Global stability in the Bénard problem for a mixture with superimposed plane parallel shear flows
Author(s) -
Lombardo S.,
Mulone G.,
Rionero S.
Publication year - 2000
Publication title -
mathematical methods in the applied sciences
Language(s) - English
Resource type - Journals
SCImago Journal Rank - 0.719
H-Index - 65
eISSN - 1099-1476
pISSN - 0170-4214
DOI - 10.1002/1099-1476(20001110)23:16<1447::aid-mma173>3.0.co;2-l
Subject(s) - mathematics , prandtl number , stability (learning theory) , reynolds number , shear flow , linear stability , plane (geometry) , mathematical analysis , convection , mechanics , turbulence , geometry , instability , physics , machine learning , computer science
The Lyapunov direct method is used to study the non‐linear stability of parallel convective shear flows of a mixture heated and salted from below for any Schmidt and Prandtl numbers. Global non‐linear exponential stability for small values of Reynolds number R is found and conditional stability results up to the criticality which are independent of R are given for rigid and stress‐free boundaries. Copyright © 2000 John Wiley & Sons, Ltd.