On Nonlinear Instability and Stability for Stratified Shear Flow |
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Authors: | S Friedlander |
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Institution: | University of Illinois—Chicago, Department of Mathematics, 85l S. Morgan Street, Chicago, Illinois 60607, USA, e-mail: susan@math.uic.edu, US
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Abstract: | An example of stratified shear flow is presented in which an explicit construction is given for unstable eigenvalues with smooth eigenfunctions for the Taylor--Goldstein equation. It is proved for any stratified, plane parallel shear flow that the unstable spectrum of the linear operator is purely discrete. A general theorem is then invoked to prove that the specific example is nonlinearly unstable. A sufficient condition for nonlinear stability for stratified shear flow is discussed. |
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