Published June 25, 1984
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Richardson Number Criterion for the Nonlinear Stability of Three-Dimensional Stratified Flow
Chicago
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Abstract
With use of a method of Arnol'd, we derive the necessary and sufficient conditions for the formal stability of a parallel shear flow in a three-dimensional stratified fluid. When the local Richardson number defined with respect to density variations is everywhere greater than unity, the equilibrium is formally stable under nonlinear pertrubations. The essential physical content of the nonlinear stability result is that the total energy acts as a "potential well" for deformations of the fluid across constant density surfaces; this well is required to have definite curvature to assure stability under these deformations.
Additional Information
©1984 The American Physical Society Received 15 March 1984 One of us (H.D.I.A.) would like to thank J. W. Miles and W. H. Munk for illuminating discussions on the physical content of this work. This work was supported in part by the U.S. Department of Energy under Contracts No. W-7405-ENG-36 and No. AT-3-82ER12097, and by the Office of Basic Energy Sciences, Division of Applied Mathematical Sciences, and by the Office of Naval Research, Code 422PO. One of us (T.R.) was a National Science Foundation postdoctoral fellow while at the University of California, Berkeley.Files
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