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Richardson Number Criterion for the Nonlinear Stability of Three-Dimensional Stratified Flow

Abarbanel, Henry D. I. and Holm, Darryl D. and Marsden, Jerrold E. and Ratiu, Tudor (1984) Richardson Number Criterion for the Nonlinear Stability of Three-Dimensional Stratified Flow. Physical Review Letters, 52 (26). pp. 2352-2355. ISSN 0031-9007. http://resolver.caltech.edu/CaltechAUTHORS:ABAprl84

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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.


Item Type:Article
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.
Record Number:CaltechAUTHORS:ABAprl84
Persistent URL:http://resolver.caltech.edu/CaltechAUTHORS:ABAprl84
Alternative URL:http://dx.doi.org/10.1103/PhysRevLett.52.2352
Usage Policy:No commercial reproduction, distribution, display or performance rights in this work are provided.
ID Code:3315
Collection:CaltechAUTHORS
Deposited By: Archive Administrator
Deposited On:30 May 2006
Last Modified:18 Sep 2014 18:11

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