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Nonlinear Stability Analysis of Stratified Fluid Equilibria

Abarbanel, H. D. I. and Holm, D. D. and Marsden, J. E. and Ratiu, T. S. (1986) Nonlinear Stability Analysis of Stratified Fluid Equilibria. Philosophical Transactions A: Mathematical, Physical and Engineering Sciences, 318 (1543). pp. 349-409. ISSN 1364-503X. doi:10.1098/rsta.1986.0078.

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Nonlinear stability is analysed for stationary solutions of incompressible inviscid stratified fluid flow in two and three dimensions. Both the Euler equations and their Boussinesq approximations are treated. The techniques used were initiated by Arnold around 1965. These techniques combine energy methods, conserved quantities and convexity estimates. The resulting nonlinear stability criteria involve standard quantities, such as the Richardson number, but they differ from the linearized stability criteria. For example, the full three-dimensional problem has nonlinearly stable stationary solutions with Richardson number greater than unity, provided the gradients of the variations in density satisfy explicitly given bounds. Specific examples and the associated Hamiltonian structures for the problems are given.

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Ratiu, T. S.0000-0003-1972-5768
Additional Information:© 1985 Royal Society of London. Communicated by T. B. Benjamin, F.R.S. - Received 7 January 1985. Published 11 July 1986. H.D.I.A. was supported by U.S. Department of Energy and Office of Naval Research, Code 422 PD; D.D.H was supported by D.O.E. contract no. W-7405-Eng-36 and Office of Basic Energy Sciences, Department of Applied Mathematics; J. E. M. was partly supported by D.O.E. contract no. AT03-82ER12097; T.S.R. was supported by an N.S.F. postdoctoral fellowship and an A. P. Sloan Foundation Fellowship while at the University of California, Berkeley.
Funding AgencyGrant Number
Department of Energy and Office of Naval Research422 PD
Department of EnergyW-7405-Eng-36
Office of Basic Energy SciencesUNSPECIFIED
Department of EnergyAT03-82ER12097
A. P. Sloan Foundation FellowshipUNSPECIFIED
Issue or Number:1543
Record Number:CaltechAUTHORS:20100701-133449029
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Official Citation:Nonlinear Stability Analysis of Stratified Fluid Equilibria Author(s): H. D. I. Abarbanel, D. D. Holm, J. E. Marsden and T. S. Ratiu Source: Philosophical Transactions of the Royal Society of London. Series A, Mathematical and Physical Sciences, Vol. 318, No. 1543 (Jul. 11, 1986), pp. 349-409
Usage Policy:No commercial reproduction, distribution, display or performance rights in this work are provided.
ID Code:18899
Deposited By: Ruth Sustaita
Deposited On:07 Jul 2010 15:24
Last Modified:08 Nov 2021 23:47

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