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Euler-Poincaré Models of Ideal Fluids with Nonlinear Dispersion

Holm, Darryl D. and Marsden, Jerrold E. and Ratiu, Tudor S. (1998) Euler-Poincaré Models of Ideal Fluids with Nonlinear Dispersion. Physical Review Letters, 80 (19). pp. 4173-4176. ISSN 0031-9007. doi:10.1103/PhysRevLett.80.4173.

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We propose a new class of models for the mean motion of ideal incompressible fluids in three dimensions, including stratification and rotation. In these models, the amplitude of the rapid fluctuations introduces a length scale, α, below which wave activity is filtered by both linear and nonlinear dispersion. This filtering enhances the stability and regularity of the new fluid models without compromising either their large scale behavior, or their conservation laws. These models also describe geodesic motion on the volume-preserving diffeomorphism group for a metric containing the H1 norm of the fluid velocity.

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Ratiu, Tudor S.0000-0003-1972-5768
Additional Information:©1998 The American Physical Society Received 6 January 1998 We thank R. Camassa, S.Y. Chen, P. Constantin, C. Doering, C. Foias, R. Kinney, J.C. McWilliams, V. L’vov, A. Mahalov, E. Titi, and V. Zeitlin for their time, encouragement, and valuable input. Work by D.H. was conducted under the auspices of the U.S. Department of Energy. Work of J.M. was supported by the California Institute of Technology and NSF Grant No. DMS 96–33161. Work by T. R. was partially supported by NSF Grant No. DMS-9503273 and DOE Contract No. DEFG03-95ER25245-A000.
Issue or Number:19
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Deposited On:30 Aug 2006
Last Modified:08 Nov 2021 20:18

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