Hamilton's principle for quasigeostrophic motion

被引：24
作者：
Holm, DD [1 ]
Zeitlin, V
机构：
[1] Univ Calif Los Alamos Natl Lab, Div Theoret, Los Alamos, NM 87545 USA
[2] Univ Calif Los Alamos Natl Lab, Ctr Nonlinear Studies, Los Alamos, NM 87545 USA
[3] Univ Paris 06, Meteorol Dynam Lab, F-75252 Paris, France
[4] Univ Cambridge, Isaac Newton Inst Math Sci, Cambridge CB2 1TN, England
来源：
PHYSICS OF FLUIDS | 1998年 / 10卷 / 04期
关键词：
D O I：
10.1063/1.869623
中图分类号：
O3 [力学];
学科分类号：
08 ; 0801 ;
摘要：
We show that the equation of quasigeostrophic (QG) potential vorticity conservation in geophysical fluid dynamics follows from Hamilton's principle for stationary variations of an action for geodesic motion in the f-plane case or its prolongation in the beta-plane case. This implies a new momentum equation and an associated Kelvin circulation theorem for QG motion. We treat the barotropic and two-layer baroclinic cases, as well as the continuously stratified case. (C) 1998 American Institute of Physics.
引用
收藏
页码：800 / 806
页数：7
相关论文
共 31 条
[1]   Extended-geostrophic Hamiltonian models for rotating shallow water motion [J].
Allen, JS ;
Holm, DD .
PHYSICA D, 1996, 98 (2-4) :229-248
[2]  
ARNOLD VI, 1989, MATH METHODS CLASSIF
[3]  
Bennett A.F, 1992, CAMBRIDGE MONOGRAPHS
[4]  
DUBROVIN BA, 1992, MODERN GEOMETRY ME 1, pCH5
[5]  
Holm D. D., 1985, Physics Reports, V123, P1, DOI 10.1016/0370-1573(85)90028-6
[6]   Hamiltonian balance equations [J].
Holm, DD .
PHYSICA D-NONLINEAR PHENOMENA, 1996, 98 (2-4) :379-414
[7]   POISSON BRACKETS AND CLEBSCH REPRESENTATIONS FOR MAGNETOHYDRODYNAMICS, MULTIFLUID PLASMAS, AND ELASTICITY [J].
HOLM, DD ;
KUPERSHMIDT, BA .
PHYSICA D, 1983, 6 (03) :347-363
[8]   HAMILTONIAN-FORMULATION OF THE BAROCLINIC QUASIGEOSTROPHIC FLUID EQUATIONS [J].
HOLM, DD .
PHYSICS OF FLUIDS, 1986, 29 (01) :7-8
[9]   HAMILTONIAN DIFFERENCING OF FLUID-DYNAMICS [J].
HOLM, DD ;
KUPERSHMIDT, BA ;
LEVERMORE, CD .
ADVANCES IN APPLIED MATHEMATICS, 1985, 6 (01) :52-84
[10]  
HOLM DD, 1991, NONLINEAR TOPICS OCE, P133
1234