Lateral boundary contributions to wave-activity invariants and nonlinear stability theorems for balanced dynamics

Journal of Fluid Mechanics

Volumn 345, Issue , 1997, Pages 287-305

  Ren, Shuzhan ^a   Shepherd, Theodore G ^a  

^a UNIVERSITY OF TORONTO   (Canada)

Author keywords

[No Author keywords available]

Indexed keywords

BOUNDARY LAYERS; MATHEMATICAL MODELS; THEOREM PROVING; WATER WAVES;

BALANCED DYNAMICS; LATERAL BOUNDARY CONTRIBUTIONS; NONLINEAR STABILITY THEOREMS; QUASI GEOSTROPHIC MODEL; WAVE ACTIVITY INVARIANTS;

FLUID DYNAMICS;

ATMOSPHERE; DYNAMICS; OCEAN; STABILITY; WAVE;

DYNAMICAL OCEANOGRAPHY; STABLITY; WAVE MOTION;

EID: 0031200732     PISSN: 00221120     EISSN: None     Source Type: Journal    
DOI: 10.1017/S0022112097006216     Document Type: Article

References (33)

1. ALLEN, J. S., BARTH, J. A. & NEWBERGER, P. A. 1990a On intermediate models for barotropic continental shelf and slope flow fields. Part I: Formulation and comparison of exact solutions. J. Phys. Oceanogr. 20, 1017-1042.
2. ALLEN, J. S., BARTH, J. A. & NEWBERGER, P. A. 1990b On intermediate models for barotropic continental shelf and slope flow fields. Part III: Comparison of numerical model solutions in periodic channels. J. Phys. Oceanogr. 20, 1949-1973.
3. ALLEN, J. S. & HOLM, D. D. 1996 Extended-geostrophic Hamiltonian models for rotating shallow water motion. Physica D 98, 229-248.
4. ARNOL'D, V. I. 1966 On an a priori estimate in the theory of hydrodynamical stability. Izv. Vyssh. Uchebn. Zaved. Matematika 54(5), 3-5. (English transl. Am. Math. Soc. Transl., Series 2 79, 267-269 (1969).)
5. ARNOL'D, V. I. 1966 On an a priori estimate in the theory of hydrodynamical stability. Izv. Vyssh. Uchebn. Zaved. Matematika 54(5), 3-5. (English transl. Am. Math. Soc. Transl., Series 2 79, 267-269 (1969).)
6. BARTH, J. A., ALLEN, J. S. & NEWBERGER, P. A. 1990 On intermediate models for barotropic continental shelf and slope flow fields. Part II: Comparison of numerical model solutions in doubly periodic domains. J. Phys. Oceanogr. 20, 1044-1076.
7. BOKHOVE, O. 1996 On balanced models in geophysical fluid dynamics. PhD thesis, Department of Physics, University of Toronto.
8. COURANT, R. & HILBERT, D. 1962 Methods of Mathematical Physics, Volume II. John Wiley & Sons.
9. FORD, R. 1993 Gravity wave generation by vortical flows in a rotating frame. PhD thesis, Department of Applied Mathematics and Theoretical Physics, Cambridge University.
10. HOLM, D. D., MARSDEN, J. E., RATIU, T. & WEINSTEIN, A. 1985 Nonlinear stability of fluid and plasma equilibria. Phys. Rep. 123, 1-116.
11. HOSKINS, B. J. 1975 The geostrophic momentum approximation and the semi-geostrophic equations. J. Atmos. Sci. 32, 233-242.
12. KLISHNER, P. J., MCINTYRE, M. E. & SHEPHERD, T. G. 1997 Coupled Kelvin-wave and mirage-wave instabilities in semi-geostrophic dynamics. J. Phys. Oceanogr. in press.
13. KUSHNER, P. J. & SHEPHERD, T. G. 1995a Wave-activity conservation laws and stability theorems for semi-geostrophic dynamics. Part 1. Pseudomomentum-based theory. J. Fluid Mech. 290, 67-104.
14. KUSHNER, P. J. & SHEPHERD, T. G. 1995b Wave-activity conservation laws and stability theorems for semi-geostrophic dynamics. Part 2. Pseudoenergy-based theory. J. Fluid Mech. 290, 105-129.
15. LORENZ, E. N. 1960 Energy and numerical weather prediction. Tellus 12, 364-373.
16. MAGNUSDOTTIR, G. & SCHUBERT, W. H. 1990 The generalization of semi-geostrophic theory to the β-plane. J. Atmos. Sci. 47, 1714-1720.
17. MAGNUSDOTTIR, G. & SCHUBERT, W. H. 1991 Semigeostrophic theory on the hemisphere. J. Atmos. Sci. 48, 1449-1456.
18. MCINTYRE, M. E. & ROULSTONE, I. 1997 Hamiltonian balanced models: constraints, slow manifolds and velocity splitting. J. Fluid Mech., submitted.
19. MCINTYRE, M. E. & SHEPHERD, T. G. 1987 An exact local conservation theorem for finite-amplitude disturbances to non-parallel shear flows, with remarks on Hamiltonian structure and on Arnol'd's stability theorems. J. Fluid Mech. 181, 527-565.
20. NORE, C. & SHEPHERD, T. G. 1997 A Hamiltonian weak-wave model for shallow-water flow. Proc. R. Soc. Lond. A 453, 563-580.
21. PEDLOSKY, J. 1987 Geophysical Fluid Dynamics, 2nd edn. Springer.
22. RIPA, P. 1983 General stability conditions for zonal flows in a one-layer model on the β-plane or the sphere. J. Fluid Mech. 126, 463-489.
23. RIPA, P. 1991 General stability conditions for a multi-layer model. J. Fluid Mech. 222, 119-137.
24. SADOURNY, R. 1975 The dynamics of finite-difference models of the shallow water equations. J. Atmos. Sci. 32, 680-689.
25. SALMON, R. 1983 Practical use of Hamilton's principle. J. Fluid Mech. 132, 431-444.
26. SALMON, R. 1985 New equations for nearly geostrophic flow. J. Fluid Mech. 153, 461-477.
27. SHEPHERD, T. G. 1989 Nonlinear saturation of baroclinic instability. Part II: Continuously stratified fluid. J. Atmos. Sci. 46, 888-907.
28. SHEPHERD, T. G. 1990 Symmetries, conservation laws, and Hamiltonian structure in geophysical fluid dynamics. Adv. Geophys. 32, 287-338.
29. SHEPHERD, T. G. 1992 Arnol'd stability applied to fluid flow: successes and failures. In Nonlinear Phenomena in Atmospheric and Oceanic Sciences (ed. G. F. Carnevale & R. T. Pierrehumbert), pp. 187-206. Springer.
30. SHEPHERD, T. G. 1993 A unified theory of available potential energy. Atmos.-Ocean 31, 1-26.
31. SHEPHERD, T. G. 1994 Applications of Hamiltonian theory to geophysical fluid dynamics. In Geometrical Methods in Fluid Dynamics (ed. R. Salmon & B. Ewing-Deremer). Woods Hole Oceanographic Institution Tech. Rep. WHOI-94-12, pp. 113-152.
32. SHUTTS, G. J. 1989 Planetary semi-geostrophic equations derived from Hamilton's principle. J. Fluid Mech. 208, 545-573.
33. WARN, T., BOKHOVE, O., SHEPHERD, T. G. & VALLIS, G. K. 1995 Rossby-number expansions, slaving principles, and balance dynamics. Q. J. R. Met. Soc. 121, 723-739.