Linear stability theorems for shallow water semi-geostrophic dynamics

Geophysical and Astrophysical Fluid Dynamics

Volumn 90, Issue 3-4, 1999, Pages 189-227

  Shuzhan, Ren ^a  

^a ENVIRONMENT CANADA   (Canada)

Author keywords

Linear stability theorem; Pseudoenergy; Pseudomomentum; Shallow water semi geostrophic dynamics

Indexed keywords

FLUID FLOW; STABILITY;

FLUID FLOW; STABILITY ANALYSIS;

EID: 0342393094     PISSN: 03091929     EISSN: None     Source Type: Journal    
DOI: 10.1080/03091929908204119     Document Type: Article

References (24)

1. Allen, J. S., Barth, J. A. and Newberger, P. A. "On intermediate models for barotropic continental shelf and slope flow fields. Part I: formulation and comparison of exact solutions," J. Phys. Ocean 20(7), 1017-1042 (1990).
2. Arnold, V. I. "On an a priori estimate in the theory of hydrodynamical stability," Izv. Vyssh. Uchebn. Zaved. Matematika 54(5), 3-5 (1996).
3. Case, K. M. "Stability of inviscid plane Coutte flow," Phys. Fluid 3(14), 3-146 (1960).
4. Eliassen, A. "The Charney-Stern theorem on barotropic-baroclinic instability," Pure Appl. Geophys. 121, 563-572 (1983).
5. Held, S. M. "Pseudomomentum and orthogonality of modes in shear flows," J. Atoms. Sci. 42, 2280-2288 (1985).
6. Hoskins, B. J. "The geostrophic momentum approximation and semi-geostrophic equations," J. Atmos. Sci. 32, 233-242 (1975).
7. Hoskins, B. J. and Bretherton, F. P. "Atmospheric frontogenesis models: mathematical formulation and solution," J. Atmos. Sci. 29, 11 -37 (1972).
8. Hoskins, B. J., McIntyre, M. E. and Robertson, A. W. "On the use and significance of isentropic potential-vorticity maps," Q. J. R. Met. Soc. 111, 877-946 (1985).
9. Kuo, H. L. "Dynamics of quasi-geostrophic flows and instability theory," In: Advances in Applied Mechanics 13, 247-330 (1973).
10. Kushner, P. J. and Shepherd, T. G. "Wave-activity conservation laws and stability theorems for semi-geostrophic dynamics. Part 1. Pseudomomentum-based theory," J. Fluid Mech. 290, 67-104 (1995a).
11. Kushner, P. J. and Shepherd, T. G. "Wave-activity conservation laws and stability theorems for semi-geostrophic dynamics. Part 2. Pseudoenergy-based theory," J. Fluid Mech. 290, 105-129 (1995b).
12. Kushner, P. J., McIntyre, M. E. and Shepherd, T. G. "Coupled Kelvin-wave and mirage-wave instabilities in semi-geostrophic dynamics", J. Phys. Ocean 28, 513-518 (1997).
13. Liu, Yongming Mu, Mu and Shepherd, T. G. "Nonlinear stability of continuously stratified quasi-geostrophic flow," J. Fluid Mech. 325, 419-439 (1996).
14. Lu, P. S., Lu, L. and Zeng, Q. C. "Evolution of spectra and disturbances in barotropic quasi-geostrophic model," Chinese Science (B) 11, 1225-1233 (in Chinese) (1986).
15. Malardel, S., Thorpf, A. J. and Joly, A. "Consequences of the geostrophic momentum approximation on barotropic instability," J. Atmos. Sci. 54, 103-112 (1997).
16. Pedlosky, J., Geophysical Fluid Dynamics. Springer-Verlag, New York, p. 710 (1987).
17. Ren, S. Z. "Finite-amplitude wave-activity invariants and nonlinear stability theorems for shallow water semi-geostrophic dynamics," J. Atmos. Sci. (submitted) (1997).
18. Ren, S. Z. "Stability of three-dimensional semi-geostrophic equations in physical coordinates," J. Atmos. Sci. 55, 3392-3402 (1998).
19. Ren, S. Z. and Shepherd, T. G. "Lateral boundary contributions to wave-activity invariants and nonlinear stability theorems for balanced dynamics," J. Fluid. Mech. 345, 287-305 (1997).
20. Richtmyer, R. D. Principle of Advanced mathematical physics 1, Springer-Verlag. New York (1978).
21. Ripa, P. "General stability conditions for zonal flows in a one-layer model on the β-plane or the sphere," J. Fluid Mech. 126, 463-489 (1983).
22. Roulstone, I. and Norbury, J. "A Hamiltonian structure with contact geometry for the semi-geostrophic equations," J. Fluid Mech. 272, 211-233 (1994).
23. Salmon, R. "Practical use of Hamiltonian's principle," J. Fluid Mech. 132, 431-444 (1983).
24. Salmon, R. "New equations for nearly geostrophic flow," J. Fluid Mech. 153, 461-477 (1985).