Nonlinear geostrophic adjustment of long-wave disturbances in the shallow-water model on the equatorial beta-plane

Journal of Fluid Mechanics

Volumn 515, Issue , 2004, Pages 135-170

  Le Sommer, J ^a   Reznik, G M ^b   Zeitlin, V ^a  

^a ECOLE NORMALE SUPÉRIEURE   (France)

^b SHIRSHOV INSTITUTE OF OCEANOLOGY   (Russian Federation)

Author keywords

[No Author keywords available]

Indexed keywords

ASPECT RATIO; ASYMPTOTIC STABILITY; COMPUTER SIMULATION; FINITE VOLUME METHOD; GRAVITY WAVES; JETS; PERTURBATION TECHNIQUES; WATER;

AD HOC FILTERING; GEOSTROPHIC ADJUSTMENT; INERTIA-GRAVITY WAVES; KELVIN WAVES;

FLUID MECHANICS;

ATMOSPHERIC DYNAMICS; ATMOSPHERIC WAVE; FLUID MECHANICS; GRAVITY WAVE; KELVIN WAVE; ROSSBY NUMBER; SHALLOW-WATER EQUATION;

EID: 5444241923     PISSN: 00221120     EISSN: None     Source Type: Journal    
DOI: 10.1017/S0022112004000229     Document Type: Article

References (34)

1. AUDUSSE, E., BOUCHUT, F., BRISTEAU, M.-O., KLEIN, R. & PERTHAME, B. 2003 A fast and stable well-balanced scheme with hydrostatic projection for shallow-water flows. SIAM J. Sci. Comput. (to appear).
2. BERNDT, S. B. 1966 The vorticity jump across flow discontinuity. J. Fluid Mech. 26, 433-436.
3. BOUCHUT, F. 2002 An introduction to finite volume methods for hyperbolic systems of conservation laws with source. Lectures given at CEA-EDF-INRIA Summer School on Free-Surface Shallow Flows, available at http://www.dma.ens.fr/fbouchut/.
4. BOUCHUT, F. 2003 An entropy relaxation scheme for gas dynamics and Saint Venant system that computes vacuum. Preprint DMA-ENS, Paris.
5. BOUCHUT, F., LE SOMMER, J. & ZEITLIN, V. 2004 Frontal geostrophic adjustment and nonlinear-wave phenomena in one-dimensional rotating shallow water. Part 2. High-resolution numerical simulations. J. Fluid Mech. 514, 35-63.
6. BOYD, J. P. 1980a Equatorial solitary waves. Part 1. Rossby solitons. J. Phys. Oceanogr. 10, 1-11.
7. BOYD, J. P. 1980b The nonlinear equatorial Kelvin waves. J. Phys. Oceanogr. 10, 1699-1717.
8. BOYD, J. P. 1983 Equatorial solitary waves. Part 2. Envelope solitons. J. Phys. Oceanogr. 10, 1699-1717.
9. BOYD, J. P. 1984 Equatorial solitary waves. Part 4. Kelvin solitons in a shear flow. Dyn. Atmos. Oceans 8, 173-184.
10. BOYD, J. P. 1985 Equatorial solitary waves. Part 3. Westward traveling modons. J. Phys. Oceanogr. 15, 46-54.
11. BRETHERTON, C. S. & SOBEL, A. H. 2003 The Gill model and the weak temperature gradient approximation. J. Atmos. Sci. 60, 451-460.
12. BÜHLER, O. 2000 On the vorticity transport due to dissipating or breaking waves in shallow-water flow. J. Fluid Mech. 407, 235-263.
13. BÜHLER, O. & McINTYRE, M. E. 1998 On non-dissipative wave-mean interactions in the atmosphere or oceans. J. Fluid Mech. 354, 301-343.
14. DI PERNA, R. 1983 Convergence of the viscosity method for isentropic gas dynamics. Commun. Math. Phys. 91, 1-30.
15. FEDOROV, A. & MELVILLE, W. K. 2000 Kelvin fronts on the equatorial thermocline. J. Phys. Oceanogr 30, 1692-1705.
16. GILL, A. E. 1980 Some simple solutions for heat-induced tropical circulation. Q. J. R. Met. Soc. 106, 447-462.
17. GILL, A. E. 1982 Atmosphere-Ocean Dynamics. Academic.
18. HAYES, W. D. 1957 The vorticity jump across a gas-dynamic discontinuity. J. Fluid Mech. 2, 595-600.
19. KEVLAHAN, N. K.-R. 1997 The vorticity jump across a shock in a non-uniform flow. J. Fluid Mech. 341, 371-384.
20. LEVEQUE, R. J. 1992 Numerical Methods for Conservation Laws. Birkhäuser.
21. LEVEQUE, R. J. 2002 Finite Volume Methods for Hyperbolic Problems. Cambridge University Press.
22. LEVEQUE, R. J. & PELANTI, M. 2001 A class of approximate Riemann solvers and their relation to relaxation schemes. J. Comput. Phys. 172, 572-591.
23. LIGHTHILL, J. M. 1978 Waves in Fluids. Cambridge University Press.
24. MAJDA, A. 2003 Introduction to PDEs and Waves for the Atmosphere and Ocean, Chap. 9. American Mathematical Society.
25. MAJDA, A. & KLEIN, R. 2003 Systematic multiscale models for the tropics. J. Amos. Sci. 60, 393-408.
26. PHILANDER, S. G. 1990 El Nino, La Nina, and the Southern Oscillation. Academic.
27. PRATT, L. J. 1983 On inertial flow over topography. Part 1. Semi-geostrophic adjustment to an obstacle. J. Fluid Mech. 131, 195-218.
28. REZNIK, G. M., ZEITLIN, V. & BEN JELLOUL, M. 2001 Nonlinear theory of geostrophic adjustment. Part 1. Rotating shallow water. J. Fluid Mech. 445, 93-120.
29. RIPA, P. 1982 Nonlinear wave-wave interactions in a one-layer reduced-gravity model on the equatorial beta-plane. J. Phys. Oceanogr. 12, 97-111.
30. RIPA, P. 1983 Resonant triads of equatorial waves in a one-layer model. Part 1. Non-local triads and triads of waves with the same speed. J. Phys. Oceanogr. 13, 1208-1226.
31. SCHÄR, C. & SMITH, R. B. 1993 Shallow water flow past an isolated topography. Part 1. Vorticity production and wake formation. J. Atmos. Sci. 50, 1373-1400.
32. SOBEL, A. H., NILSSON, J. & POLVANI L. M. 2001 The weak temperature gradient approximation and balanced tropical moisture waves. J. Amos. Sci. 58, 3650-3665.
33. WHITHAM, G. B. 1974 Linear and Nonlinear Waves. Wiley Interscience.
34. ZEITLIN, V., REZNIK, G. M. & BEN JELLOUL, M. 2003 Nonlinear theory of geostrophic adjustment. Part 2. Two-layer and continuously stratified models. J. Fluid Mech. 491, 207-228.