Instability of a shallow-water potential-vorticity front

Journal of Fluid Mechanics

Volumn 561, Issue , 2006, Pages 237-254

  Dritschel, David G ^a   Vanneste, Jacques ^b  

^a UNIVERSITY OF ST ANDREWS   (United Kingdom)

^b UNIVERSITY OF EDINBURGH   (United Kingdom)

Author keywords

[No Author keywords available]

Indexed keywords

FLOW OF WATER; JETS; ROTATIONAL FLOW; VORTEX FLOW;

FROUDE NUMBER; POTENTIAL VORTICITY; ROSSBY NUMBER; SHALLOW-WATER;

UNSTEADY FLOW;

FLOW OF WATER; JETS; ROTATIONAL FLOW; UNSTEADY FLOW; VORTEX FLOW;

FROUDE NUMBER; POTENTIAL VORTICITY; ROSSBY NUMBER; SHALLOW WATER; CORIOLIS FORCE; FLOW CONTROL; OCEANIC FRONT; SHALLOW-WATER EQUATION; VORTICITY;

FROUDE NUMBER; POTENTIAL VORTICITY; ROSSBY NUMBER; SHALLOW-WATER;

EID: 33747038649     PISSN: 00221120     EISSN: 14697645     Source Type: Journal    
DOI: 10.1017/S0022112006000644     Document Type: Article

References (22)

1. Bender, C. M. & Orszag, S. A. 1978 Advanced Mathematical Methods for Scientists and Engineers. McGraw-Hill.
2. Boss, E., Paldor, N. & Thompson, L. 1996 Stability of a potential vorticity front: From quasigeostrophy to shallow water. J. Fluid Mech. 315, 65-84.
3. Dunster, T. M. 1990 Bessel functions of purely imaginary order, with application to second-order linear differential equations having a large parameter. SIAM J. Math. Anal. 21, 995-1018.
4. Ford, R. 1993 Gravity wave generation by vortical flows in a rotating frame. PhD Thesis, University of Cambridge.
5. Ford, R. 1994 The instability of an axisymmetric vortex with monotonic potential vorticity in rotating shallow water. J. Fluid Mech. 280, 303-334.
6. Ford, R., McIntyre, M. E. & Norton, W. A. 2000 Balance and the slow quasimanifold: Some explicit results. J. Atmos. Sci. 57, 1236-1254.
7. Gill, A. E. 1982 Atmosphere-Ocean Dynamics. Academic.
8. Hinch E. J. 1991 Perturbation Methods. Cambridge University Press.
9. Knessl, C. & Keller, J. B. 1992 Stability of rotating shear flow in shallow water. J. Fluid Mech. 244, 605-614.
10. Lorenz, E. N. & Krishnamurthy, V. 1987 On the nonexistence of a slow manifold. J. Atmos. Sci. 44, 2940-2950.
11. McWilliams, J. C., Molemaker, J. M. & Yavneh, I. 2001 From stirring to mixing of momentum: Cascades from balanced flows to dissipation in the oceanic interior. In Aha Huliko'a Proceedings 2001, University of Hawaii, pp. 59-66.
12. McWilliams, J. C., Molemaker, J. M. & Yavneh, I. 2004 Ageostrophic, anticyclonic instability of a barotropic boundary current. Phys. Fluids 16, 3720-3725.
13. Mohebalhojeh, A. R. & Dritschel, D. G. 2001 Hierarchies of balance conditions for the f-plane shallow water equations. J. Atmos. Sci. 58, 2411-2426.
14. Nycander, J., Dritschel, D. G. & Sutyrin, G. G. 1991 The dynamics of long frontal waves in the shallow-water equations. Phys. Fluids A 5, 1089-1091.
15. Paldor, N. 1983 Linear stability and stable modes of geostrophic currents. Geophys. Astrophys. Fluid Dyn. 24, 299-326.
16. Plougonven, R., Muraki, D. J. & Snyder, C. 2005 A baroclinic instability that couples balanced motions and gravity waves. J. Atmos. Sci. 62, 1545-1559.
17. 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.
18. Vanneste, J. 2004 Inertia-gravity wave generation by balanced motion: revisiting the Lorenz-Krishnamurthy model. J. Atmos. Sci. 61, 224-234.
19. Vanneste, J. & Yavneh, I. 2004 Exponentially small inertia-gravity waves and the breakdown of quasigeostrophic balance. J. Atmos. Sci. 61, 211-223.
20. Viúdez, A. & Dritschel, D. G. 2004 Optimal potential vorticity balance of geophysical flows. J. Fluid Mech. 521, 343-352.
21. Warn, T. 1997 Nonlinear balance and quasi-geostrophic sets. Atmos. Ocean 35, 135-145.
22. Yavneh, I., McWilliams, J. C. & Molemaker, M. J. 2001 Non-axisymmetric instability of centrifugally stable, stratified Taylor-Couette flow. J. Fluid. Mech. 448, 1-21.