Instabilities of buoyancy-driven coastal currents and their nonlinear evolution in the two-layer rotating shallow water model. Part 2. Active lower layer

Journal of Fluid Mechanics

Volumn 665, Issue , 2010, Pages 209-237

  Gula, J ^a   Zeitlin, V ^a   Bouchut, F ^b  

^a LABORATOIRE DE MÉTÉOROLOGIE DYNAMIQUE   (France)

^b UFR des Sciences et Technologie   (France)

Author keywords

gravity currents; shallow water flows; waves in rotating fluids

Indexed keywords

BUOYANCY; EQUATIONS OF MOTION; LINEAR STABILITY ANALYSIS; NONLINEAR EQUATIONS; VORTEX FLOW;

BAROCLINIC TWO-LAYER MODEL; FINITE VOLUME SCHEMES; GRAVITY CURRENTS; LARGE-SCALE INSTABILITY; NON-LINEAR STABILITIES; ROTATING SHALLOW WATER EQUATIONS; SHALLOW WATER FLOW; WAVES IN ROTATING FLUIDS;

SHEAR FLOW;

BAROCLINIC INSTABILITY; BUOYANCY; COASTAL CURRENT; FINITE VOLUME METHOD; KELVIN-HELMHOLTZ INSTABILITY; NUMERICAL MODEL; ROSSBY WAVE; ROTATING FLUID; SHALLOW-WATER EQUATION; TRAPPED WAVE; WATER FLOW;

EID: 79951675085     PISSN: 00221120     EISSN: 14697645     Source Type: Journal    
DOI: 10.1017/S0022112010003903     Document Type: Article

References (27)

1. Barth, J. A. 1989 Stability of a coastal upwelling front. Part 1. Model development and a stability theorem. J. Geophys. Res. 94, 10844-10856.
2. Boss, E., Paldor, N. & Thompson, L. 1996 Stability of a potential vorticity front: from quasi-geostrophy to shallow water. J. Fluid Mech. 315, 65-84. (Pubitemid 126467559)
3. Bouchut, F., Le Sommer, J. & Zeitlin, V. 2004 1D rotating shallow water: nonlinear semi-geostrophic adjustment, slow manifold and nonlinear wave phenomena. Part 2. High-resolution numerical simulations. J. Fluid Mech. 514, 35-63. (Pubitemid 39306261)
4. Bouchut, F. & Morales, T. 2008 An entropy satisfying scheme for two-layer shallow water equations with uncoupled treatment. M2AN 42, 683-698.
5. Bouchut, F. & Zeitlin, V. 2010 A robust well-balanced scheme for multi-layer shallow water equations. Discrete Continuous Dyn. Syst. B 13, 739-758.
6. Cairns, R. A. 1979 The role of negative energy waves in some instabilities of parallel flows. J. Fluid Mech. 92, 1-14. (Pubitemid 9460407)
7. Castro, M. J., LeFloch, P. G., Munos-Ruiz, M. L. & Parés, C. 2008 Why many theories of shock waves are necessary: convergence error in formally path-consistent schemes. J. Comput. Phys. 227, 8107-8129.
8. Griffiths, R. W. & Linden, P. F. 1982 Part I. Density-driven boundary currents. Geophys. Astrophys. Fluid Dyn. 19, 159-187.
9. Gula, J., Plougonven, R. & Zeitlin, V. 2009a Ageostrophic instabilities of fronts in a channel in the stratified rotating fluid. J. Fluid Mech. 627, 485-507.
10. Gula, J. & Zeitlin, V. 2010 Instabilities of buoyancy-driven coastal currents and their nonlinear evolution in the two-layer rotating shallow water model. Part 1. Passive lower layer. J. Fluid Mech. 659, 69-93.
11. Gula, J., Zeitlin, V. & Plougonven, R. 2009b Instabilities of two-layer shallow-water flows with vertical shear in the rotating annulus. J. Fluid Mech. 638, 27-47.
12. Hoskins, B. J., McIntyre, M. E. & Robertson, A. W. 1985 On the use and significance ofisentropic potential vorticity maps. Q. J. R. Meteorol. Soc. 111 (470), 877-946.
13. Iga, K. 1997 Instability of a front with a layer of uniform potential vorticity. J. Meteorol. Soc. Japan 75, 1-11.
14. Killworth, P. D., Paldor, N. & Stern, M. E. 1984 Wave propagation and growth on a surface front in a two-layer geostrophic current. J. Mar. Res. 42, 761-785. (Pubitemid 15455806)
15. Klemp, J. B., Rotunno, R. & Skamarock, W. C. 1997 On the propagation of internal bores. J. Fluid Mech. 331, 81-106.
16. Kubokawa, A. 1988 Instability and nonlinear evolution of a desity-driven coastal current with a surface front in a two-layer ocean. Geophys. Astrophys. Fluid Dyn. 40, 195-223.
17. Leblond, P. H. & Mysak, L. A. 1978 Waves in the Ocean. Elsevier.
18. LeSommer, J., Medvedev, S., Plougonven, R. & Zeitlin, V. 2003 Singularity formation during relaxation ofjets and fronts towards the state of geostrophic equilibrium. Commun. Nonlinear Sci. Numer. Simul. 8, 415-442. (Pubitemid 36915128)
19. Lyapidevsky, V. Y. & Teshukov, V. M. 2000 Mathematical models of long wave propagation in inhomogeneous fluid (in Russian). Siberian Branch of the Russian Academy of Science, Novosibirsk. ISBN: 5-7692-0340-4.
20. Paldor, N. & Ghil, M. 1991 Shortwave instabilities ofcoastal currents. Geophys. Astrophys. Fluid Dyn. 58, 225-241.
21. Paldor, N. & Killworth, P. D. 1987 Instabilities of a two-layer coupled front. Deep-Sea Res. 34, 1525-1539.
22. Poulin, F. J. & Flierl, G. R. 2003 The nonlinear evolution of barotropically unstable jets. J. Phys. Oceanogr. 33, 2173-2192. (Pubitemid 37477452)
23. Ripa, P. 1991 General stability conditions for a multi-layer model. J. Fluid Mech. 222, 119-137.
24. Sakai, S. 1989 Rossby-Kelvin instability: a new type of ageostrophic instability caused by a resonance between Rossby waves and gravity waves. J. Fluid Mech. 202, 149-176.
25. Scherer, E. & Zeitlin, V. 2008 Instability of coupled geostrophic density fronts and its nonlinear evolution. J. Fluid Mech. 613, 309-327.
26. Trefethen, L. N. 2000 Spectral Methods in Matlab. SIAM.
27. Whitham, G. B. 1974 Linear and Nonlinear Waves. Wiley.