Frontal geostrophic adjustment and nonlinear wave phenomena in one-dimensional rotating shallow water. Part 2. High-resolution numerical simulations

Journal of Fluid Mechanics

Volumn 514, Issue , 2004, Pages 35-63

  Bouchut, F ^a   Le Sommer, J ^a   Zeitlin, V ^a  

^a ECOLE NORMALE SUPÉRIEURE   (France)

Author keywords

[No Author keywords available]

Indexed keywords

FINITE VOLUME METHOD; JETS; MATHEMATICAL MODELS; PERTURBATION TECHNIQUES; SHOCK TESTING;

NONLINEAR WAVE PHENOMENA; POTENTIAL VORTICITY (PV); SHALLOW WATER;

FLUID MECHANICS;

GEOSTROPHIC FLOW; MATHEMATICAL MODELING; POTENTIAL VORTICITY; SHALLOW-WATER EQUATION; WAVE BEHAVIOR;

FLUID MECHANICS; GEOSTROPHIC FLOW; NUMERICAL MODEL; POTENTIAL VORTICITY; SHALLOW-WATER EQUATION; WAVE PHENOMENA;

EID: 4644292071     PISSN: 00221120     EISSN: None     Source Type: Journal    
DOI: 10.1017/S0022112004009991     Document Type: Article

References (22)

1. Audusse, E., Bouchut, F., Bristeau, M.-O., Klein, R. & Perthame, B. 2004a A fast and stable well-balanced scheme with hydrostatic reconstruction for shallow water flows. SIAM J. Sci. Comput. (to appear).
2. Audusse, E., Bristeau, M.-O. & Perthame, B. 2004b Second order kinetic scheme for saint-venant equations with source terms on unstructured grids. Preprint INRIA.
3. Bouchut, F. 2004 Nonlinear stability of finite volume methods for hyperbolic systems of conservation laws, and well-balanced schemes for sources. Frontiers in Mathematics. Birkhauser (to appear).
4. Houghton, D. D. 1969 Effect of rotation on the formation of hydraulic jumps. J. Geophys. Res. 74, 1351-1360.
5. Kuo, A. C. & Polvani, L. M. 1997 Time-dependent fully nonlinear geostrophic adjustment. J. Phys. Oceanogr. 27, 1614-1634.
6. Kuo, A. C. & Polvani, L. M. 1999 Wave-vortex interaction in rotating shallow water. Part 1. One space dimension. J. Fluid Mech. 394, 1-27.
7. LeVeque, R. 1992 Numerical Methods for Conservation Laws. Birkhauser.
8. LeVeque, R. 1997 Wave-propagation algorithms for multidimensional hyperbolic systems. J. Comput. Phys. 131, 327-353.
9. LeVeque, R. 1998 Balancing source terms and flux gradients in high-resolution Godunov methods: the quasi-steady wave-propagation algorithm. J. Comput. Phys. 146, 346-365.
10. Lighthill, J. 1978 Waves in Fluids. Cambridge University Press.
11. Nof, D. 1984 Nonlinear internal waves in a rotating ocean. J. Phys. Oceanogr. 14, 1683-1702.
12. Ostrovsky, L. 1978 Nonlinear internal waves in a rotating ocean. Oceanology 18, 119-124.
13. Peregrine, D. 1998 Surf zone currents. Theoret. Comput. Fluid Dyn. 10, 295-309.
14. Pratt, L. 1983 On inertial flow over topography. Part 1. Semigeostropic adjustment to an obstacle. J. Fluid Mech. 131, 195-218.
15. Pratt, L. 1984 On inertial flow over topography. Part 2. Rotating channel flow near the critical speed. J. Fluid Mech. 145, 95-110.
16. Rossby, C. 1938 On the mutual adjustment of pressure and velocity distributions in certain simple current systems II. J. Mar. Res. 1, 239-263.
17. Rozhdestvenskii, B. & Yanenko, N. 1983 Systems of Quasi-Linear Equations and their Applications to Gas Dynamics. AMS.
18. Schar, C. & Smith, R. 1993 Shallow-water flow past an isolated topography. part 1: Vorticity production and wake formation. J. Atmos. Sci. 50, 1373-1400.
19. Shrira, V. 1981 Propagation of nonlinear waves in a layer of rotating fluid. Izv. Atmos. Ocean. Phys. 17, 55-59.
20. Shrira, V. 1986 On long strongly nonlinear waves in a rotating ocean. Izv. Atmos. Ocean. Phys. 22, 298-305.
21. Whitham, G. B. 1974 Linear and Nonlinear Waves. Wiley.
22. Zeitlin, V., Medvedev, S. & Plougonven, R. 2003 Frontal geostrophic adjustment, slow manifold and nonlinear wave phenomena in one-dimensional rotating shallow water. Part 1. Theory. J. Fluid Mech.