New intermediate models for rotating shallow water and an investigation of the preference for anticyclones

Journal of Fluid Mechanics

Volumn 635, Issue , 2009, Pages 321-359

  Remmel, Mark ^a   Smith, Leslie ^a  

^a UNIVERSITY OF WISCONSIN MADISON   (United States)

Author keywords

[No Author keywords available]

Indexed keywords

ATMOSPHERIC PRESSURE; STORMS;

DECAYING TURBULENCE; INERTIAL GRAVITY WAVE; INTERMEDIATE MODEL; LINEARIZED EQUATIONS; NONLINEAR INTERACTIONS; QUANTITATIVE AGREEMENT; RANDOM INITIAL CONDITIONS; WAVE-WAVE INTERACTIONS;

NONLINEAR EQUATIONS;

ANTICYCLONE; EIGENVALUE; NUMERICAL MODEL; QUASI-GEOSTROPHIC FLOW; ROSSBY NUMBER; SHALLOW-WATER EQUATION; TURBULENCE; VORTICITY;

EID: 76249119663     PISSN: 00221120     EISSN: 14697645     Source Type: Journal    
DOI: 10.1017/S0022112009007897     Document Type: Article

References (48)

1. Allen, J. S. 1991 Balance equations based on momentum equations with global invariants of potential enstrophy and energy. J. Phys. Oceanogr. 21, 265-276.
2. Allen, J. S. 1993 Iterated geostrophic intermediate models. J. Phys. Oceanogr. 23 (1), 2447-2461.
3. Allen, J. S., Barth, J. A. & Newberger, P. A. 1990a On intermediate models for barotropic continental shelf and slope flow fields. Part i. Formulation and comparison of exact solutions. J. Phys. Oceanogr. 20, 1017-1042.
4. Allen, J. S., Barth, J. A. & Newberger, P. A. 1990b On intermediate models for barotropic continental shelf and slope flow fields. Part iii. Comparison of numerical model solutions in periodic channels. J. Phys. Oceanogr. 20 (2), 1949-1973.
5. Allen, J. S. & Newberger, P. A. 1993 On intermediate models for stratified flow. J. Phys. Oceanogr. 23 (2), 2462-2485.
6. Babin, A., Mahalov, A. & Nicolaenko, B. 2000 Fast singular oscillating limits and global regularity for the three-dimensional primitive equations of geophysics. Math. Model. Num. Anal. 34, 201-222.
7. Babin, A., Mahalov, A. & Nicolaenko, B. 2002 Singular oscillating limits of stably-stratified three-dimensional euler and Navier-Stokes equations and a geostrophic wave fronts. In Large-Scale Atmosphere-Ocean Dynamics I (ed. J. Norbury & I. Rhoulstone). Cambridge University Press.
8. Bartello, P. 1995 Geostrophic adjustment and inverse cascades in rotating stratified turbulence. J. Atmos. Sci. 52, 4410-4428.
9. Barth, J. A., Allen, J. S. & Newberger, P. A. 1990 On intermediate models for barotropic continental shelf and slope flow fields. Part ii. Comparison of numerical model solutions in doubly periodic domains. J. Phys. Oceanogr. 20, 1044-1076.
10. Charney, J. G. 1948 On the scale of atmospheric motions. Geofysiske Publikasjoner 17 (2), 1-17.
11. Embid, P. F. & Majda, A. J. 1996 Averaging over fast gravity waves for geophysical flows with arbitrary potential vorticity. Comm. Partial Diff. Eq. 21 (3-4), 619-658.
12. Embid, P. F. & Majda, A. J. 1998 Low Froude number limiting dynamics for stably stratified flow with small or finite Rossby numbers. Geophys. Astrophys. Fluid Dyn. 87 (1-2), 1-50.
13. Farge, M. & Sadourny, R. 1989 Wave-vortex dynamics in rotating shallow water. J. Fluid Mech. 206, 433-462.
14. Ford, R., McIntyre, M. E. & Norton, W. A. 2000 Balance and the slow quasimanifold: some explicit results. J. Atmos. Sci. 57, 1236-1254.
15. Hakim, G. J., Snyder, C. & Muraki, D. J. 2002 A new surface model for cyclone-anticyclone asymmetry. J. Atmos. Sci. 59, 2405-2420.
16. Julien, K., Knobloch, E., Milliff, R. & Werne, J. 2006 Generalized quasi-geostrophy for spatially anisotropic rotationally constrained flows. J. Fluid Mech. 555, 233-274.
17. Kraichnan, R. H. 1973 Helical turbulence and absolute equilibrium. J. Fluid Mech. 59, 745-752.
18. Kundu, P. K. & Cohen, I. M. 2004 Fluid Mechanics. Academic Press.
19. Kuo, A. C. & Polvani, L. M. 1999 Wave-vortex interaction in rotating shallow water. I. One space dimension. J. Fluid Mech. 394, 1-27.
20. Kuo, A. C. & Polvani, L. M. 2000 Nonlinear geostrophic adjustment, cyclone/anticyclone asymmetry, and potential vorticity rearrangement. Phys. Fluids 12 (5), 1087-1100.
21. Lorenz, E. N. 1960 Energy and numerical weather prediction. Tellus 4, 364-373.
22. Majda, A. & Embid, P. 1998 Averaging over fast gravity waves for geophysical flows with unbalanced initial data. Theor. Comput. Fluid Dyn. 11, 155-169. (Pubitemid 128367046)
23. Majda, A. 2003 Introduction to PDEs and Waves for the Atmosphere and Ocean. Courant Lecture Notes in Mathematics, vol.9. New York University, Courant Institute of Mathematical Sciences.
24. Maltrud, M. E. & Vallis, G. K. 1990 Energy spectra and coherent structures in forced two-dimensional and beta-plane turbulence. J. Fluid Mech. 228, 321-342.
25. Martin, Jonathan E. 2006 Mid-Latitude Atmospheric Dynamics: A First Course. Wiley.
26. McIntyre, M. E. & Norton, W. A. 2000 Potential vorticity inversion on a hemisphere. J. Atmos. Sci. 57 (9), 1214-1235.
27. McWilliams, J. C. 1984 The emergence of isolated coherent vortices in turbulent flow. J. Fluid Mech. 146, 21-43.
28. McWilliams, J. C. & Gent, P. R. 1980 Intermediate models of planetary circulations in the atmosphere and ocean. J. Atmos. Sci. 37 (8), 1657-1678.
29. Mohebalhojeh, A. R. & Dritschel, D. G. 2001 Hierarchies of balance conditions for the f-plane shallow water equations. J. Atmos. Sci. 58, 2411-2426.
30. Muraki, D. J. & Hakim, G. J. 2001 Balanced asymmetries of waves on the tropopause. J. Atmos. Sci. 58, 237-252.
31. Muraki, D., Snyder, C. & Rotunno, R. 1999 The next-order corrections to quasigeostrophic theory. J. Atmos. Sci. 56, 1547-1560.
32. Obukhov, A. M. 1949 On the problem of geostrophic wind. Izv. Geogr. Geophys. 13, 281-306 (in Russian).
33. Pedlosky, J. 1986 Geophysical Fluid Dynamics. Springer-Verlag.
34. Polvani, L., Mcwilliams, J., Spall, M. & Ford, R. 1994 The coherent structures of shallow-water turbulence: deformation radius effects, cyclone/anticyclone asymmetry and gravity-wave generation. Chaos 4, 177-186.
35. Reznik, G. M., Zeitlin, V. & Ben Jelloul, M. 2001 Nonlinear theory of geostrophic adjustment. Part 1. Rotating shallow-water model. J. Fluid Mech. 445, 93-120.
36. Rotunno, R., Muraki, D. & Snyder, C. 2000 Unstable baroclinic waves beyond quasigeostrophic theory. J. Atmos. Sci. 57, 3285-3295.
37. Sadourny, R. 1975 The dynamics of finite-difference models of the shallow-water equations. J. Atmos. Sci. 32, 680-689.
38. Salmon, R. 1998 Lectures on Geophysical Fluid Dynamics. Oxford University Press.
39. Smith, L. M. & Waleffe, F. 2002 Generation of slow, large scales in forced rotating, stratified turbulence. J. Fluid Mech. 451, 145-168.
40. Spall, M. A. & McWilliams, J. C. 1992 Rotational and gravitational influences on the degree of balance in the shallow-water equations. Geophys. Astrophys. Fluid Dyn. 64, 1-29.
41. Stegner, A. & Zeitlin, V. 1995 What can asymptotic expansions tell us about large-scale quasi-geostrophic anticyclonic vortices? Nonlinear Process. Geophys. 2 (3/4), 186-193.
42. Sukhatme, J. & Smith, L. 2008 Vortical and wave modes in three-dimensional rotating stratified flows: random large-scale forcing. Geophys. Astrophys. Fluid Dyn. 102 (19), 437-455.
43. Vallis, G. K. 1996 Potential vorticity inversion and balanced equations of motion for rotating and stratified flows. Q. J. Royal Meteorol. Soc. 122, 291-322.
44. Waite, M. L. & Bartello, P. 2006 The transition from geostrophic to stratified turbulence. J. Fluid Mech. 568, 89-108.
45. Warn, T. 1986 Statistical mechanical equilibria of the shallow water equations. Tellus Ser. Dynamic Meteorol. Oceanogr. 38, 1-11.
46. Warn, T., Bokhove, O., Shepherd, T. G. & Vallis, G. K. 1995 Rossby number expansions, slaving principles and balance dynamics. Q. J. Royal Meteorol. Soc. 121, 723-739.
47. Yavneh, I. & McWilliams, J. C. 1994 Breakdown of the slow manifold in the shallow-water equations. Geophys. Astrophys. Fluid Dyn. 75, 131-161.
48. Yuan, L. & Hamilton, K. 1994 Equilibrium dynamics in a forced-dissipative f-plane shallow-water system. J. Fluid Mech. 280, 369-394.