A baroclinic instability that couples balanced motions and gravity waves

Journal of the Atmospheric Sciences

Volumn 62, Issue 5, 2005, Pages 1545-1559

  Plougonven, Riwal ^a,b   Muraki, David J ^c   Snyder, Chris ^a  

^a NATIONAL CENTER FOR ATMOSPHERIC RESEARCH   (United States)

^b UNIVERSITY OF ST ANDREWS   (United Kingdom)

^c SIMON FRASER UNIVERSITY   (Canada)

Author keywords

[No Author keywords available]

Indexed keywords

BOUNDARY CONDITIONS; COUPLINGS; FLOW OF FLUIDS; LINEAR EQUATIONS;

BAROCLINIC INSTABILITY; LINEARIZED PRIMITIVE EQUATIONS; ROSSBY NUMBER; ROTATING STRATIFIED FLUID;

GRAVITY WAVES;

BAROCLINIC INSTABILITY; GRAVITY WAVE;

EID: 20444443436     PISSN: 00224928     EISSN: None     Source Type: Journal    
DOI: 10.1175/JAS3426.1     Document Type: Article

References (45)

1. Abramowitz, M., and I. Stegun, Ed., 1964: Handbook of Mathematical Functions. National Bureau of Standards, Applied Mathematics Series, Vol. 55, U.S. Government Printing Office, 1046 pp.
2. Bender, C. M., and S. A. Orszag, 1978: Advanced Mathematical Methods for Scientists and Engineers. International Series in Pure and Applied Mathematics, McGraw Hill, 593 pp.
3. Blumen, W., 1972: Geostrophic adjustment. Rev. Geophys. Space Phys., 10, 485-528.
4. Booker, J., and F. Bretherton, 1967: The critical layer for internal gravity waves in a shear flow. J. Fluid Mech., 27, 513-539.
5. Braun, M., 1993: Differential Equations and their Applications. Springer Verlag, 578 pp.
6. Charney, J. G., 1947: The dynamics of long waves in a baroclinic westerly current. J. Meteor., 4, 135-162.
7. Dewar, W., and P. Killworth, 1995: Do fast gravity waves interact with geostrophic motions? Deep-Sea Res., 42, 1063-1081.
8. Eady, E., 1949: Long waves and cyclone waves. Tellus, 1, 33-52.
9. Ford, R., 1994a: The response of a rotating ellipse of uniform potential vorticity to gravity wave radiation. Phys. Fluids, 6, 3694-3704.
10. Ford, R., 1994b: The instability of an axisymmetric vortex with monotonic potential vorticity in rotating shallow water. J. Fluid Mech., 280, 303-334.
11. Ford, R., M. E. McIntyre, and W. A. Norton, 2000: Balance and the slow quasimanifold: Some explicit results. J. Atmos. Sci., 57, 1236-1254.
12. Gill, A. E., 1982: Atmosphere - Ocean Dynamics. Academic Press, 662 pp.
13. Hoskins, B. J., and F. P. Bretherton, 1972: Atmospheric frontogenesis models: Mathematical formulation and solution. J. Atmos. Sci., 29, 11-37.
14. Hoskins, B. J., M. McIntyre, and A. Robertson, 1985: On the use and significance of isentropic potential vorticity maps. Quart. J. Roy. Meteor. Soc., 111, 877-946.
15. Iga, K., 1993: Reconsideration of Orlanski's instability theory of frontal waves. J. Fluid Mech., 255, 213-236.
16. Inverarity, G., and G. Shutts, 2000: A general, linearized vertical structure equation for the vertical velocity: Properties, scalings and special cases. Quart. J. Roy. Meteor. Soc., 126, 2709-2724.
17. Jones, W., 1967: Propagation of internal gravity waves in fluids with shear flow and rotation. J. Fluid Mech., 30, 439-448.
18. Leith, C., 1980: Nonlinear normal mode initialization and quasigeostrophic theory. J. Atmos. Sci., 37, 958-968.
19. Lorenz, E., 1980: Attractor sets and quasigeostrophic equilibrium. J. Atmos. Sci., 37, 1685-1699.
20. Lozenz, E., and V. Krishnamurty, 1987: On the nonexistence of a slow manifold. J. Atmos. Sci., 44, 2940-2950.
21. McIntyre, M., 1965: A separable nongeostrophic baroclinic stability problem. J. Atmos. Sci., 22, 730-731.
22. McWilliams, J. C., and P. R. Gent, 1980: Intermediate models of planetary circulations in the atmosphere and ocean. J. Atmos. Sci., 37, 1657-1678.
23. Molemaker, M. J., J. C. McWilliams, and P. R. Gent, 2005: Baroclinic instability and loss of balance. J. Phys. Oceanogr., in press.
24. Nakamura, N., 1988: Scale selection of baroctmic instability - Effects of stratification and nongeostrophy. J. Atmos. Sci., 45, 3253-3267.
25. O'Sullivan, D., and T. Dunkerton, 1995: Generation of inertia - gravity waves in a simulated life cycle of baroclinic instability. J. Atmos. Sci., 52, 3695-3716.
26. Plougonven, R., and V. Zeitlin, 2002: Internal gravity wave emission from a pancake vortex: An example of wave - vortex interaction in strongly stratified flows. Phys. Fluids, 14, 1259-1268.
27. Reeder, M. J., and M. Griffiths, 1996: Stratospheric inertia - gravity waves generated in a numerical model of frontogenesis. Part II: Wave sources, generation mechanisms and momentum fluxes. Quart. J. Roy. Meteor. Soc., 122, 1175-1195.
28. 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.
29. Saujani, S., and T. Shepherd, 2002: Comments on "Balance and the slow manifold: Some explicit results." J. Atmos. Sci., 59, 2874-2877.
30. Shen, B.-W., and Y.-L. Lin, 1999: Effects of critical levels on two-dimensional back-sheared flow over an isolated mountain ridge on an f plane. J. Atmos. Sci., 56, 3286-3302.
31. Shutts, G., 2001: A linear model of back-sheared flow over an isolated hill in the presence of rotation. J. Atmos. Sci., 58, 3293-3311.
32. Shutts, G., 2003: Inertia - gravity wave and neutral Eady wave trains forced by directionally sheared flow over isolated hills. J. Atmos. Sci., 60, 593-606.
33. Snyder, C., 1995: Stability of steady fronts with uniform potential vorticity. J. Atmos. Sci., 52, 724-736.
34. Snyder, C., W. Skamarock, and R. Rotunno, 1993: Frontal dynamics near and following frontal collapse. J. Atmos. Sci., 50, 3194-3211.
35. Stone, P., 1966: On non-geostrophic baroclinic instability. J. Atmos. Sci., 23, 390-400.
36. Stone, P., 1970: On non-geostrophic baroclinic instability. Part II. J. Atmos. Sci., 27, 721-726.
37. Tokioka, T., 1970: Non-geostrophic and non-hydrostatic stability of a baroclinic fluid. J. Meteor. Soc. Japan, 48, 503-520.
38. Vanneste, J., and I. Yavneh, 2004: Exponentially small inertia - gravity waves and the breakdown of quasigeostrophic balance. J. Atmos. Sci., 61, 211-223.
39. Vautard, R., and B. Legras, 1986: Invariant manifolds, quasigeostrophy, and initialization. J. Atmos. Sci., 43, 565-584.
40. Wurtele, M., A. Datta, and R. Sharman, 2000: The propagation of a gravity - inertia wave in a positively sheared flow. J. Atmos. Sci., 57, 3703-3715.
41. Yamanaka, M., and H. Tanaka, 1984: Propagation and breakdown of internal inertia - gravity waves near critical levels in the middle atmosphere. J. Meteor. Soc. Japan, 62, 1-17.
42. Yamazaki, Y. H., and W. R. Peltier, 2001a: The existence of subsynoptic-scale baroclinic instability and the nonlinear evolution of shallow disturbances. J. Atmos. Sci., 58, 657-683.
43. Yamazaki, Y. H., and W. R. Peltier, 2001b: Baroclinic instability in an Euler equations-based column model: The coexistence of a deep synoptic-scale mode and shallow subsynoptic-scale modes. J. Atmos. Sci., 58, 780-792.
44. Zeitlin, V., 1991: On the backreaction of acoustic radiation for distributed two-dimensional vortex structures. Phys. Fluids, A3, 1677-1680.
45. Zhang, F., 2004: Generation of mesoscale gravity waves in upper-tropospheric jet-front systems. J. Atmos. Sci., 61, 440-457.