The slow manifold for the shallow water equations on the f plane

Journal of the Atmospheric Sciences

Volumn 56, Issue 8, 1999, Pages 1050-1054

  Medvedev, Serguei B ^a,b  

^a INSTITUTE OF COMPUTATIONAL TECHNOLOGIES   (Russian Federation)

^b UNIVERSITY OF TORONTO   (Canada)

Author keywords

[No Author keywords available]

Indexed keywords

DIFFERENTIAL EQUATIONS; FLUID DYNAMICS; GRAVITY WAVES; NONLINEAR EQUATIONS; PROBLEM SOLVING; VORTEX FLOW; WATER;

DYNAMIC INITIALIZATION; EXPANSION IN POWERS OF NONLINEARITY; INERTIAL GRAVITY WAVES; SHALLOW WATER EQUATIONS;

EQUATIONS OF MOTION;

ATMOSPHERIC DYNAMICS; GEOPOTENTIAL; GRAVITY WAVE; SHALLOW-WATER EQUATION;

EID: 0033560453     PISSN: 00224928     EISSN: None     Source Type: Journal    
DOI: 10.1175/1520-0469(1999)056<1050:TSMFTS>2.0.CO;2     Document Type: Article

References (12)

1. Arnold, V. I., and Y. S. Il'yashenko, 1988: Ordinary differential equations. Dynamical Systems I, D. V. Arnold and V. I. Arnold, Eds., Encyclopedia of Mathematical Sciences, Vol. 1, 1-146.
2. Baer, F., and J. J. Tribbia, 1977: On complete filtering of gravity modes through nonlinear initialization. Mon. Wea. Rev., 105, 1536-1539.
3. Carr, J., 1981: Applications of Centre Manifold Theory. Applied Mathematical Sciences. Vol. 35, Springer-Verlag, 142 pp.
4. Falkovich, G. E., and S. B. Medvedev, 1992: Kolmogorov-like spectrum for turbulence of inertial-gravity waves. Europhys. Lett., 19, 279-284.
5. Kreiss, H.-O., and J. Lorenz, 1994: On the existence of slow manifolds for problem with different time scale. Philos. Trans. Roy. Soc. London, 346A, 159-171.
6. Leith, C. E., 1980: Nonlinear normal mode initialization and quasigeostrophic theory. J. Atmos. Sci., 37, 958-968.
7. Lorenz, E. N., 1992: The slow manifold - What is it? J. Atmos. Sci., 49, 2449-2451.
8. Machenhauer. B., 1977: On the dynamics of gravity oscillations in a shallow water model, with applications to normal mode initialization. Contrib. Atmos. Phys., 50, 253-271.
9. Temperton, C., 1988: Implicit normal mode initialization. Mon. Wea. Rev., 116, 1013-1031.
10. Tribbia, J. J., 1984: A simple scheme for high-order nonlinear normal mode initialization. Mon. Wea. Rev., 112, 278-284.
11. Vautard, R., and B. Legras, 1986: Invariant manifolds, quasi-geostrophy and initialization. J. Atmos. Sci., 43, 565-584.
12. Warn, T., O. Bokhove, T. G. Shepherd, and G. K. Vallis, 1995: Rossby number expansion, slaving principles, and balance dynamics. Quart. J. Roy. Meteor. Soc., 121, 723-739.