×

zbMATH — the first resource for mathematics

Generation of zonal flows by Rossby waves. (English) Zbl 1006.76019
Summary: It is shown that large scale zonal flows in a rotating fluid can be excited due to Reynolds stresses of short-scale Rossby waves. By employing the equations for a shallow rotating fluid in geostrophic approximation, we obtain a Charney equation for nonlinearly coupled Rossby waves and zonal flows. The equation is then decomposed into two equations: one for short-scale (comparable to Rossby radius) Rossby waves in the presence of zonal flows, and another for zonal flows which are driven by Reynolds stresses of Rossby waves. Our pair of equations is then Fourier transformed to obtain a nonlinear dispersion relation, which admits the excitation of zonal flows due to Rossby pumping energy. The present investigation thus provides a nonlinear mechanism for the energy transfer from short-scale Rossby waves to large-scale zonal flows.

MSC:
76B65 Rossby waves (MSC2010)
76U05 General theory of rotating fluids
86A05 Hydrology, hydrography, oceanography
PDF BibTeX XML Cite
Full Text: DOI
References:
[1] Hasegawa, A., Adv. phys., 1, 234, (1985)
[2] Nezlin, M.V., Sov. phys. usp., 29, 807, (1986)
[3] Pedlosky, J., Geophysical fluid dynamics, (1987), Springer New York · Zbl 0713.76005
[4] Snezhkin, E.N.; Nezlin, M.V., Rossby vortices, spiral structures, solitons: astrophysics and plasma physics in shallow water experiments, (1994), Springer-Verlag Berlin
[5] Busse, F.H., Chaos, 4, 123, (1994)
[6] Soomere, T., Phys. rev. lett., 75, 2440, (1995)
[7] Petviashvili, V.I.; Pokhotelov, O.A., Solitary waves in plasmas and in the atmosphere, (1992), Gordon and Breach Reading · Zbl 0793.76002
[8] Falkovich, G., Phys. rev. lett., 69, 3173, (1992)
[9] Marcus, P.S.; Kundu, T.; Lee, C., Phys. plasmas, 7, 1630, (2000)
[10] Vranješ, J.; Poedts, S., Phys. rev. lett., 89, 131102, (2002)
[11] Rossby, C.G., Q.J. meteorol. soc. suppl., 66, 68, (1940)
[12] Charney, J.G., Publ. kosjones. nors. videnshap. akad. Oslo, 17, 3, (1948)
[13] Larichev, V.D.; Reznik, G.M., Dokl. akad. nauk SSSR, 231, 1077, (1976)
[14] de Verdiere, A.C., J. fluid mech., 94, 39, (1979)
[15] McEwan, A.D.; Thompson, R.O.R.Y.; Plumb, R.A., J. fluid mech., 99, 655, (1980)
[16] Aubert, J.; Jung, S.; Swinney, H.L., Geophys. res. lett., 29, (2002)
[17] Stuart, J.T., J. fluid mech., 29, 417, (1967)
[18] Vranješ, J., Phys. rev. E, 58, 931, (1998)
[19] Mallier, R.; Maslowe, S.A., Phys. fluids A, 5, 1074, (1993) · Zbl 0778.76022
This reference list is based on information provided by the publisher or from digital mathematics libraries. Its items are heuristically matched to zbMATH identifiers and may contain data conversion errors. It attempts to reflect the references listed in the original paper as accurately as possible without claiming the completeness or perfect precision of the matching.