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Modulational instability of Rossby and drift waves and generation of zonal jets

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Connaughton, Colm, Nadiga, Balasubramanya T., Nazarenko, Sergey and Quinn, Brenda E.. (2010) Modulational instability of Rossby and drift waves and generation of zonal jets. Journal of Fluid Mechanics, Vol.654 . pp. 207-231. ISSN 0022-1120

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Official URL: http://dx.doi.org/10.1017/S0022112010000510

Abstract

We study the modulational instability of geophysical Rossby and plasma drill waves within the Charney-Hasegawa-Mima (CH M) model both theoretically, using truncated (four-mode and three-mode) models, and numerically, using direct simulations of CHM equation in the Fourier space. We review the linear theory of Gill (Geophys. Fluid Dyn., vol. 6, 1974, p. 29) and extend it to show that for strong primary waves the most unstable modes are perpendicular to the primary wave, which correspond to generation of a zonal flow if the primary wave is purely meridional. For weak waves, the maximum growth occurs for off-zonal inclined modulations that are close to being in three-wave resonance with the primary wave. Our numerical simulations confirm the theoretical predictions of the linear theory as well as the nonlinear jet pinching predicted by Manin & Nazarenko (Pit vs. Fluids, vol. 6, 1994, p. 1158). We find that, for strong primary waves, these narrow zonal jets further roll up into Karman-like vortex streets, and at this moment the truncated models fail. For weak primary waves, the growth of the unstable mode reverses and the system oscillates between a dominant jet and a dominate primary wave, so that the truncated description holds for longer. The two-dimensional vortex streets appear to be more stable than purely one-dimensional zonal jets, and their zonal-averaged speed can reach amplitudes much stronger than is allowed by the Rayleigh-Kuo instability criterion for the one-dimensional case. In the long term, the system transitions to turbulence helped by the vortex-pairing instability (for strong waves) and the resonant wave wave interactions (for weak waves).

Item Type:	Journal Article
Subjects:	Q Science > QC Physics
Divisions:	Faculty of Science > Centre for Complexity Science Faculty of Science > Mathematics
Library of Congress Subject Headings (LCSH):	Rossby waves, Drift waves
Journal or Publication Title:	Journal of Fluid Mechanics
Publisher:	Cambridge University Press
ISSN:	0022-1120
Date:	2010
Volume:	Vol.654
Number of Pages:	25
Page Range:	pp. 207-231
Identification Number:	10.1017/S0022112010000510
Status:	Peer Reviewed
Publication Status:	Published
Access rights to Published version:	Open Access
Related URLs:	Other Repository
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URI:	http://wrap.warwick.ac.uk/id/eprint/5549