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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. 207231. ISSN 00221120

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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 CharneyHasegawaMima (CH M) model both theoretically, using truncated (fourmode and threemode) 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 offzonal inclined modulations that are close to being in threewave 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 Karmanlike 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 twodimensional vortex streets appear to be more stable than purely onedimensional zonal jets, and their zonalaveraged speed can reach amplitudes much stronger than is allowed by the RayleighKuo instability criterion for the onedimensional case. In the long term, the system transitions to turbulence helped by the vortexpairing 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:  00221120  
Official Date:  2010  
Dates: 


Volume:  Vol.654  
Number of Pages:  25  
Page Range:  pp. 207231  
Identification Number:  10.1017/S0022112010000510  
Status:  Peer Reviewed  
Publication Status:  Published  
Access rights to Published version:  Open Access  
Related URLs:  
References:  Arnold, V. I. & Meshalkin, L. D. 1960 Seminar led by A. N. Kolmogorov on selected problems 

URI:  http://wrap.warwick.ac.uk/id/eprint/5549 
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