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The stability of a two-dimensional vorticity filament under uniform strain

Published online by Cambridge University Press:  26 April 2006

D. G. Dritschel ,
P. H. Haynes ,
M. N. Juckes  and
T. G. Shepherd
D. G. Dritschel
Affiliation:
Department of Applied Mathematics and Theoretical Physics, University of Cambridge, Silver Street, Cambridge CB3 9EW, UK
P. H. Haynes
Affiliation:
Department of Applied Mathematics and Theoretical Physics, University of Cambridge, Silver Street, Cambridge CB3 9EW, UK
M. N. Juckes
Affiliation:
Department of Applied Mathematics and Theoretical Physics, University of Cambridge, Silver Street, Cambridge CB3 9EW, UK Present affiliation: Department of Meteorology, University of Reading, RG6 2AU, UK.
T. G. Shepherd
Affiliation:
Department of Applied Mathematics and Theoretical Physics, University of Cambridge, Silver Street, Cambridge CB3 9EW, UK Present affiliation: Department of Physics, University of Toronto, Toronto M5S 1A7, Canada.
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Abstract

The quantitative effects of uniform strain and background rotation on the stability of a strip of constant vorticity (a simple shear layer) are examined. The thickness of the strip decreases in time under the strain, so it is necessary to formulate the linear stability analysis for a time-dependent basic flow. The results show that even a strain rate γ (scaled with the vorticity of the strip) as small as 0.25 suppresses the conventional Rayleigh shear instability mechanism, in the sense that the r.m.s. wave steepness cannot amplify by more than a certain factor, and must eventually decay. For γ < 0.25 the amplification factor increases as γ decreases; however, it is only 3 when γ ė 0.065. Numerical simulations confirm the predictions of linear theory at small steepness and predict a threshold value necessary for the formation of coherent vortices. The results help to explain the impression from numerous simulations of two-dimensional turbulence reported in the literature that filaments of vorticity infrequently roll up into vortices. The stabilization effect may be expected to extend to two- and three-dimensional quasi-geostrophic flows.

Information

Type
Research Article
Information
Journal of Fluid Mechanics , Volume 230 , September 1991 , pp. 647 - 665
Copyright
© 1991 Cambridge University Press

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