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Linear and nonlinear barotropic instability of geostrophic shear layers

Published online by Cambridge University Press:  26 April 2006

L. J. Pratt  and
J. Pedlosky
L. J. Pratt
Affiliation:
Department of Physical Oceanography, Woods Hole Oceanographic Institution, Woods Hole, MA 02543, USA
J. Pedlosky
Affiliation:
Department of Physical Oceanography, Woods Hole Oceanographic Institution, Woods Hole, MA 02543, USA
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Abstract

The linear, weakly nonlinear and strongly nonlinear evolution of unstable waves in a geostrophic shear layer is examined. In all cases, the growth of initially small-amplitude waves in the periodic domain causes the shear layer to break up into a series of eddies or pools. Pooling tends to be associated with waves having a significant varicose structure. Although the linear instability sets the scale for the pooling, the wave growth and evolution at moderate and large amplitudes is due entirely to nonlinear dynamics. Weakly nonlinear theory provides a catastrophic time ts at which the wave amplitude is predicted to become infinite. This time gives a reasonable estimate of the time observed for pools to detach in numerical experiments with marginally unstable and rapidly growing waves.

Type
Research Article
Information
Journal of Fluid Mechanics , Volume 224 , March 1991 , pp. 49 - 76
Copyright
© 1991 Cambridge University Press

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