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A scenario for finite-time singularity in the quasigeostrophic model

Published online by Cambridge University Press:  14 October 2011

Richard K. Scott
Richard K. Scott*
Affiliation:
School of Mathematics and Statistics, University of St Andrews, St Andrews KY16 9SS, Scotland, UK
*
†Email address for correspondence: rks@mcs.st-and.ac.uk
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Abstract

A possible route to finite-time singularity in the quasigeostrophic system, via a cascade of filament instabilities of geometrically decreasing spatial and temporal scales, is investigated numerically using a high-resolution hybrid contour dynamical algorithm. A number of initial temperature distributions are considered, of varying degrees of continuity. In all cases, primary, secondary, and tertiary instabilities are apparent before the algorithm loses accuracy due to limitations of finite resolution. Filament instability is also shown to be potentially important in the closing saddle scenario investigated in many previous studies. The results do not provide a rigorous demonstration of finite-time singularity, but suggest avenues for further investigation.

JFM classification

Geophysical and Geological Flows: Geophysical and Geological Flows Instability: Instability
Type
Papers
Information
Journal of Fluid Mechanics , Volume 687 , 25 November 2011 , pp. 492 - 502
Copyright
Copyright © Cambridge University Press 2011

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