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Scale-invariant singularity of the surface quasigeostrophic patch

Published online by Cambridge University Press:  28 January 2019

R. K. Scott Open the ORCID record for R. K. Scott [Opens in a new window]  and
D. G. Dritschel Open the ORCID record for D. G. Dritschel [Opens in a new window]
R. K. Scott*
Affiliation:
School of Mathematics and Statistics, University of St Andrews, St Andrews KY16 9SS, Scotland
D. G. Dritschel
Affiliation:
School of Mathematics and Statistics, University of St Andrews, St Andrews KY16 9SS, Scotland
*
†Email address for correspondence: rks4@st-andrews.ac.uk
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Abstract

Numerical simulations of the surface quasigeostrophic patch indicate the development of a scale-invariant singularity of the boundary curvature in finite time, with some evidence of universality across a variety of initial conditions. At the time of singularity, boundary segments are shown to possess an exact and simple analytic form, described by branches of a logarithmic spiral centred on the point of singularity. The angles between the branches depend non-trivially on the shape of the smooth connecting boundary as the singularity is approached, but are independent of the global boundary.

JFM classification

Vortex Flows: Contour dynamics Geophysical and Geological Flows: Quasi-geostrophic flows
Type
JFM Rapids
Information
Journal of Fluid Mechanics , Volume 863 , 25 March 2019 , R2
Copyright
© 2019 Cambridge University Press 

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