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On the late-time behaviour of a bounded, inviscid two-dimensional flow

Published online by Cambridge University Press:  13 October 2015

David G. Dritschel ,
Wanming Qi  and
J. B. Marston
David G. Dritschel*
Affiliation:
School of Mathematics and Statistics, University of St Andrews, St Andrews KY16 9SS, UK
Wanming Qi
Affiliation:
School of Physics, Korea Institute for Advanced Study, Seoul 130-722, Korea Kavli Institute for Theoretical Physics, University of California, Santa Barbara, CA 93106-4030, USA Department of Physics, Brown University, Providence, RI 02912-1843, USA
J. B. Marston
Affiliation:
Kavli Institute for Theoretical Physics, University of California, Santa Barbara, CA 93106-4030, USA Department of Physics, Brown University, Providence, RI 02912-1843, USA
*
†Email address for correspondence: david.dritschel@st-andrews.ac.uk
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Abstract

Using complementary numerical approaches at high resolution, we study the late-time behaviour of an inviscid incompressible two-dimensional flow on the surface of a sphere. Starting from a random initial vorticity field comprised of a small set of intermediate-wavenumber spherical harmonics, we find that, contrary to the predictions of equilibrium statistical mechanics, the flow does not evolve into a large-scale steady state. Instead, significant unsteadiness persists, characterised by a population of persistent small-scale vortices interacting with a large-scale oscillating quadrupolar vorticity field. Moreover, the vorticity develops a stepped, staircase distribution, consisting of nearly homogeneous regions separated by sharp gradients. The persistence of unsteadiness is explained by a simple point-vortex model characterising the interactions between the four main vortices which emerge.

JFM classification

Mixing: Turbulent mixing Vortex Flows: Vortex dynamics Vortex Flows: Vortex Flows

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Papers
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Journal of Fluid Mechanics , Volume 783 , 25 November 2015 , pp. 1 - 22
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© 2015 Cambridge University Press 

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