On the late-time behaviour of a bounded, inviscid two-dimensional flow
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.
Citation
Dritschel , D G , Qi , W & Marston , J B 2015 , ' On the late-time behaviour of a bounded, inviscid two-dimensional flow ' , Journal of Fluid Mechanics , vol. 783 , pp. 1-22 . https://doi.org/10.1017/jfm.2015.535
Publication
Journal of Fluid Mechanics
Status
Peer reviewed
ISSN
0022-1120Type
Journal article
Description
We thank the Kavli Institute for Theoretical Physics for supporting our participation in the 2014 Program “Wave-Flow Interaction in Geophysics, Climate, Astrophysics, and Plasmas” where this work was initiated. The KITP is supported in part by the NSF Grant No. NSF PHY11-25915. This work was also supported in part by the NSF under grant Nos. DMR-1306806 and CCF-1048701 (JBM and WQ).Collections
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