On the late-time behaviour of a bounded, inviscid two-dimensional flow
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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.
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 . DOI: 10.1017/jfm.2015.535
Journal of Fluid Mechanics
© 2015 Cambridge University Press This work is made available online in accordance with the publisher’s policies. This is the author created, accepted version manuscript following peer review and may differ slightly from the final published version. The final published version of this work is available at https://dx.doi.org/10.1017/jfm.2015.535
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).