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

Speaker: David Dritschel, St Andrews

Date: Wednesday, May 13th

Time: 3.00pm

Location: Science Hub, Room H2.20

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.

Joint work with Wanming Qi and Brad Marston

 

Series: ACM