Two-dimensional magneto-hydrodynamics at zero Prandtl number

Astronomy Unit Seminars
Prof David G. Dritschel (University of St Andrews)
January 25th, 2013 at 14:30
GO Jones UG1

In the interior of the sun, there exists a strongly stratified, rotating, magnetised zone called the tachocline where fluid motions are predominantly horizontal, or layerwise two-dimensional.  This zone is also characterised by weak magnetic dissipation, and exceptionally weak viscous dissipation, such that viscosity plays a negligible role in the dynamics.  This "zero Prandtl number" regime has been difficult to study computationally due to the need for exceedingly high numerical resolution.  Here, we discuss an alternative numerical method which enables one to study this regime efficiently, and accurately, and we apply it to study statistics of two-dimensional magneto-hydrodynamical turbulence.  It is shown that these statistics depend essentially on a single parameter, related to the peak magnetic to kinetic energy ratio in the fully-developed flow, a parameter that can be estimated a priori.  In physical space, the key competition is between vortical twisting an magnetic tension.  We isolate this competition in a case study of a single vortex patch, illustrating how this tension impedes twisting and induces non-conservative changes in fluid circulation.