Due to the downscale cascade of vorticity in (quasi-) two-dimensional fluid flows, a numerical simulation inevitably becomes under-resolved.
Any finite discretization includes a closure model, either explicit or implied. Using a simple point vortex model as proof of concept, we propose a statistically consistent closure based on the idea of canonical statistical mechanics, which models the exchange between a system of particles and a large reservoir. We construct a thermostat device that simulates the exchange of vorticity with a large reservoir of point vortices, but using just a single additional degree of freedom.
With this approach we are able to reproduce numerical results of Bühler (2002), who studied the equilibrium statistics of a set of 4 strong vortices coupled with a set of 96 weak vortices. For an accurate comparison, the usual canonical ensemble must be modified to account for finite-reservoir effects. In my talk I will also discuss how this approach may be extended to grid-based models.