**Marc Brachet**

CNRS, France

**April 23, 2010**

**Mesa Laboratory, Chapman Room**

**Lecture 3:30pm**

### Simulations of Finite-temperature Superfluids using the Truncated Gross-Pitaevskii Equation

We first give a short review of the thermalization that is known to take place in the truncated (finite range of spatial Fourier modes) Euler equation for incompressible fluids. The statistical equilibria of the (conservative) Gross-Pitaevskii Equation (GPE) dynamics will then be characterized using an algorithm based on a stochastically forced Ginzburg-Landau equation (SGLE) that directly generates grand canonical distributions. A standard finite-temperature second-order ?-transition will be exhibited. A new turbulent mechanism of GPE thermalization at small scales through a direct cascade of energy will be demonstrated. Dynamical counter-flow effects on vortex evolution will be investigated and a dilatation of vortex rings will be obtained for counter flows larger than their longitudinal velocity.