GALERKIN-TRUNCATED DYNAMICS OF IDEAL FLUIDS AND SUPERFLUIDS: CASCADES, THERMALIZATION AND DISSIPATIVE EFFECTS
My Ph. D. thesis was done at the Laboratoire de Physique Statistique de l’École Normale Supérieure de Paris between September 2006 and March 2010 and it was directed by Marc Brachet.
Abstract of the thesis:
Superfluid vortex reconnection at finite temperature. Truncated Gross-Pitaevskii equation. Finally, the radiation produced by moving point Gross-Pitaevskii vortices is studied analytically and numerically.
The first part of this work is concerned with the study of the effective viscosity of the truncated Euler equation, making use of the EDQNM closure theory and Monte-Carlo methods. We propose a two-fluid model of the system and this work is extended to the case of helical flows. The relaxation dynamics described by the two-dimensional truncated magnetohydrodynamics equations and three-dimensional compressible fluids is then characterized.
In a second part, a generalization of the previous study to the truncated Gross-Pitaevski equation is given. Finite-temperature effects that are present in superfluids, such as mutual friction and counterflow, are found to be naturally included in the truncated Gross-Pitaevski equation. This system thus appears as simple and rich model of superfluidity at finite temperature.
Sound radiation emitted by point superfluid vorticesIn this thesis several different Fourier Galerkin-truncated conservative systems are studied. It is shown that, in a very general way, these systems relax toward the thermodynamic equilibrium with a small-scale thermalization that induces an effective dissipation at large scales while conserving the global invariants.
Ph.D thesis file
Finite-temperature superfluid turbulence. Projected Gross-Pitaevskii equation.
