The Gibbs ensemble of a vortex filament. (English) Zbl 0992.60058

Flandoli, Franco; Gubinelli, Massimiliano

Probab. Theory Relat. Fields 122, No. 3, 317-340 (2002).

Summary: We introduce a statistical ensemble for a single vortex filament of a three-dimensional incompressible fluid. The core of the vortex is modeled by a quite generic stochastic process. We prove the existence of the partition function for both positive and a limited range of negative temperatures.

MSC:

60H05	Stochastic integrals
76F05	Isotropic turbulence; homogeneous turbulence
76M23	Vortex methods applied to problems in fluid mechanics
82B99	Equilibrium statistical mechanics
60H30	Applications of stochastic analysis (to PDEs, etc.)

Keywords:

single vortex filament; three-dimensional incompressible fluid