Dispersion and collapse in stochastic velocity fields on a cylinder

Antonio Celani (1) , Sylvain Rubenthaler (2) , Dario Vincenzi (2)

1 Génétique in Silico
2 JAD - Laboratoire Jean Alexandre Dieudonné

The dynamics of fluid particles on cylindrical manifolds is investigated. The velocity field is obtained by generalizing the isotropic Kraichnan ensemble, and is therefore Gaussian and decorrelated in time. The degree of compressibility is such that when the radius of the cylinder tends to infinity the fluid particles separate in an explosive way. Nevertheless, when the radius is finite the transition probability of the two-particle separation converges to an invariant measure. This behavior is due to the large-scale compressibility generated by the compactification of one dimension of the space.

Mots clés: Turbulence; Lagrangian trajectories; Kraichnan ensemble; Cylindrical manifolds

Domaines: Dynamique Chaotique [nlin.CD]; Physique mathématique [math-ph]; Physique mathématique [math-ph]

Antonio Celani, Sylvain Rubenthaler, Dario Vincenzi. Dispersion and collapse in stochastic velocity fields on a cylinder. Journal of Statistical Physics, 2010, 138 (4-5), pp.579-597. ⟨10.1007/s10955-009-9875-1⟩. ⟨hal-00429864⟩