A self-consistent analysis for two-dimensional hydrodynamics

Abstract

We study a stochastic model for 2-d incompressible fluids. We show that the kinetic equation governing the evolution of the velocity correlation function has a remarkable property which suggests that a regime of time and wave number exists over which self-consistent transport modes are exponentially decaying. The characteristic time of this regime is shorter than the characteristic time of classical hydrodynamics: it is defined by the limit k → 0, t → ∞ and k 2√In(1/ k) t finite.