A Statistical Mechanical Model for Two Dimensional Turbulence

Abstract

A statistical mechanical model for two dimensional homogeneous isotropic turbulence is proposed. This model is based on a hypothesis that the extremely high Reynolds number two dimensional turbulence is, at each instant, in a state of equal probability on the intersections of energy and palinstrophy planes in the phase space. An energy spectrum is obtained which shows the k⁻³ dependence for large wave numbers and represents the energy equipartition state for small wave numbers.