Equilibrium statistics of twodimensional viscous flows with arbitrary random forcing
Abstract
A method to solve the Liouville equation for an ensemble of twodimensional viscous flows that are driven by random forcing with arbitrary statistics is outlined. By appropriate transformations of both the dependent variable (probability distribution) and independent variables, and by expansion of the solution in eigenfunctions of the separable part of the Liouville operator, it is found possible to reduce the problem to that of solving a simultaneous system of nonhomogeneous linear algebraic equations. The equilibrium kinetic energy and energytransfer spectra can be calculated directly from the equilibrium probability distribution.
 Publication:

Physics of Fluids
 Pub Date:
 December 1983
 DOI:
 10.1063/1.864128
 Bibcode:
 1983PhFl...26.3461T
 Keywords:

 Equilibrium Flow;
 Liouville Equations;
 Random Processes;
 Turbulent Flow;
 Two Dimensional Flow;
 Viscous Flow;
 Energy Spectra;
 Energy Transfer;
 Flow Theory;
 FokkerPlanck Equation;
 Kinetic Energy;
 Probability Distribution Functions;
 Statistical Mechanics;
 Fluid Mechanics and Heat Transfer