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Some exact statistics of two-dimensional viscous flow with random forcing

Published online by Cambridge University Press:  29 March 2006

Philip Duncan Thompson
Philip Duncan Thompson
Affiliation:
National Center for Atmospheric Research, Boulder, Colorado
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Abstract

By regarding the amplitudes of a set of orthogonal modes as the co-ordinates in an infinite-dimensional phase space, the probability distribution for an ensemble of randomly forced two-dimensional viscous flows is determined as the solution of the continuity equation for the phase flow. For a special, but infinite, class of types of random forcing, the exact equilibrium probability distribution can be found analytically from the Navier-Stokes equations. In these cases, the probability distribution is the product of exponential functions of the integral invariants of unforced inviscid flow.

Type
Research Article
Information
Journal of Fluid Mechanics , Volume 55 , Issue 4 , 24 October 1972 , pp. 711 - 717
Copyright
© 1972 Cambridge University Press

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