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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.

Information

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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