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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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References

Batchelor, G. K. 1946 The theory of axisymmetric turbulence. Proc. Roy. Soc. A 186, 480.Google Scholar
Batchelor, G. K. 1969 Phys. Fluids, 12 (suppl. II), II–233.
Fjörtoft, R. 1953 On the changes in the spectral distribution of kinetic energy for two-dimensional non-divergent flow. Tellus, 5, 225.Google Scholar
Fox, D. & Orszag, S. A. 1972 Spectral simulation of two-dimensional homogeneous turbulence. To be published.
Kolmogoroff, A. N. 1941 The local structure of turbulence in incompressible viscous flow for very large Reynolds numbers. C. R. Acad. Sci. U.R.S.S. 30, 301.Google Scholar
Kraichnan, R. 1967 Inertial ranges in two-dimensional turbulence. Phys. Fluids, 10, 1417.Google Scholar
Leith, C. 1968 Diffusion approximation for two-dimensional turbulence. Phys. Fluids, 11, 671.Google Scholar
Lilly, D. K. 1969 Numerical simulation of two-dimensional turbulence. Phys. Fluids, 12, (suppl. II), II–240.Google Scholar