Equilibrium statistics of two‐dimensional viscous flows with arbitrary random forcing
作者:
Philip Duncan Thompson,
期刊:
Physics of Fluids(00319171)
(AIP Available online 1983)
卷期:
Volume 26,
issue 12
页码: 3461-3470
ISSN:0031-9171
年代: 1983
DOI:10.1063/1.864128
出版商: AIP
数据来源: AIP
摘要:
A method to solve the Liouville equation for an ensemble of two‐dimensional 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 energy‐transfer spectra can be calculated directly from the equilibrium probability distribution.
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