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Random measures and their application to motion in an incompressible fluid

Published online by Cambridge University Press:  14 July 2016

Sidney C. Port  and
Charles J. Stone
Sidney C. Port
Affiliation:
University of California, Los Angeles
Charles J. Stone
Affiliation:
University of California, Los Angeles
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Abstract

A generalization of a theorem of Geman and Horowitz concerning random measures is obtained. Their theorem in turn is used to extend a well-known result of Lumley, which asserts that for homogeneous turbulence in an incompressible fluid the probability distributions of the Eulerian and Lagrangian velocities coincide with each other at all times.

Keywords

RANDOM MEASURESHOMOGENEOUS TURBULENCEINCOMPRESSIBLE FLUID
Type
Research Papers
Information
Journal of Applied Probability , Volume 13 , Issue 3 , September 1976 , pp. 498 - 506
Copyright
Copyright © Applied Probability Trust 1976 

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References

Coddington, E. A. and Levinson, N. (1955) Theory of Ordinary Differential Equations. McGraw-Hill, New York.Google Scholar
Geman, D. and Horowitz, J. (1975) Random shifts which preserve measure. Proc. Amer. Math. Soc. To appear.Google Scholar
Lumley, J. L. (1957) Some Problems Connected with the Motion of Small Particles in Turbulent Fluid. Doctoral Dissertation, The Johns Hopkins University.Google Scholar
Lumley, J. L. (1962) The mathematical nature of the problem of relating Lagrangian and Eulerian statistical functions in turbulence. Mécanique de la turbulence (Coll. Intern. du CNRS à Marseille), Ed. CNRS, Paris.Google Scholar
Monin, A. S. and Yaglom, A. M. (1971) Statistical Fluid Mechanics: Mechanics of Turbulence, Volume 1. M.I.T. Press, Cambridge, Mass. Google Scholar