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On Markov modelling of turbulence

Published online by Cambridge University Press:  26 April 2006

Gianni Pedrizzetti  and
Evgeny A. Novikov
Gianni Pedrizzetti
Affiliation:
Dipartimento di Ingegneria Civile, Università di Firenze, via S. Marta 3, 50139 Firenze, Italy
Evgeny A. Novikov
Affiliation:
Institute for Nonlinear Science, University of California San Diego, CA 92093–0402, USAand Center for Turbulent Research, Stanford University, Stanford, CA 95305–3030, USA
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Abstract

We consider Lagrangian stochastic modelling of the relative motion of two fluid particles in the inertial range of a turbulent flow. Eulerian analysis of such modelling corresponds to an equation for the Eulerian probability distribution of velocity-vector increments which introduces a hierarchy of constraints for making the model consistent with results from the theory of locally isotropic turbulence. A nonlinear Markov process is presented, which is able to satisfy exactly, in the statistical sense, incompressibility, the exact results on the third-order structure function, and the experimental second-order statistics. The corresponding equation for the Eulerian probability density of velocity-vector increments is solved numerically. Numerical results show non-Gaussian statistics of the one-dimensional Lagrangian probability distributions, and a complex shape of the three-dimensional Eulerian probability density function. The latter is then compared with existing experimental data.

Type
Research Article
Information
Journal of Fluid Mechanics , Volume 280 , 10 December 1994 , pp. 69 - 93
Copyright
© 1994 Cambridge University Press

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