Statistical Descriptions of Inhomogeneous Anisotropic Turbulence

Author:

Brouwers J. J. H.ORCID

Abstract

Descriptions are given of the Langevin and diffusion equation of passively marked fluid particles in turbulent flow with spatially varying and anisotropic statistical properties. The descriptions consist of the first two terms of an expansion in powers of C0−1, where C0 is an autonomous Lagrangian-based Kolmogorov constant: C0≈7. Solutions involve the application of methods of stochastic analysis while complying with the basic laws of physics. The Lagrangian-based descriptions are converted into Eulerian-based fixed-point expressions through asymptotic matching. This leads to novel descriptions for the mean values of the fluctuating convective terms of the conservation laws of continua. They can be directly implemented in CFD codes for calculating fluid flows in engineering and environmental analysis. The solutions are verified in detail through comparison with direct numerical simulations of turbulent channel flows at large Reynolds numbers.

Publisher

MDPI AG

Subject

General Mathematics,Engineering (miscellaneous),Computer Science (miscellaneous)

Reference19 articles.

1. Monin, A.S., and Yaglom, A.M. (2007). Statistical Fluid Mechanics, Dover.

2. Bernard, P.S., and Wallace, J.K. (2002). Turbulent Flow: Analysis, Measurement and Prediction, Wiley.

3. Hanjalić, K., and Launder, B. (2011). Modelling Turbulence in Engineering and the Environment: Second-Moment Routes to Closure, Cambridge University Press.

4. Stratonovich, R.L. (1967). Topics in the Theory of Random Noise, Gordon and Breach.

5. van Kampen, N.G. (2007). Stochastic Processes in Physics and Chemistry, Elsevier. [3rd ed.].

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