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Drift-free kinetic equations for turbulent dispersion

Lookup NU author(s): Dr David Swailes

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Abstract

The dispersion of passive scalars and inertial particles in a turbulent flow can be described in terms of probability density functions (PDFs) defining the statistical distribution of relevant scalar or particle variables. The construction of transport equations governing the evolution of such PDFs has been the subject of numerous studies, and various authors have presented formulations for this type of equation, usually referred to as a kinetic equation. In the literature it is often stated, and widely assumed, that these PDF kinetic equation formulations are equivalent. In this paper it is shown that this is not the case, and the significance of differences among the various forms is considered. In particular, consideration is given to which form of equation is most appropriate for modeling dispersion in inhomogeneous turbulence and most consistent with the underlying particle equation of motion. In this regard the PDF equations for inertial particles are considered in the limit of zero particle Stokes number and assessed against the fully mixed (zero-drift) condition for fluid points. A long-standing question regarding the validity of kinetic equations in the fluid-point limit is answered; it is demonstrated formally that one version of the kinetic equation (derived using the Furutsu-Novikov method) provides a model that satisfies this zero-drift condition exactly in both homogeneous and inhomogeneous systems. In contrast, other forms of the kinetic equation do not satisfy this limit or apply only in a limited regime.


Publication metadata

Author(s): Bragg A, Swailes DC, Skartlien R

Publication type: Article

Publication status: Published

Journal: Physical Review E

Year: 2012

Volume: 86

Issue: 5

Print publication date: 01/11/2012

ISSN (print): 1539-3755

ISSN (electronic): 1550-2376

Publisher: American Physical Society

URL: http://dx.doi.org/10.1103/PhysRevE.86.056306

DOI: 10.1103/PhysRevE.86.056306


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