Kinetic theory representation for turbulence modeling and computation
Seminar Room 1, Newton Institute
One of the most common approximations in turbulence for the averaged effect of small scales is by the so called eddy viscosity modeling. That is, one approximates the Reynolds stress as a linear function of the local rate of strain of the averaged flow field. The proportionality constant is referred to as an eddy viscosity. This concept was first proposed over a century ago. It stems from an analogy for small eddy interactions with collisions of molecules resulting in Newtonian fluid constitutive relations. This approximation has made enormous impact particularly in computational fluid dynamics for turbulent flows. Many theoretical works were also developed since then, with various successes, in order to analytically derive such a functional relationship. However, unlike molecular interactions in a fluid, one of the apparent criticisms or difficulties in this analogy is the lack of scale separations between averaged fluid motions and fluctuating eddies. In this presentation, the speaker will give a somewhat provocative argument in favor of such analogy, provided that this concept be expanded in a generalized kinetic theory framework. In such an expanded framework, the analogy between eddy interactions and molecular collisions has a broader physical validity, while the eddy viscosity approximation is its consequence in the very long wave length limit. The kinetic theory representation itself needs not depend on scale separations. Using such an expanded analogy, one can also draw similarities between turbulent flow phenomena to that of non-Newtonian fluid flows in micro/nano scales. Nevertheless, other than phenomenological argument, as far as the speaker is aware, so far there have been little theoretical attempts to produce such a kinetic theory for turbulence on a concrete footing via first principle, if its physical soundness is acceptable.