Multi-scale turbulence modeling and the maximum information principle

Abstract

We discuss averaged turbulence modeling of multi-scales of length for an incompressible Newtonian fluid, with the help of the maximum information principle. We suppose that there exists a function basis to decompose the turbulent fluctuations in a flow of our concern into the components associated with various spatial scales and that there is a probability density function f of these fluctuation components. The unbiased form for f is determined and the turbulence model is closed, with the multi-scale correlations up to the fourth order, through maximizing the information under the constraints for that flow. Due to the computational difficulty to maximize the information, a closely related but simple alternative objective is sought, like the determinant or the trace of the second order correlations of the turbulent flow. The issues still yet to be resolved are indicated.

Homogeneous shear turbulence as a second-order cone program

“…The structure of Eqs. (9) provides the ground to introduce the second-order model and the third-order model.…”

“…Our attention is restricted to a framework accounting for the multi-point spatial correlations of velocity and pressure fluctuations up to the degenerate fourth order. It is guided by the general structure of analytical theories, the consideration of mathematical and computational demands, and the availability of experimental and * luoyitao@iitm.ac.in observational data [9]. One part of the relations concerns the dynamical equations of evolution for the correlations and is derived in a conventional fashion.…”