Two-Point Closures and Statistical Equilibrium

Abstract

A two-point, or spectral, turbulence transport model describes the evolution of the two-point velocity covariance tensor, or its Fourier transform, the spectral tensor. Such a model describes the turbulent dynamics as functions of length-scale or wave-number. This permits a more general description of turbulence than is available with a one-point closure. This greater generality is useful in understanding the behavior of turbulent flows that are undergoing rapid transients and that are therefore not in “equilibrium”. If the turbulent flow is in an “equilbrium” environment wherein the mean forces on the flow are relatively constant in time, the turbulent spectra tend toward self-similar forms. When applied to a specific spectral model (Besnard et al., 1996) (Clark and Zemach, 1995), these selfsimilar forms may be exploited to reduce the model to the more familiar R ij — E and K — E models. These one-point models have coefficients that are functions of the spectral distributions. We discuss the limits of validity of the two-point descriptions as well as the consequences of the equilibrium assumptions embedded in the one-point variants.KeywordsTurbulent Kinetic EnergyIsotropic TurbulenceScale Dissipation RateAnisotropy TensorAnisotropic TurbulenceThese keywords were added by machine and not by the authors. This process is experimental and the keywords may be updated as the learning algorithm improves.