Characterizing velocity fluctuations in partially resolved turbulence simulations

Abstract

Many current turbulence model simulations follow the accuracy-on-demand paradigm to partially resolve the flow field for achieving optimal compromise between accuracy and computational effort. In many such approaches, the sub-grid viscosity is modeled using kinetic energy and dissipation of unresolved scales. It is of scientific value and practical utility to characterize the resolved velocity fluctuations of such flow fields to: (i) establish if the computed fields exhibit the self-similarity and scaling properties consistent with physical turbulence and (ii) demonstrate if the flow field tends to the limit of fully-resolved turbulence in a prescribed and controlled manner. Toward this end, we begin by characterizing partially-resolved flow computations as direct numerical simulations of non-Newtonian fluids. This paradigm permits the extension of the Kolmogorov and finite Reynolds number scaling to the computed fields. The statistical behavior of the intermediate and smallest computed scales is then postulated as a function of the degree of resolution. Then it is demonstrated that the flow field in partially-averaged Navier-Stokes simulations behaves in accordance with the adapted Kolmogorov hypotheses in isotropic turbulence computations. Further, the statistics of sub-Kolmogorov fluctuations are demonstrated to be self-similar over a range of resolutions.