Parameterization of Small Scales of Three-Dimensional Isotropic Turbulence Utilizing Spectral Closures

Abstract

A spectral equation derived from two-point closures applied to three-dimensional isotropic turbulence is studied from the subgrid-scale modeling point of view, with a cutoff wavenumber kc located in the inertial range of turbulence. Ideas of Kraichnan concerning eddy viscosities are then used to evaluate the parameterized subgrid-scale transfer. This, together with a suitable boundary condition at kc, allows us to predict statistically the large scales (k<kc) without further information about the small scales (k>kc). A k?5/3 energy spectrum extending to kc is recovered without any artificial dissipation range in the neighborhood of kc. This procedure is valid both for forced stationary turbulence and for freely decaying turbulence. The same eddy-viscosity is then introduced in a direct numerical simulation of three-dimensional homogeneous isotropic turbulence without external forcing. Again, the energy spectrum, evaluated by averaging on a spherical shell of radius k, follows the Kolmogorov law up to the cutoff wavenumber. Finally, predictability studies calculating the correlation between two fields with different resolutions are performed.