EDQNM closure: A homogeneous simulation to support it. A quasi-homogeneous simulation to disprove it
It is known that two-point closures are useful tools for understanding and predicting turbulence. Among the various closures, the Eddy Damped Quasi-Normal Markovian (EDQNM) approach is one of the simplest and, at the same time, most useful. Direct numerical simulations (DNS) can provide information that can be used to test the validity of two-point theories. It is the purpose of the present work to use DNS to validate, or improve upon, EDQNM. A case was selected for which EDQNM is known to give satisfactory results: homogeneous isotropic turbulence. Quantities were then evaluated which may be used to test the assumptions of two-point closure approximations: spectral Lagrangian time scales. The goal was to make a careful and refined study to validate the EDQNM theory. A reference case was built for which EDQNM is likely to give poor results. An attempt to generate a quasi-homogeneous turbulent field containing organized structures, was built by artifically injecting them in the initial conditions. The results of direct simulations using such initial conditions are expected to provide a challenge for EDQNM since this kind of field is simple enough to allow comparisons with two-point theories, but at the same time contains coherent structures which cannot be expected to be accurately accounted for by closures based on expansions about Gaussianity.