Small-Scale Structures in Turbulence: Their Implications for Turbulence Closures

Abstract

We compare high-resolution direct numerical simulations (DNS) to the predictions of moment closure for two- and three-dimensional turbulence. Our goal is to assess the impact of vortical structures on two-point covariances, through a comparison of DNS to simple closures, which make no explicit reference to structures at all. In two dimensions, we note that there is a profound effect, and this is associated with the development of isolated vortex structures. We interpret their presence in terms of a shutting down of the enstrophy transfer process, and give phenomenological estimates in terms of a modified closure. In three dimensions, the DNS spectra at R λ ~ 100 is in good agreement with the Direct Interaction Approximation (DIA). The agreement is poorer for Markovian theories, such as the Eddy Damped Quasinormal Markovian (EDQNM) approximation. We also comment on the possible development of finite time singularities in the vorticity for inviscid flows.KeywordsDirect Numerical SimulationVortex TubeInertial RangeInviscid FlowMoment ClosureThese 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.