A free basic EDQNM code for isotropic turbulence

Abstract

Isotropic turbulence is an ideal state where the motion properties, in the statistical sense, do not show any directional dependence. More strictly, they satisfy rotational and translational invariance. Isotropic turbulence is the simplest form of turbulent flow still maintaining all its fundamental characteristics. It has been the playground for theoretical work through the last century. Isotropy as a statistical notion is not manifest at the level of the velocity field dynamics but at the level of the correlation functions, where the averaging has removed all the irrelevant direction dependencies. Isotropic turbulence lives strictly in an infinite physical space. Via this energy cascade, turbulent flow can be realized as a superposition of a spectrum of flow velocity fluctuations and eddies upon a mean flow. The eddies are loosely defined as coherent patterns of flow velocity, vorticity and pressure. However, the isotropic flow, requiring first of all an infinite physical space to live in, is an idealization that cannot be strictly realized even in the clinical environment of numerical simulations. In the direct numerical simulations (DNS) of isotropic turbulence one usually solves the Navier-Stokes equation imposing periodicity. The idea is to introduce finiteness in space in a smooth manner. Isotropic flows are replaced by another kind of ideal flows that can be handled numerically. In the infinite space the infinite sequence of equations has to be closed at some finite order, this is being done semi-empirically. In other words, we must truncate this set of equations by a model, each reasonable model is called a closure model. The Eddy Damped Quasi-Normal Markovian (EDQNM) is a subfilter closure model applied in spectral wavenumber space rather than physical space which considers interactions between resolved and subfilter wavenumbers by considering the statistics of their possible interactions. The EDQNM achieves closure by modeling the 4th spectral moments. An EDQNM code for resolving forced isotropic turbulence was created in this work. The work may be considered as continuation of previous work done by Michalis Pieris (2016) who wrote an EDQNM code for equally distant wave-numbers, however permitting the possibility of resolving large Reynolds numbers. The new code was applied in the case of for forced turbulence at Reynolds number around 1000, resembling high Reynolds DNS from the past. The comparison shows significant similarities in the macroscopic characteristics of the stationary state, however, it reveals a different behavior at the dissipative range with sharper tails and lower palinstrophy values at the EDQNM spectra.