The large-eddy simulation (LES) equations are obtained from the application of two operators to the Navier-Stokes equations: a smooth filter and a discretization operator. The introduction ab initio of the discretization influences the structure of the unknown stress in the LES equations, which now contain a subgrid-scale stress tensor mainly due to discretization, and a filtered-scale stress tensor mainly due to filtering. Theoretical arguments are proposed supporting eddy viscosity models for the subgrid-scale stress tensor. However, no exact result can be derived for this term because the discretization is responsible for a loss of information and because its exact nature is usually unknown. The situation is different for the filtered-scale stress tensor for which an exact expansion in terms of the large-scale velocity and its derivatives is derived for a wide class of filters including the Gaussian, the tophat and all discrete filters. As a consequence of this generalized result, the filtered-scale stress tensor is shown to be invariant under the change of sign of the large-scale velocity. This implies that the filtered-scale stress tensor should lead to reversible dynamics in the limit of zero molecular viscosity when the discretization effects are neglected. Numerical results that illustrate this effect are presented together with a discussion on other approaches leading to reversible dynamics like the scale similarity based models and, surprisingly, the dynamic procedure.

A spectral analysis of the energy cascade in magnetohydrodynamics (MHD) is presented using high-resolution direct numerical simulation of decaying isotropic turbulence. The Fourier representations of both the velocity and the magnetic fields are split into subsets that correspond to shells of wave vectors. A detailed study of the shell-to-shell interactions is performed and a comparison with theoretical prediction based on field-theoretic method is proposed. Two different definitions for the forward and backward energy transfers are suggested. They provide diagnostics that can be used in order to assess subgrid-scale modeling in large eddy simulation for turbulent MHD systems.

The performance of different dynamic gradient-diffusion type subgrid models is evaluated in large-eddy simulations (LES) of magnetohydrodynamic (MHD) turbulence with a maximum of 643 collocation points. The reference data stems from high-resolution direct numerical simulations of decaying and forced MHD turbulence with up to 5123 spectral modes. Comparisons between LES’ and the grid filtered reference systems are carried out regarding the temporal evolution of the global quantities kinetic and magnetic energy, cross helicity, magnetic helicity, and the spectra of energy and energy flux. The influence of the subgrid models on the statistical properties of the simulated flows is also examined. Apart from unconditionally dissipative models, direct divergence modeling and the effects of additional explicit filtering in combination with a tensor-diffusivity term are considered. A new genuine MHD subgrid model, based on the cross-helicity invariant, is presented and observed to perform outstandingly well.

The dynamic localization model is a recently developed method that allows one to compute rather than prescribe the unknown coefficients in a subgrid scale model as a function of position at each time-step. A realistic subgrid scale model should describe both the direct and reverse (backscatter) energy transfers at the local level. A previously developed dynamic localization model accounted for backscatter by means of a (deterministic) eddy viscosity that could locally assume positive as well as negative values. Here this paper presents an alternative stochastic model of backscatter in the context of the dynamic procedure. A comparative discussion of the merits of stochastic versus deterministic modeling of backscatter is presented. These models are applied to a large eddy simulation of isotropic decaying and forced turbulence. Tests are also performed with versions of the model that do not account for backscatter. The results are compared to experiments and direct numerical simulation. It is shown that the models correctly predict the energy and three-dimensional (3D) energy spectra in decaying turbulence. In the forced case the Kolmogorov 5/3 law seems better predicted by models accounting for backscatter. A relative evaluation of the various versions of the model in terms of predictive capability and cost is provided.

A spectral analysis of anisotropic magnetohydrodynamic turbulence, in presence of a constant magnetic field, is presented using high-resolution direct numerical simulations. A method of decomposing the spectral space into ring structures is presented and the energy transfers between such rings are studied. This decomposition method takes into account the angular dependency of energy transfers in anisotropic systems, while it allows one to recover easily the known shell-to-shell energy transfers in the limit of isotropic turbulence. For large values of the constant magnetic field, the total-energy transfer appears to be most dominant in the direction perpendicular to the mean magnetic field. The linear transfer due to the constant magnetic also appears to be important in redistributing the energy between the velocity and the magnetic fields.