A dynamic localization model with stochastic backscatter

The modeling of subgrid scales in large-eddy simulation (LES) has been rationalized by the introduction of the dynamic localization procedure. This method allows one to compute rather than prescribe the unknown coefficients in the subgrid-scale model. Formally, the LES equations are supposed to be obtained by applying to the Navier-Stokes equations a 'grid filter' operation. Though the subgrid stress itself is unknown, an identity between subgrid stresses generated by different filters has been derived. Although preliminary tests of the Dynamic Localization Model (DLM) with k-equation have been satisfactory, the use of a negative eddy viscosity to describe backscatter is probably a crude representation of the physics of reverse transfer of energy. Indeed, the model is fully deterministic. Knowing the filtered velocity field and the subgrid-scale energy, the subgrid stress is automatically determined. We know that the LES equations cannot be fully deterministic since the small scales are not resolved. This stems from an important distinction between equilibrium hydrodynamics and turbulence. In equilibrium hydrodynamics, the molecular motions are also not resolved. However, there is a clear separation of scale between these unresolved motions and the relevant hydrodynamic scales. The result of molecular motions can then be separated into an average effect (the molecular viscosity) and some fluctuations. Due to the large number of molecules present in a box with size of the order of the hydrodynamic scale, the ratio between fluctuations and the average effect should be very small (as a result of the 'law of large numbers'). For that reason, the hydrodynamic balance equations are usually purely deterministic. In turbulence, however, there is no clear separation of scale between small and large eddies. In that case, the fluctuations around a deterministic eddy viscosity term could be significant. An eddy noise would then appear through a stochastic term in the subgrid-scale model and could be the source of backscatter

Dynamo Transition in Low-dimensional Models

Two low-dimensional magnetohydrodynamic models containing three velocity and three magnetic modes are described. One of them (nonhelical model) has zero kinetic and current helicity, while the other model (helical) has nonzero kinetic and current helicity. The velocity modes are forced in both these models. These low-dimensional models exhibit a dynamo transition at a critical forcing amplitude that depends on the Prandtl number. In the nonhelical model, dynamo exists only for magnetic Prandtl number beyond 1, while the helical model exhibits dynamo for all magnetic Prandtl number. Although the model is far from reproducing all the possible features of dynamo mechanisms, its simplicity allows a very detailed study and the observed dynamo transition is shown to bear similarities with recent numerical and experimental results.Comment: 7 page

Dynamic Procedure for Filtered Gyrokinetic Simulations

Large Eddy Simulations (LES) of gyrokinetic plasma turbulence are investigated as interesting candidates to decrease the computational cost. A dynamic procedure is implemented in the GENE code, allowing for dynamic optimization of the free parameters of the LES models (setting the amplitudes of dissipative terms). Employing such LES methods, one recovers the free energy and heat flux spectra obtained from highly resolved Direct Numerical Simulations (DNS). Systematic comparisons are performed for different values of the temperature gradient and magnetic shear, parameters which are of prime importance in Ion Temperature Gradient (ITG) driven turbulence. Moreover, the degree of anisotropy of the problem, that can vary with parameters, can be adapted dynamically by the method that shows Gyrokinetic Large Eddy Simulation (GyroLES) to be a serious candidate to reduce numerical cost of gyrokinetic solvers.Comment: 10 pages, 10 figures, submitted to Physics of Plasma

On the locality of MHD turbulence scale fluxes

The scale locality of energy fluxes for magnetohydrodynamics (MHD) is investigated numerically for stationary states of turbulence. Two types of forces are used to drive turbulence, a kinetic force that acts only on the velocity field and a kinetic-inductive forcing mechanism, which acts on the velocity and magnetic fields alike. The analysis is performed in spectral space, which is decomposed into a series of shells following a power law for the boundaries. The triadic transfers occurring among these shells are computed and the fluxes and locality functions are recovered by partial summation over the relevant shells. Employing Kraichnan locality functions, values of 1/3 and 2/3 for the scaling exponents of the four MHD energy fluxes are found. These values are smaller compared with the value of 4/3 found for hydrodynamic turbulence. To better understand these results, an in depth analysis is performed on the total energy flux.Comment: submitted to Physics of Plasmas, 10 pages, 8 figure

Energy transfers in shell models for MHD turbulence

A systematic procedure to derive shell models for MHD turbulence is proposed. It takes into account the conservation of ideal quadratic invariants such as the total energy, the cross-helicity and the magnetic helicity as well as the conservation of the magnetic energy by the advection term in the induction equation. This approach also leads to simple expressions for the energy exchanges as well as to unambiguous definitions for the energy fluxes. When applied to the existing shell models with nonlinear interactions limited to the nearest neighbour shells, this procedure reproduces well known models but suggests a reinterpretation of the energy fluxes.Comment: 8 page

The Effect of Coherent Structures on Stochastic Acceleration in MHD Turbulence

We investigate the influence of coherent structures on particle acceleration in the strongly turbulent solar corona. By randomizing the Fourier phases of a pseudo-spectral simulation of isotropic MHD turbulence (Re $\sim 300$), and tracing collisionless test protons in both the exact-MHD and phase-randomized fields, it is found that the phase correlations enhance the acceleration efficiency during the first adiabatic stage of the acceleration process. The underlying physical mechanism is identified as the dynamical MHD alignment of the magnetic field with the electric current, which favours parallel (resistive) electric fields responsible for initial injection. Conversely, the alignment of the magnetic field with the bulk velocity weakens the acceleration by convective electric fields - \bfu \times \bfb at a non-adiabatic stage of the acceleration process. We point out that non-physical parallel electric fields in random-phase turbulence proxies lead to artificial acceleration, and that the dynamical MHD alignment can be taken into account on the level of the joint two-point function of the magnetic and electric fields, and is therefore amenable to Fokker-Planck descriptions of stochastic acceleration.Comment: accepted for publication in Ap