The scaling properties of dissipation in incompressible isotropic three-dimensional magnetohydrodynamic turbulence

Abstract

The statistical properties of the dissipation process constrain the analysis of large scale numerical simulations of three dimensional incompressible magnetohydrodynamic (MHD) turbulence, such as those of Biskamp and Müller [Phys. Plasmas 7, 4889 (2000)]. The structure functions of the turbulent flow are expected to display statistical self-similarity, but the relatively low Reynolds numbers attainable by direct numerical simulation, combined with the finite size of the system, make this difficult to measure directly. However, it is known that extended self-similarity, which constrains the ratio of scaling exponents of structure functions of different orders, is well satisfied. This implies the extension of physical scaling arguments beyond the inertial range into the dissipation range. The present work focuses on the scaling properties of the dissipation process itself. This provides an important consistency check in that we find that the ratio of dissipation structure function exponents is that predicted by the She and Leveque [Phys. Rev. Lett 72, 336 (1994)] theory proposed by Biskamp and Müller. This supplies further evidence that the cascade mechanism in three dimensional MHD turbulence is non-linear random eddy scrambling, with the level of intermittency determined by dissipation through the formation of current sheets.

Universal hierarchical symmetry for turbulence and general multi-scale fluctuation systems

“…This expression was found in very good agreement with the results of the numerical simulations at different conditions [57]; hence, an interesting "g-class" of multi-scale phenomena are discovered. The above analysis focuses on the Elsässer field (z ± ), the other two fields (velocity v and magnetic field B) are equally important physically.…”

Vorticity scaling and intermittency in drift-interchange plasma turbulence

“…Studies include direct measurements in the solar wind, 22,23 and the outputs of numerical simulations of turbulence in plasmas using various levels of description. [9][10][11][12][13][14][15][16] We present the first higher order analysis of the velocity, density, and vorticity fluctuations for the extended H-W equations, which are capable of modelling and comparing drift-interchange turbulence on the high field side (HFS) and low field side (LFS) of a tokamak. 17 In the context of MCF plasma turbulence, the scaling properties of fluctuations are important for several reasons.…”

“…These changes are of particular practical interest in relation to vorticity, which is known to play a key role in the transport of energy and particles in plasmas and fluids. [10][11][12][13][14][15] The ability to extrapolate transport properties between experiments of different sizes, or between simulation and experiment, rests on understanding how the statistical properties of the physical processes that drive transport scale with length and time. Insofar as the scaling is nonlinear, practical extrapolation becomes more difficult.…”

Intermittency, nonlinear dynamics and dissipation in the solar wind and astrophysical plasmas

“…Frequently these take the form of current sheets along borders between adjoining, and sometimes interacting, magnetic flux tubes. The hierarchical structure of flux tubes and current sheets over the several decade range of solar wind turbulence may well be described by an extension of the KRSH which has been discussed in phenomenological terms [20,21,161], but has yet not been fully formulated or tested. On the other hand, it seems evident that the hierarchy of structure found in coronal and solar wind turbulence has important implications for transport phenomena including plasma, suprathermal particles, heat flux and so on.…”