Intermittency, dissipation, and scaling in two-dimensional magnetohydrodynamic turbulence

Abstract

Direct numerical simulations (DNS) provide a means to test phenomenological models for the scaling properties of intermittent MHD turbulence. The well-known model of She and Leveque, when generalized to MHD, is in good agreement with the DNS in three dimensions, however, it does not coincide with DNS in two dimensions (2D). This is resolved here using the results of recent DNS of driven MHD turbulence in 2D which directly determine the scaling of the rate of dissipation. Specifically, a simple modification to generalized refined similarity is proposed that captures the results of the 2D MHD simulations. This leads to a new generalization of She and Leveque in MHD that is coincident with the DNS results in 2D. A key feature of this model is that the most intensely dissipating structures, which are responsible for the intermittency, are thread-like in 2D, independent of whether the underlying phenomenology of the cascade is Kolmogorov or Iroshnikov Kraichnan.

Generation of non-Gaussian statistics and coherent structures in ideal magnetohydrodynamics

“…This would have interesting implications, yet to be explored, for understanding refined similarity, the connection between scaling laws in the inertial range and the statistics of the dissipation in both 2D and 3D. 31 In particular, in the ideal case the dissipation is undefined, yet the present results suggest that a connection persists between inertial range scalings and gradients of the coherent structures. These ideas may also be relevant to the relationship between bottleneck effects, statistical mechanics, and effective viscosity caused by eddy noise.…”

Intermittent character of interplanetary magnetic field fluctuations

“…Recent studies have shown that the slow wind is more intermittent than the fast wind and, as largely reported in literature, the solar wind magnetic field is more intermittent than the velocity field [2,9,10,11,12]. The difference between velocity and magnetic field intermittency has also been observed in two-dimensional incompressive magnetohydrodynamics (MHD) numerical simulations [13,14,15,16], and seems to be a robust feature of MHD turbulence.…”

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

“…There have also been suggestions that even more information could be embedded in the primitive increment functions entering the MHD KRSH, for example by allowing for a scaling of alignment angles between v and b [20]. All such suggestions are permissible from a dimensional standpoint, but we have not yet seen in the literature either a precise statement of an MHD KRSH (however, see [21,22]) or a full statistical test of any such hypothesis, as has been carried out repeatedly in the hydrodynamic case [23,24].…”