J. A. Merrifield

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

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 Muller [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 predicte...

Off-axis electron cyclotron heating and the sandpile paradigm for transport in tokamak plasmas

Previous observations that suggest a substantial role for nondiffusive energy transport in tokamaks subjected to off-axis electron cyclotron heating (ECH) are compared to the output from a sandpile model. The observations considered include local and global aspects of temperature profile evolution in the DIII-D [for example, C. C. Petty and T. C. Luce, Nucl. Fusion 34, 121 (1994)] and RTP (Rijnhuizen Tokamak Project) [for example, M. R. de Baar, M. N. A. Beurskens, G. M. D. Hogeweij, and N. J. Lopes Cardozo, Phys. Plasmas 6, 4645 (1999)] tokamaks. The sandpile model employed is an extension, to incorporate noncentral fueling, of one used previously to address tokamak physics issues [S. C. Chapman, R. O. Dendy, and B. Hnat, Phys. Rev. Lett. 86, 2814 (2001)]. It is found that there are significant points of resemblance between the phenomenology of the noncentrally fueled sandpile and of the tokamaks with off-axis ECH. This suggests that the essential ingredient of the sandpile model, namely avalanching cond...

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

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.