Theory and Transport of Nearly Incompressible Magnetohydrodynamic Turbulence

Abstract

The theory of nearly incompressible magnetohydrodynamics (NI MHD) was developed largely in the early 1990s, together with an important extension to inhomogeneous flows in 2010. Much of the focus in the earlier work was to understand the apparent incompressibility of the solar wind and other plasma environments, and the relationship of density fluctuations to apparently incompressible manifestations of turbulence in the solar wind and interstellar medium. Further important predictions about the “dimensionality” of solar wind turbulence and its relationship to the plasma beta were made and subsequently confirmed observationally. However, despite the initial success of NI MHD in describing fluctuations in the solar wind, a detailed application to solar wind turbulence has not been undertaken. Here, we use the equations of NI MHD to describe solar wind turbulence, rewriting the NI MHD system in terms of Elsässer variables. Distinct descriptions of 2D and slab turbulence emerge naturally from the Elsässer formulation, as do the nonlinear couplings between 2D and slab components. For plasma beta order 1 or less regions, predictions for 2D and slab spectra result from the NI MHD description, and predictions for the spectral characteristics of density fluctuations can be made. We conclude by presenting a NI MHD formulation describing the transport of majority 2D and minority slab turbulence throughout the solar wind. A preliminary comparison of theory and observations is presented.

Solar Wind Turbulent Cascade from MHD to Sub-ion Scales: Large-size 3D Hybrid Particle-in-cell Simulations

“…As a final remark, we note that the good agreement between the 2D and the 3D numerical results may find theoretical support and a possible interpretation in Zank et al (2017). There, the nearly incompressible magnetohydrodynamic turbulence in the intermediate-and small-beta regimes is shown to comprise the presence of majority 2D and minority slab fluctuations.…”

Coherent Structures at Ion Scales in Fast Solar Wind: Cluster Observations

“…Our results (in the present paper for fast solar wind and in Perrone et al (2016) for slow solar wind) show that the vortex-like structures are the dominant form in the observed structures; thus, they may play a major role in the dynamics of the solar wind plasma at ion scales. A very recent theoretical study in nearly incompressible magnetohydrodynamic (NI MHD) turbulence by Zank et al (2017) has shown that two-dimensional vortex structures are explicitly predicted by the model. In particular the NI MHD formulation describes the transport of majority 2D, and minority slab, turbulence throughout the solar wind.…”

Modulation of Galactic Cosmic Rays in the Inner Heliosphere, Comparing with PAMELA Measurements

“…The development of magnetic turbulence transport models (TTMs, see, e.g., Zank et al 1996Zank et al , 2012Zank et al , 2017Breech et al 2008;Pei et al 2010a;Oughton et al 2011;Engelbrecht & Burger 2013a;Guo & Florinski 2016), which allows us to have a better scenario of the heliosphere, plays an important role in the ab initio models for cosmic ray diffusion. Especially in the numerical modulation study, the analytical expressions of diffusion is essential, which are directly based on the spatial dependence of magnetic turbulence.…”