Nonlinear and Statistical Behavior of Plasma Turbulence: the appearance and effects of structure

Abstract: Turbulence in general is an unsolved problem, and relative to ordinary fluids, it is even more complex in plasma or magnetofluids (“MHD”).   In fluids, the usual scenario involves driving, cascade and dissipation. In plasma models, one deals with additional effects such as multiplicity of wave modes, anisotropy and multiple ideal conserved quantities. There are however strong connections between diverse models, as seen in the parallelism between 2D incompressible flow and 2D strongly magnetized guiding center fluid. This simple model demonstrates nonlinear effects such as self-organization, nonlocal couplings, selective decay, dual cascades of multiple invariants, and even generation of 1/f noise.  The goal in this presentation is to demonstrate dynamical features in several fluid and plasma models that give rise to real space structure both at large scales and at small scales. Illustrations are provided in simulations and solar wind observations. For the large scales, some guidance is provided by the equilibrium Gibbs ensemble, which predicts formation of large scale coherent circulations in 2D hydro, and large magnetic islands in 2D MHD.  These theoretical constructs are precursors to identifying relaxation processes in both 2D and 3D. Global relaxation is better known, taking shape for example in Taylor relaxation and selective decay processes. However, there is mounting evidence that essentially the same relaxation processes, leading towards Beltrami, force free, Alfvenic and pressure balances states, also occur locally, and rapidly.  This implies patches of these several associated correlations, and these are indeed observed and seen in simulations. As local relaxation occurs almost ubiquitously, suppressing but not eliminating nonlinearities, sharp gradients are formed at the local margins, leading to small scale coherent structures such as vortices and current sheets.  Finally, we suggest that the formation of large scale coherent structures may be viewed as the long wavelength bursty behavior envisioned by Oubhukov, which historically acted as a motivation for the Kolomogorov’s Refined Similarity Hypothesis (RSH). The latter is usually employed to describe small scale dissipative structures. In this perspective, both large scale and small structures appearing in turbulence may be viewed as intermittency in a more general sense.