Transition to Equilibrium and Coherent Structure in Ideal MHD Turbulence, Part 2

We continue our study of the transition ideal, homogeneous, incompressible, magnetohydrodynamic (MHD) turbulence from non-equilibrium initial conditions to equilibrium using long-time numerical simulations on a 1283 periodic grid. A Fourier spectral transform method is used numerically integrate dynamical equations forward in time. The six runs that previously went near are here extended into equilibrium. As before, we neglect dissipation as primarily concerned with behavior at largest scale where this has been shown be essentially same for ideal and real (forced dissipative) MHD turbulence. These have various combinations imposed rotation mean magnetic field represent five cases turbulence: Case I (Run 1), no or field; II (Runs 2a 2b), only imposed; III 3), which IV 4), vector direction aligned; V 5), non-aligned directions. Statistical mechanics predicts dynamic coefficients zero-mean random variables, but largest-scale coherent structures emerge manifest themselves very large, quasi-steady, values compared their standard deviations, i.e., there ‘broken ergodicity.’ appeared all during Here, report that, were continued, these remained quasi-steady energetic Cases II, while maintained its structure comparatively low energy. seen collapse associated creation largest-scale, appears dynamo process inherent turbulence, particularly those most pertinent planets stars. Furthermore, statistical theory proven apply scale, even when forcing included. This, along discovery explanation dynamically broken ergodicity, solution ‘dynamo problem’.