Intermittency in fluid and magnetohydrodynamics (MHD) turbulence analyzed through the prism of moment scaling predictions of multifractal models

In the presence of waves due, e.g., to gravity, rotation, or a quasi-uniform magnetic field, energy transfer timescales, spectra, and physical structures within turbulent flows differ from the fully developed fluid case, but some features remain, e.g., intermittency or quasi-parabolic behaviors of normalized moments of relevant fields, for the most part in that intermediate regime where waves and nonlinear eddies interact strongly.

After reviewing some of the roles intermittency can play in various geophysical flows, we present the results of direct numerical simulations at moderate resolution and run for long times. We show that the power law scaling relations between kurtosis K and skewness S found in multiple and diverse environments can be recovered using a selection of existing multifractal intermittency frameworks. Indeed, in the specific context of the She–Lévêque model (She and Lévêque, 1994) generalized to magnetohydrodynamics (MHD) and developed as a two-parameter system in Politano and Pouquet (1995), we find that a parabolic K(S) law can be recovered for maximal intermittency involving the most extreme dissipative structures.