Interplay between turbulence and waves: large-scale helical transfer, and small-scale dissipation and mixing in fluid and Hall-MHD turbulence

Abstract

Novel features of turbulent flows have been analyzed recently, for example: (i) the possibility of an ideal invariant, such as the energy, to be transferred both to the small scales and to the large scales, in each case with a constant flux; (ii) the existence of non-Gaussian wings in Probability Distribution Functions of kinetic, magnetic and temperature fluctuations, together with their gradients, thus displaying large-scale as well as small-scale intermittency; and (iii) the linear dependence on the control parameter of the e↵ective dissipation in turbulence when non-linear eddies and waves interact. We shall briefly review these results with examples stemming from Solar Wind data, the atmosphere and the ocean with either magnetic fields, stratification and/or rotation. In a second part, we shall examine numerically the inverse cascades of magnetic and of generalized helicity for Hall MHD in the presence of forcing. These helical invariants in the ideal non-dissipative case involve various cross-correlations between the velocity and vorticity, the magnetic field and the magnetic potential. For an ion inertial length larger than the forcing scale, the e↵ect of the waves is significant. It leads to an exponential attenuation of the inverse cascade to large scales, since, through the velocity and vorticity, small scales play an increasing dynamical role for a strong Hall current.

Statistical properties of three-dimensional Hall magnetohydrodynamics turbulence

“…At the simplest level, such fluids can be modeled by using the equations of magnetohydrodynamics (MHD). [1][2][3][4][5][6][7][8][9] Examples of such conducting-fluid flows can be found in liquid metals, in the interiors of planets or in laboratories, [10][11][12][13] solar or stellar settings, [1][2][3][4] the solar wind, [14][15][16][17][18][19] and the interstellar medium. [1][2][3][4]20 The MHD description of a plasma is based on a single-fluid approximation.…”

The role of field correlations on turbulent dissipation

“…As a final note, intermittency of the large scales (velocity, induction, temperature, density), as opposed to the small scales (vorticity, current, temperature or density gradients) has also been found in many contexts in the presence of waves [105][106][107][108] , as well as in the solar wind 72,109 and in magnetic storms 110 . For example, in stratified turbulence, the vertical velocity can have high kurtosis in a narrow range of the governing weak turbulence parameter, i.e.…”

The role of field correlations on turbulent dissipation

“…In a final note, intermittency of the large scales (velocity, induction, temperature, and density), as opposed to the small scales (vorticity, current, temperature or density gradients) has also been found in many contexts in the presence of waves [105][106][107][108], as well as in the solar wind [72,109] and in magnetic storms [110]. For example, in stratified turbulence, the vertical velocity can have high kurtosis in a narrow range of the governing weak turbulence parameter, i.e.…”