Uncovering the varieties of three-dimensional Hall magnetohydrodynamics turbulence

We carry out extensive pseudospectral direct numerical simulations (DNSs) of decaying three-dimensional (3D) Hall magnetohydrodynamics (3D HMHD) plasma turbulence at three magnetic Prandtl numbers Prm=0.1, 1.0, and 10.0. Our DNSs have been designed to uncover the dependence of the statistical properties of 3D HMHD turbulence on Prm. We find two different inertial regions: in the first inertial region k<ki∼1/di, both the kinetic-energy and magnetic-energy spectra, Eu(k) and Eb(k), respectively, display power-law regions with an exponent that is consistent with Kolmogorov-type −5/3 scaling, at all values of Prm. In the second inertial region k>ki, the scaling of Eb(k) depends upon Prm. At Prm=0.1, the spectral-scaling exponent is −17/3, but for Prm=1 and 10 this exponent is −11/3. We then show theoretically that Eb(k)∼k−2Eu(k) for Prm≪1 and Eb(k)∼k2Eu(k) for Prm≫1; our DNS results are consistent with our theoretical predictions. We examine, furthermore, left- and right-polarized fluctuations of the fields that lead, respectively, to the dominance of ion-cyclotron or whistler waves. We also show that 3D HMHD turbulence shows signatures of intermittency that we uncover by analyzing the scale dependence of probability distribution functions of velocity- and magnetic-field increments, their structure functions, and their flatness as functions of di and Prm.