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The decay of isotropic magnetohydrodynamics turbulence and the effects of cross-helicity

Abstract : Decaying homogeneous and isotropic magnetohydrodynamics (MHD) turbulence is investigated numerically at large Reynolds numbers thanks to the eddy-damped quasi-normal Markovian (EDQNM) approximation. Without any background mean magnetic field, the total energy spectrum E scales as k −3/2 in the inertial range as a consequence of the modelling. Moreover, the total energy is shown, both analytically and numerically, to decay at the same rate as kinetic energy in hydrodynamic isotropic turbulence: this differs from a previous prediction, and thus physical arguments are proposed to reconcile both results. Afterwards, the MHD turbulence is made imbalanced by an initial non-zero cross-helicity. A spectral modelling is developed for the velocity-magnetic correlation in a general homogeneous framework, which reveals that cross-helicity can contain subtle anisotropic effects. In the inertial range, as the Reynolds number increases, the slope of the cross-helical spectrum becomes closer to k −5/3 than k −2. Furthermore, the Elsässer spectra deviate from k −3/2 with cross-helicity at large Reynolds numbers. Regarding the pressure spectrum E P , its kinetic and magnetic parts are found to scale with k −2 in the inertial range, whereas the part due to cross-helicity rather scales in k −7/3. Finally, the two 4/3rd laws for the total energy and cross-helicity are assessed numerically at large Reynolds numbers.
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Antoine Briard, Thomas Gomez. The decay of isotropic magnetohydrodynamics turbulence and the effects of cross-helicity. Journal of Plasma Physics, Cambridge University Press (CUP), 2018, 84 (1), ⟨10.1017/S0022377818000120⟩. ⟨hal-02112143⟩

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