https://hal-amu.archives-ouvertes.fr/hal-02112143Briard, AntoineAntoineBriardDALEMBERT - Institut Jean le Rond d'Alembert - UPMC - Université Pierre et Marie Curie - Paris 6 - CNRS - Centre National de la Recherche ScientifiqueM2P2 - Laboratoire de Mécanique, Modélisation et Procédés Propres - AMU - Aix Marseille Université - ECM - École Centrale de Marseille - CNRS - Centre National de la Recherche ScientifiqueGomez, ThomasThomasGomezLML - Laboratoire de Mécanique de Lille - FRE 3723 - Université de Lille, Sciences et Technologies - Centrale Lille - CNRS - Centre National de la Recherche ScientifiqueThe decay of isotropic magnetohydrodynamics turbulence and the effects of cross-helicityHAL CCSD2018plasma dynamicsplasma nonlinear phenomenaplasma simulation[PHYS.PHYS.PHYS-PLASM-PH] Physics [physics]/Physics [physics]/Plasma Physics [physics.plasm-ph]Boutin, Olivier2019-04-26 14:37:132023-02-08 17:11:072019-04-29 11:38:34enJournal articleshttps://hal-amu.archives-ouvertes.fr/hal-02112143/document10.1017/S0022377818000120application/pdf1Decaying 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.