Spectral modelling for isotropic MHD; effects of cross-helicity on decay and inertial scalings

What is it about?

In this work, we address numerically and theoretically the decay of isotropic magnetohydrodynamics turbulence. More precisely, we use a well-known method, namely the EDQNM developed in 1976 for MHD, to predict and assess the decay of the total (kinetic + magnetic) energy. We highlight strong similarities and differences with isotropic hydrodynamics turbulence. Then, we investigate the effects of cross-helicity, who is an inviscid invariant of the equations like total energy, on the global dynamics, and analyze the inertial scalings of the spectra. Finally, we assess numerically the asymptotic exact 4/3 laws at large Reynolds numbers for total energy and helicity, and discuss the impact of the modelling on the results.

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Why is it important?

Because of the modelling, a -3/2 spectral slope is imposed for the kinetic and magnetic energy spectra: more precisely, the characteristic time of the inertial range is prescribed, which yields -3/2. Nevertheless, the asymptotic decay of total energy is predicted to be the same as kinetic energy in isotropic hydrodynamic turbulence, despite the -5/3 scaling of the kinetic energy spectrum in the latter case. Furthermore, both 4/3 laws are assessed numerically as well, once again despite the -3/2 inertial scaling. One important conclusion is thus that a -3/2 inertial scaling, instead of a -5/3 one obtained in several direct numerical simulations of isotropic MHD, does not prevent to obtain decay laws similar to hydrodynamic turbulence, and the asymptotic 4/3 laws.

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