Spatio-temporal behavior of magnetohydrodynamic fluctuations with cross-helicity and a background magnetic field

R. LUGONES, P. MININNI, P. DMITRUK

Conferencia; StatPhys 2019; 2019

Turbulent fluctuations are essentially broadband, both in spatialand temporal scales, involving non-linear couplings among the different scales. In incompressible magnetohydrodynamics (MHD)these couplings are based on interactions of triads of modes whichcan be of different types, such as local (in wavenumber) nonlineardistortions of eddies or sweeping (non-local in wavenumber space)of small eddies by larger ones.When linearized the MHD equations sustain Alfvén waves, whichin presence of a background magnetic field B0 are described by alinear dispersion relation of frequency ω = k · VA for wavevectork, Alfvén velocity VA = B0/√4πρ, with density ρ.It is well known that these waves, when considered in isolation,are also exact solutions of the nonlinear MHD (ideal) equations.Simultaneous presence of counter-propagating fluctuations however activate nonlinear interactions among modes, producing dispersion, and in consequence the waves are no longer solutionsof the equations. As the background magnetic field controls thewave velocity (Alfvén velocity) the nonlinear interaction is influenced by the Alfvén crossing time of counter propagating wavepackets. There is a competence therefore between nonlinear interactions (i.e., turbulence) and wave propagation. The amplitudeof counter-propagating fluctuations can be measured by the crosshelicity, a quantity which is a rugged invariant of the (ideal) MHDequations. A spatio-temporal analysis of fluctuations can be performed to quantitatively study the importance of these differenteffects and distinguish which is the dominant timescale amongthe different ones, depending on the controlling parameters of thesystem.In this work we perform this type of spatio-temporal analysis, controlling simultaneously the intensity of the background magneticfield and the amount of cross-helicity. We show different numerical solutions of the MHD equations in a quasi-stationary regime,analyzing each kind of timescale in the system.MHD equations and Elsä