CONICET | Buscador de Institutos y Recursos Humanos

Three-dimensional direct numerical simulations are used to study the energy cascade rate in isothermal compressible magnetohydrodynamic turbulence. Our analysis is guided by a two-point exact law derived recently for this problem in which flux, source, hybrid{,} and mixed terms are present. The relative importance of each term is studied for different initial subsonic Mach numbers $M_S$ and different magnetic guide fields ${f B}_0$. The dominant contribution to the energy cascade rate comes from the compressible flux, which depends weakly on the magnetic guide field ${f B}_0$, unlike the other terms whose modulus increase significantly with $M_S$ and {${f B}_0$}. In particular, for strong {${f B}_0$} the source and hybrid terms are dominant at small scales with almost the same amplitude but with a different sign. A statistical analysis made with {an isotropic} decomposition based on the SO(3) rotation group is shown to generate spurious results in presence of ${f B}_0${, when compared with an axisymmetric decomposition better suited to the geometry of the problem.} Our numerical results are compared with previous analyses made with in-situ measurements in the solar wind and the terrestrial magnetosheath.