Abstract Three-dimensional direct numerical simulations are implemented to investigate the energy cascade rate in compressible isothermal magnetohydrodynamic turbulence. Utilizing an exact law derived from the Kármán–Howarth equation, we examine the contributions of flux and nonflux terms to the cascade rate across a broad range of sonic and Alfvénic Mach numbers, from subsonic to supersonic regimes and with varying mean magnetic fields. The cascade rates are computed using on-grid 3D decomposition and two plasma increment approaches: signed and absolute values. The anisotropy induced by strong magnetic fields is analyzed through angular-dependent scaling of the cascade terms. Moreover, the increment calculation method significantly influences the relative contributions of the flux and nonflux terms, with absolute methods tending to overestimate the latter. These findings extend current studies of compressible turbulence and offer critical insights into energy transfer mechanisms relevant to many astrophysical phenomena.
Álvarez et al. (Thu,) studied this question.