Compressible magnetohydrodynamic turbulence in the Earth's magnetosheath: estimation of the energy cascade rate using in situ spacecraft data

The first estimation of the energy cascade rate ${|\epsilon_C|}$ of magnetosheath turbulence is obtained using the CLUSTER and THEMIS spacecraft data and an exact law of compressible isothermal magnetohydrodynamics turbulence. ${|\epsilon_C|}$ is found to be of the order of ${10{^{-13}} J.m^{3}.s^{-1}}$, at least two orders of magnitude larger than its value in the solar wind (order of ${10{^{-16}} J.m^{3}.s^{-1}}$ in the fast wind). Two types of turbulence are evidenced and shown to be dominated either by incompressible Alfv\'enic or magnetosonic-like fluctuations. Density fluctuations are shown to amplify the cascade rate and its spatial anisotropy in comparison with incompressible Alfv\'enic turbulence. Furthermore, for compressible magnetosonic fluctuations, large cascade rates are found to lie mostly near the linear kinetic instability of the mirror mode. New empirical power-laws are evidenced and relate ${|\epsilon_C|}$ to the turbulent Mach number and the internal energy. These new finding have potential applications in distant astrophysical plasmas that are not accessible to in situ measurements.