General exact law of compressible isentropic magnetohydrodynamic flows: Theory and spacecraft observations in the solar wind

Pauline Simon

In 1941, Kolmogorov introduced the formalism of exact laws to describe turbulent HD flows. Here we propose a more general method based on the isentropic internal energy equation that allows us to obtain the isentropic MHD exact law. Then, we obtain known MHD and HD exact laws and a new polytropic MHD one as particular cases of the isentropic one. Finally, we apply the incompressible, isothermal and polytropic MHD forms to Parker Solar Probe (PSP) data taken in the inner heliosphere to highlight how the different closure equations affect the energy cascade rate estimates.

Related paper: https://arxiv.org/pdf/2105.08011.pdf