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

TL;DR

This paper develops a comprehensive theoretical framework for exact laws of compressible isentropic MHD turbulence and applies it to spacecraft data, enhancing understanding of energy cascades in the solar wind.

Contribution

It introduces a general method to derive exact laws for any turbulent isentropic flow, unifying existing laws and applying them to real spacecraft observations.

Findings

Unified exact laws for compressible isentropic MHD turbulence.

Revealed differences in energy cascade estimates based on closure equations.

Applied laws to Parker Solar Probe data to analyze solar wind turbulence.

Abstract

Various forms of exact laws governing magnetohydrodynamic (MHD) turbulence have been derived either in the incompressibility limit, or for isothermal compressible flows. Here we propose a more general method that allows us to obtain such laws for any turbulent isentropic flow (i.e., constant entropy). We demonstrate that the known MHD exact laws (incompressible and isothermal) and the new (polytropic) one can be obtained as specific cases of the general law when the corresponding closure equation is stated. We also recover all known exact laws of hydrodynamic (HD) turbulence (incompressible, isothermal and polytropic) from this law in the limit ${\bf B}=0$. We furthermore show that the difference between the two forms (isothermal and polytropic) of the MHD exact laws of interest in this work resides in some of the source terms and in the explicit form of the flux term that depends on internal energy. Finally, we apply these two 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.