General Exact Law of Compressible Isentropic Magnetohydrodynamic Flows: Theory and Spacecraft Observations in the Solar Wind

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 any turbulent isentropic flow (i.e., constant entropy). We demonstrate known MHD (incompressible and isothermal) new (polytropic) one can be obtained as specific cases law when corresponding closure equation is stated. also recover all hydrodynamic (HD) (incompressible, polytropic) from this limit ${\bf B}=0$. furthermore show difference between two (isothermal interest work resides some source terms explicit form flux term depends on internal energy. Finally, apply these Parker Solar Probe (PSP) data taken inner heliosphere highlight how different equations affect energy cascade rate estimates.