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

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 $\mathbf{B}=0$. 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.

12 pages, 2 figures. Submitted to Astrophysical Journal

References in corpus (13)

• Observation of inertial energy cascade in interplanetary space plasma
• On the von Karman-Howarth equations for Hall MHD flows
• Energy Cascade Rate In Compressible Fast And Slow Solar Wind Turbulence
• Turbulence-driven ion beams in the magnetospheric Kelvin-Helmholtz instability
• Energy cascade rate measured in a collisionless space plasma with MMS data and compressible Hall magnetohydrodynamic turbulence theory
• Scaling of compressible magnetohydrodynamic turbulence in the fast solar wind
• Exact law for homogeneous compressible Hall magnetohydrodynamics turbulence
• Alternative derivation of exact law for compressible and isothermal magnetohydrodynamics turbulence
• An alternative formulation for exact scaling relations in hydrodynamic and magnetohydrodynamic turbulence
• Compressible turbulence in the interstellar medium: New insights from a high-resolution supersonic turbulence simulation
• Exact scaling laws for helical three-dimensional two-fluid turbulent plasmas
• Scale-to-scale energy transfer rate in compressible two-fluid plasma turbulence
• Examination of the four-fifths law for longitudinal third-order moments in incompressible magnetohydrodynamic turbulence in a periodic box

Cited by in corpus (4)

• The incompressible energy cascade rate in anisotropic solar wind turbulence
• An in-depth numerical study of exact laws for compressible Hall magnetohydrodynamic turbulence
• Energy transfer, discontinuities and heating in the inner solar wind measured with a weak and local formulation of the Politano-Pouquet law
• Variability of the Incompressible Energy Cascade Rate in Solar Wind Turbulence Around Mars