Alternative derivation of exact law for compressible and isothermal magnetohydrodynamics turbulence

Abstract

The exact law for fully developed homogeneous compressible magnetohydrodynamics (CMHD) turbulence is derived. For an isothermal plasma, without the assumption of isotropy, the exact law is expressed as a function of the plasma velocity field, the compressible Alfvén velocity and the scalar density, instead of the Elsässer variables used in previous works. The theoretical results show four different types of terms that are involved in the nonlinear cascade of the total energy in the inertial range. Each category is examined in detail, in particular those that can be written either as source or flux terms. Finally, the role of the background magnetic field $B_0$ is highlighted and comparison with the incompressible MHD (IMHD) model is discussed. This point is particularly important when testing the exact law on numerical simulations and in situ observations in space plasmas.

References in corpus (5)

• Observation of inertial energy cascade in interplanetary space plasma
• On the von Karman-Howarth equations for Hall MHD flows
• Scaling of compressible magnetohydrodynamic turbulence in the fast solar wind
• Dynamic Alignment and Exact Scaling Laws in MHD Turbulence
• Exact scaling laws for helical three-dimensional two-fluid turbulent plasmas

Cited by in corpus (19)

• Physical Processes in Star Formation
• Energy cascade rate measured in a collisionless space plasma with MMS data and compressible Hall magnetohydrodynamic turbulence theory
• Exact law for homogeneous compressible Hall magnetohydrodynamics turbulence
• The evolution of compressible solar wind turbulence in the inner heliosphere: PSP, THEMIS and MAVEN observations
• Compressible turbulence in the interstellar medium: New insights from a high-resolution supersonic turbulence simulation
• The incompressible energy cascade rate in anisotropic solar wind turbulence
• General exact law of compressible isentropic magnetohydrodynamic flows: theory and spacecraft observations in the solar wind
• Scale-to-scale energy transfer rate in compressible two-fluid plasma turbulence
• A Statistical Study of the Compressible Energy Cascade Rate in Solar Wind Turbulence: Parker Solar Probe Observations
• Local cascade and dissipation in incompressible Hall magnetohydrodynamic turbulence: the Coarse-Graining approach
• Exact law for compressible pressure-anisotropic magnetohydrodynamic turbulence: toward linking energy cascade and instabilities
• An in-depth numerical study of exact laws for compressible Hall magnetohydrodynamic turbulence
• Spatio temporal analysis of waves in compressively driven magnetohydrodynamics turbulence
• Energy transfer, discontinuities and heating in the inner solar wind measured with a weak and local formulation of the Politano-Pouquet law
• Fluid energy cascade rate and kinetic damping: new insight from 3D Landau-fluid simulations
• Variability of the Incompressible Energy Cascade Rate in Solar Wind Turbulence Around Mars
• Observation of Turbulent Magnetohydrodynamic Cascade in the Jovian Magnetosheath
• Analytic characterization of sub-Alfvénic turbulence energetics
• Impact of pressure anisotropy on the cascade rate of Hall-MHD turbulence with biadiabatic ions