Exact law for compressible pressure-anisotropic magnetohydrodynamic turbulence: toward linking energy cascade and instabilities

Abstract

We derive a first exact law for compressible pressure-anisotropic magnetohydrodynamic turbulence. For a gyrotropic pressure tensor, we study the double-adiabatic case and show the presence of new flux and source terms in the exact law, reminiscent of the plasma instability conditions due to pressure anisotropy. The Hall term is shown to bring ion-scale corrections to the exact law without affecting explicitly the pressure terms. In the pressure isotropy limit we recover all known results obtained for isothermal and polytropic closures. The incompressible limit of the gyrotropic system leads to a generalization of the Politano and Pouquet's law where a new {\it incompressible} source term is revealed and reflects exchanges of the magnetic and kinetic energies with the no-longer-conserved internal energy. We highlight the possibilities offered by the new laws to investigate potential links between turbulence cascade and instabilities widely observed in laboratory and astrophysical plasmas.

9 pages. Some corrections and reorganisation, results unchanged

References in corpus (15)

• 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
• Exact relations for energy transfer in self-gravitating isothermal 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
• Magnetised plasma turbulence in clusters of galaxies

Cited by in corpus (5)

• Fast magneto-acoustic wave turbulence and the Iroshnikov-Kraichnan spectrum
• Subion Scale Turbulence Driven by Magnetic Reconnection
• A Statistical Study of the Compressible Energy Cascade Rate in Solar Wind Turbulence: Parker Solar Probe Observations
• Temperature anisotropy instabilities driven by intermittent velocity shears in the solar wind
• Impact of pressure anisotropy on the cascade rate of Hall-MHD turbulence with biadiabatic ions