Exact law for homogeneous compressible Hall magnetohydrodynamics turbulence

Abstract

We derive the exact law for three-dimensional (3D) homogeneous compressible isothermal Hall magnetohydrodynamics (CHMHD) turbulence, without the assumption of isotropy. The Hall current is shown to introduce new flux and sources terms that act at the small scales (comparable or smaller than the ion skin depth) to significantly impact the turbulence dynamics. The new law provides an accurate means to estimate for the first time the energy cascade rate over a broad range of scales covering the MHD inertial range and the sub-ion dispersive range in 3D numerical simulations and {\it in situ} spacecraft observations of compressible turbulence. This work is particularly relevant to astrophysical flows in which small scale density fluctuations cannot be ignored such as the solar wind, planetary magnetospheres and the interstellar medium (ISM).

References in corpus (8)

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Cited by in corpus (16)

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• Energy cascade rate measured in a collisionless space plasma with MMS data and compressible Hall magnetohydrodynamic turbulence theory
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• 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
• Fast magneto-acoustic wave turbulence and the Iroshnikov-Kraichnan spectrum
• 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
• Space-filter techniques for quasi-neutral hybrid-kinetic models
• 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
• On the contribution of the Hall term in small-scale magnetohydrodynamic dynamo
• Proof of the zeroth law of turbulence in one-dimensional compressible magnetohydrodynamics and shock heating
• On cascade of kinetic energy in compressible hydrodynamic turbulence
• Ion-scale transition of plasma turbulence: Pressure-strain effect