Energy cascade rate measured in a collisionless space plasma with MMS data and compressible Hall magnetohydrodynamic turbulence theory

Abstract

The first complete estimation of the compressible energy cascade rate $|{\epsilon }_{\text{C}}|$ at magnetohydrodynamic (MHD) and sub-ion scales is obtained in the Earth's magnetosheath using Magnetospheric MultiScale (MMS) spacecraft data and an exact law derived recently for {\it compressible} Hall MHD turbulence. A multi-spacecraft technique is used to compute the velocity and magnetic gradients, and then all the correlation functions involved in the exact relation. It is shown that when the density fluctuations are relatively small, $|{\epsilon }_{\text{C}}|$ identifies well with its incompressible analogue $|{\epsilon }_{\text{I}}|$ at MHD scales but becomes much larger than $|{\epsilon }_{\text{I}}|$ at sub-ion scales. For larger density fluctuations, $|{\epsilon }_{\text{C}}|$ is larger than $|{\epsilon }_{\text{I}}|$ at every scale with a value significantly higher than for smaller density fluctuations. Our study reveals also that for both small and large density fluctuations, the non-flux terms remain always negligible with respect to the flux terms and that the major contribution to $|{\epsilon }_{\text{C}}|$ at sub-ion scales comes from the compressible Hall flux.

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Cited by in corpus (9)

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• Turbulent cascade and energy transfer rate in a solar coronal mass ejection
• Anisotropy of Magnetic Field Spectra at Kinetic Scales of Solar Wind Turbulence as Revealed by Parker Solar Probe in the Inner Heliosphere
• 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
• An in-depth numerical study of exact laws for compressible Hall magnetohydrodynamic turbulence
• Proof of the zeroth law of turbulence in one-dimensional compressible magnetohydrodynamics and shock heating
• Current sheets, plasmoids and flux ropes in the heliosphere. Part II: Theoretical aspects