Local cascade and dissipation in incompressible Hall magnetohydrodynamic turbulence: the Coarse-Graining approach
arXiv:2203.01050 · doi:10.1103/PhysRevE.106.035202
Abstract
We derive the coarse-graining (CG) equations of incompressible Hall Magnetohydrodynamics (HMHD) turbulence to investigate the {\it local (in space)} energy cascade rate as a function of the filtering scale . First, the CG equations are space averaged to obtain the analytical expression of the mean cascade rate. Its application to 3 dimensional (3D) simulations of (weakly compressible) HMHD shows a cascade rate consistent with the value of the mean dissipation rate in the simulations and with the classical estimates based on the "third-order" law. Furthermore, we developed an anisotropic version of CG that allows us to study the magnitude of the cascade rate along different directions with respect to the mean magnetic field. Its implementation on the numerical data with moderate background magnetic field shows a weaker cascade along the magnetic field than in the perpendicular plane, while an isotropic cascade is recovered in the absence of a background field. The strength of the CG approach is further revealed when considering the {\it local-in-space} energy transfer, which is shown theoretically and numerically to match at a given position , when locally averaged over a neighboring region, the (quasi-)local dissipation. Prospects of exploiting this new model to investigate local dissipation in spacecraft data are discussed.
arXiv comment14 pages, 8 figures, submitted to Physical Review E
References in corpus (32)
- Astrophysical gyrokinetics: kinetic and fluid turbulent cascades in magnetized weakly collisional plasmas
- The Anisotropy of MHD Alfvénic Turbulence
- Observation of inertial energy cascade in interplanetary space plasma
- Anisotropy of Solar Wind Turbulence between Ion and Electron Scales
- Localness of energy cascade in hydrodynamic turbulence, I. Smooth coarse-graining
- Energy transfer, pressure tensor and heating of kinetic plasma
- Compressible Turbulence: The Cascade and its Locality
- Exact Relation with Two-point Correlation Functions and Phenomenological Approach for Compressible Magnetohydrodynamic Turbulence
- Localness of energy cascade in hydrodynamic turbulence, II. Sharp spectral filter
- Compressible magnetohydrodynamic turbulence in the Earth's magnetosheath: estimation of the energy cascade rate using in situ spacecraft data
- Energy Cascade Rate In Compressible Fast And Slow Solar Wind Turbulence
- Turbulence-driven ion beams in the magnetospheric Kelvin-Helmholtz instability
- Direct measurements of anisotropic energy transfers in a rotating turbulence experiment
- Von Karman-Howarth equation for Hall magnetohydrodynamics: Hybrid simulations
- Coarse-Grained Incompressible Magnetohydrodynamics: analyzing the turbulent cascades
- Cascades and Dissipative Anomalies in Compressible Fluid Turbulence
- On the statistical properties of turbulent energy transfer rate in the inner Heliosphere
- A magnetic reconnection event in the solar atmosphere driven by relaxation of a twisted arch filament system
- Alternative derivation of exact law for compressible and isothermal magnetohydrodynamics turbulence
- On exact laws in incompressible Hall magnetohydrodynamic turbulence
- Energy cascade rate in isothermal compressible magnetohydrodynamic turbulence
- Cascades and Dissipative Anomalies in Nearly Collisionless Plasma Turbulence
- Local energy transfer rate and kinetic processes: the fate of turbulent energy in two-dimensional Hybrid Vlasov-Maxwell numerical simulations
- An alternative formulation for exact scaling relations in hydrodynamic and magnetohydrodynamic turbulence
- Solar Wind Turbulence Around Mars: Relation Between The Energy Cascade Rate And The Proton Cyclotron Waves Activity
- A local approach to the study of energy transfers in incompressible magnetohydrodynamic turbulence
- General exact law of compressible isentropic magnetohydrodynamic flows: theory and spacecraft observations in the solar wind
- Statistical Properties of Turbulent Fluctuations Associated with Electron-only Magnetic Reconnection
- 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
- Fluid energy cascade rate and kinetic damping: new insight from 3D Landau-fluid simulations
- Proof of the zeroth law of turbulence in one-dimensional compressible magnetohydrodynamics and shock heating