Local cascade and dissipation in incompressible Hall magnetohydrodynamic turbulence: the Coarse-Graining approach

Abstract

We derive the coarse-graining (CG) equations of incompressible Hall Magnetohydrodynamics (HMHD) turbulence to investigate the 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 local-in-space energy transfer, which is shown theoretically and numerically to match at a given position x, 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. II. COARSE-GRAINED INCOMPRESSIBLE HMHD EQUATIONSWe introduce the notion of a coarse grained (CG) measurement of a field f with a scale resolution . We choose a kernel function G normalized to one drG(r) = 1, centered drrG(r) = 0 and with variance of order unity

Scaling Laws for the Energy Transfer in Space Plasma Turbulence

“…Foldes et al (2022) implemented a refined space-filter approach to characterize the local energy release by extreme vertical drafts in stratified geophysical flows, whereas Camporeale et al (2018) combined the space-filter approach with wavelet analysis to prove that coherent structures in plasmas, described by 2.5D Hall-MHD simulations, correlate with regions where the energy transfer is enhanced, in a particular range of scales. Space filters were also used by Manzini et al (2022) to emphasize, in fully 3D Hall-MHD simulations, how magnetic reconnection sites do affect energy dissipation. The concept of space filtering has been also implemented to obtain a local version of the third-order law hydrodynamic turbulence and in MHD, which makes it relevant for the purpose of this review.…”