Spectral Transfer and Karman-Howarth-Monin Equations for Compressible Hall Magnetohydrodynamics

0545155 - ÚFA 2022 RIV US eng J - Journal Article
Hellinger, Petr - Papini, E. - Verdini, A. - Landi, S. - Franci, L. - Matteini, L. - Montagud-Camps, V.
Spectral Transfer and Karman-Howarth-Monin Equations for Compressible Hall Magnetohydrodynamics.
Astrophysical Journal. Roč. 917, č. 2 (2021), č. článku 101. ISSN 0004-637X. E-ISSN 1538-4357
Institutional support: RVO:68378289
Keywords : solar-wind turbulence * energy-transfer * scale dependence * mhd turbulence * proton * energetics * cascade
OECD category: Astronomy (including astrophysics,space science)
Impact factor: 5.521, year: 2021
Method of publishing: Open access
https://iopscience.iop.org/article/10.3847/1538-4357/ac088f

We derive two new forms of the Karman-Howarth-Monin (KHM) equation for decaying compressible Hall magnetohydrodynamic (MHD) turbulence. We test them on results of a weakly compressible, 2D, moderate-Reynolds-number Hall MHD simulation and compare them with an isotropic spectral transfer (ST) equation. The KHM and ST equations are automatically satisfied during the whole simulation owing to the periodic boundary conditions and have complementary cumulative behavior. They are used here to analyze the onset of turbulence and its properties when it is fully developed. These approaches give equivalent results characterizing the decay of the kinetic + magnetic energy at large scales, the MHD and Hall cross-scale energy transfer/cascade, the pressure dilatation, and the dissipation. The Hall cascade appears when the MHD one brings the energy close to the ion inertial range and is related to the formation of reconnecting current sheets. At later times, the pressure dilatation energy exchange rate oscillates around zero, with no net effect on the cross-scale energy transfer when averaged over a period of its oscillations. A reduced 1D analysis suggests that all three methods may be useful to estimate the energy cascade rate from in situ observations.
Permanent Link: http://hdl.handle.net/11104/0321985