Rugged magneto-hydrodynamic invariants in weakly collisional plasma turbulence: Two-dimensional hybrid simulation results

Abstract

Aims. We investigated plasma turbulence in the context of solar wind. We concentrated on properties of ideal second-order magneto-hydrodynamic (MHD) and Hall MHD invariants. Methods. We studied the results of a two-dimensional hybrid simulation of decaying plasma turbulence with an initial large cross helicity and a negligible magnetic helicity. We investigated the evolution of the combined energy and the cross, kinetic, mixed, and magnetic helicities. For the combined energy and the cross, kinetic, and mixed helicities, we analysed the corresponding Kármán-Howarth-Monin (KHM) equation in the hybrid (kinetic proton and fluid electron) approximation. Results. The KHM analysis shows that the combined energy decays at large scales. At intermediate scales, this energy cascades (from large to small scales) via the MHD non-linearity and this cascade partly continues via Hall coupling to sub-ion scales. The cascading combined energy is transferred (dissipated) to the internal energy at small scales via the resistive dissipation and the pressure-strain effect. The Hall term couples the cross helicity with the kinetic one, suggesting that the coupled invariant, referred to here as the mixed helicity, is a relevant turbulence quantity. However, when analysed using the KHM equations, the kinetic and mixed helicities exhibit very dissimilar behaviours to that of the combined energy. On the other hand, the cross helicity, in analogy to the energy, decays at large scales, cascades from large to small scales via the MHD+Hall non-linearity, and is dissipated at small scales via the resistive dissipation and the cross-helicity equivalent of the pressure-strain effect. In contrast to the combined energy, the Hall term is important for the cross helicity over a wide range of scales. The magnetic helicity is scantily generated through the resistive term and does not exhibit any cascade.

References in corpus (21)

• Cascades and transitions in turbulent flows
• Observation of inertial energy cascade in interplanetary space plasma
• 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
• High-resolution hybrid simulations of kinetic plasma turbulence at proton scales
• Pressure anisotropy and small spatial scales induced by velocity shear
• Energy transfer in Hall-MHD turbulence: cascades, backscatter, and dynamo action
• Violation of the zeroth law of turbulence in space plasmas
• Energy transfer in compressible magnetohydrodynamic turbulence
• Anisotropy of third-order structure functions in MHD turbulence
• In-situ observation of Hall Magnetohydrodynamic Cascade in Space Plasma
• Pressure-Strain Interaction as the Energy Dissipation Estimate in Collisionless Plasma
• The third-order law for increments in magnetohydrodynamic turbulence with constant shear
• An alternative formulation for exact scaling relations in hydrodynamic and magnetohydrodynamic turbulence
• Chiral Exact Relations for Helicities in Hall Magnetohydrodynamic Turbulence
• Spectral transfer and Kármán-Howarth-Monin equations for compressible Hall magnetohydrodynamics
• Spectral properties and energy transfer at kinetic scales in collisionless plasma turbulence
• Spectrum of kinetic plasma turbulence at 0.3-0.9 astronomical units from the Sun
• Local cascade and dissipation in incompressible Hall magnetohydrodynamic turbulence: the Coarse-Graining approach
• Electron-ion heating partition in imbalanced solar-wind turbulence