MHD turbulence in the Earth's plasma sheet: Dynamics, dissipation, and driving

Abstract

The turbulent flows and tangled magnetic fields of the Earth's plasma sheet are explored theoretically and by means of ISEE‐2 plasma and magnetic‐field measurements. The goal is to obtain a basic understanding of (1) the dynamics, (2) the driving, and (3) the dissipation of the turbulence. Dynamically, the turbulence of the plasma sheet appears to be a turbulence of eddies, rather than a turbulence of Alfven waves or other MHD modes. In this respect, it is similar to the two‐dimensional turbulence of the solar wind. Previously published statistical arguments that the correlation length (= integral scale = eddy size) of the turbulence fluctuations in the plasma sheet is ℓeddy ∼ 1.6 RE are confirmed by analyzing plasma sheet magnetic‐field measurements during two special “sweeping” intervals that follow the passage of interplanetary shocks. For dissipation of the turbulence, two mechanisms appear to be important. The first is a cascade of energy in the turbulence to small spatial scales, where internal dissipation at non‐MHD spatial scales should occur. The second mechanism is electrical coupling of the turbulent flows to the resistive ionosphere, which introduces a “quasi‐viscosity” to the plasma sheet. This quasi‐viscosity is complicated owing (1) to a time delay associated with Alfven‐transit‐time coupling (introducing a viscoelasticity to the turbulence), (2) to a scalesize dependence of the coupling (introducing a hypoviscosity), and (3) to a dependence of the coupling on the sign of the flow shear (introducing a sign‐vorticity effect). For the coupling of the plasma sheet turbulence to the ionosphere, retarded‐time Reynolds numbers R* are derived to describe the importance of the resulting dissipation (quasi‐viscosity) and a Deborah number D is derived to describe the importance of the time lag (elasticity). The difference of the plasma sheet turbulence from homogeneous turbulence is discussed; this dissimilarity is owed to (a) dissipation at all wave numbers in the plasma sheet, (b) the presence of boundaries, and (c) the limited range of spatial scales that will allow scale‐invariant dynamics. A better description of the plasma sheet turbulence would be “turbulence in a box” or a turbulent wake.