The bulk flows and magnetic-field fluctuations of the plasma sheet are investigated using single-point measurements from the ISEE-2 Fast Plasma Experiment and fluxgate magnetometer. Ten several-hour-long intervals of continuous data (with 3 s and 12 s time resolution) are analysed. The plasma-sheet flow appears to be strongly ‘turbulent’ (i.e. the flow is dominated by fluctuations that are unpredictable, with rms velocities[Gt ]mean velocities and with field fluctuations≈mean fields). The flow velocities are typically sub-Alfvénic. The flow-velocity probability distribution P(v) is constructed, and is found to be well fitted by exponential functions. Autocorrelation functions [Ascr ](τ) are constructed, and the autocorrelation times τcorr for the flow velocities are found to be about 2 min. From the flow measurements, an estimate of the mixing length in the plasma sheet is produced, yielding Lmix≈2 Earth radii; correspondingly, the plasma-sheet material appears to be well mixed in density and temperature. An eddy viscosity for the plasma sheet is also estimated. Power spectra, which are constructed from the v(t) and B(t) time series, have portions that are power laws with spectral indices that are near the range of those expected for turbulence theories. The plasma sheet may provide a laboratory for the study of turbulence in parameter regimes different from that of solar-wind turbulence: the plasma sheet is a β[Gt ]1, hot-ion plasma, and the turbulence may be strongly driven rather than well developed. The turbulent nature of the flow and the disordered nature of the magnetic field have implications for the transport of plasma-sheet material, for the penetration of the solar-wind electric field into the plasma sheet, and for the calculation of particle orbits in the magnetotail.

Electric current sheets develop in the solar corona when different flux systems come into contact. At these sheets magnetic energy is transformed into heat and kinetic energy by means of reconnection. We have previously demonstrated how to accelerate neutral sheet energy conversion by means of a transition to turbulent reconnection via ideal, three-dimensional secondary instabilities, as conjectured by Montgomery. In this paper we describe how our previous results are modified by the presence of a finite mean sheetwise magnetic field. We find a stabilization from this field, due to a decrease in energy transfer from the basic magnetic field to the three-dimensional perturbed fields. An increase in perturbed dissipative energy losses is also observed.

The two-dimensional spatial and temporal evolution of the components of a plasma surrounding an electrode whose potential is suddenly decreased is investigated numerically. The electrode contains a localized convex or a localized concave voltage perturbation. The quasineutral plasma consists of positive ions and various proportions of negative ions and electrons. The results are compared and contrasted with those obtained with a uniform electrode under identical plasma conditions.

In this paper commemorating the 60th birthday of David Montgomery, issues tantalizing to me that evolved from my collaborations with him are highlighted: sustainment of the magnetohydrodynamic dynamo, relationships between discrete and continuous models of media, and closures for nonlinear theories of discrete and continuous media. In particular, it is speculated that a tractable statistical model of a magnetohydrodynamic dynamo may arise from a proper formulation of a solenoidal expansion basis for the magnetic and velocity fields in the context of an appropriate closure, such as the eddy-damped quasinormal Markovian model.

Scaling analysis is used to derive approximations of magnetohydrodynamics with self-consistent leading-order dynamics under general conditions of anisotropy. Both incompressible and weakly compressible limits are considered. The horizontal magnetic and velocity fields obey dynamics given by a reduced closed set of equations, but the vertical components have different decoupled dynamics in the different regimes. Conservation laws are also discussed. It is shown that the reduced equations are not self-consistent unless either the ratio of vertical to horizontal length scales is large or the fluid is gravitationally stratified and the ratio of length scales is small. New equations are derived for a rotating stratified plasma, which are an extension of the quasigeostrophic equations of neutral fluids.

Reduced, approximate MHD equations are derived for the case where the magnetic field is close to a potential field. The potential field can have an arbitrary three-dimensional structure, as long as it is non-vanishing. Finite current and pressure effects are included.

The general theory developed in Part I of the present series is here applied to axisymmetric solutions of the equations governing the magnetohydrodynamics of ideal incompressible fluids. We first show a helpful analogy between axisymmetric MHD flows and flows of a stratified fluid in the Boussinesq approximation. We then construct a general Casimir as an integral of an arbitrary function of two conserved fields, namely the vector potential of the magnetic field and the scalar field associated with the ‘modified vorticity field’, the additional frozen-in field introduced in Part I. Using this Casimir, sufficient conditions for linear stability to axisymmetric perturbations are obtained by standard Arnold techniques. We exploit Arnold's method to obtain sufficient conditions for nonlinear (Lyapunov) stability of the MHD flows considered. The appropriate norm is a sum of the magnetic and kinetic energies and the mean square vector potential of the magnetic field.

In earlier work, we have noted on semi-empirical grounds that the electrical conductivity σ in strongly coupled plasmas can be written as a linear form σ=σ0Γ in terms of the usual plasma coupling parameter Γ. Here, this is combined with the Wiedemann–Franz law to yield a zeroth-order treatment of thermal conductivity κ in such strongly coupled plasmas. Some refinement is needed to explain the properties of the heavier liquid alkali metals beginning with Na. This refinement follows from the nearly free-electron theory of electrical resistivity ρ=σ−1. Finally, a relation is forged between ρ, κ and the shear viscosity η at the freezing point of liquid alkali metals.

The development of anisotropies in an initially isotropic spectrum is studied numerically for compressible magnetohydrodynamic (MHD) turbulence in the presence of the Hall term. Building on a previous study where it was shown that spectral cascades in the Hall MHD system differ from the standard MHD case, particularly at high cross-helicities, we use an isotropic high cross-helicity initial state to study anisotropies of the Hall MHD system for a variety of mean magnetic field strengths and sonic Mach numbers. Strong anisotropies, which maximize at the ion-inertial length scale, appear for several plasma states and are categorized according to their plasma beta β: high-β Hall MHD simulations (β>1) show strong anisotropies relative to the standard MHD case, intermediate-β Hall MHD simulations (β≈1) show smaller anisotropy differences relative to the standard MHD case, and low-β Hall MHD simulations (β<1) again show strong anisotropies relative to the standard model. It is suggested that these anisotropy enhancements are due to nonlinear cascade suppression of propagating Alfvén waves in the field-aligned direction. This is different from the dynamics in the highly oblique directions, where non-propagating density and magnetic-energy anticorrelations appear.

Recent experiments and 2D laminar plasma–fluid simulations have indicated that plasma detachment from the divertor plate is strongly tied to plasma recombination. With plasma recombination, a neutral gas blanket will form between the divertor plate and the plasma frame front. Because of plasma-neutral coupling, the plasma flow along the field lines will drive neutral gas flow with Mach number [ges ]1 and Reynolds number [ges ]1000. A compressible set of conservation and transport equations are solved with 2D mean toroidal flow and 3D turbulence effects over various toroidal cavity geometries. The radial structure of the temperature profile is determined for both turbulent and laminar flow as the flame front propagates down the toroidal cavity. Quantitative results are obtained for the increased heat transfer to the toroidal walls due to turbulence as well as radial profiles for the transport coefficients. It is found that heat loads to the toroidal walls can be increased by factors of 5–20 over that for laminar flow for the cavity geometries studied here. This increased heat transfer to the toroidal walls will lead to decreased levels of heat flux impinging on the divertor plate.

We describe the existence of an entropy for lattice gas systems of Fermi–Dirac type based on a generalized semi-detailed balance condition. We demonstrate some essential equilibrium and non-equilibrium fluctuation and dissipation properties, including the so-called Onsager's reciprocity relations, as a consequence of this condition. Requirements for the existence of certain statistical properties in discrete lattice gas systems are not directly inferred from those in real continuous systems, but are closely related. Hence understanding in detail the causes and results for lattice gas systems may provide further insights into fundamental microscopic physical processes.

The effects of large-scale sweeping velocity on the turbulent cascade to small scales are examined for two problems: the advection of a passive scalar by a multivariate-Gaussian velocity field and incompressible Alfvén-wave turbulence. In both cases, the sweeping produces anisotropy and reduces the strength of cascade. If the direction of the sweep velocity varies with time, a balance is reached between this anisotropy and isotropizing effects associated with the change of direction.

High-resolution, direct numerical simulations of three-dimensional incompressible Navier–Stokes equations are carried out to study the energy spectrum in the dissipation range. An energy spectrum of the form A(k/kd)α exp[−βk/kd] is confirmed. The possible values of the parameters α and β, as well as their dependence on Reynolds numbers and length scales, are investigated, showing good agreement with recent theoretical predictions. A ‘bottleneck’-type effect is reported at k/kd≈4, exhibiting a possible transition from near-dissipation to far-dissipation.

There is abundant experimental, theoretical and computational evidence that certain constrained turbulent fluid systems self-organize into large-scale structures. Examples include two-dimensional (geostrophic) fluids, guiding-centre plasmas and pure-electron plasmas, as well as two- and three-dimensional magnetofluids such as reversed-field pinches and spheromaks. The theoretical understanding of relaxation phenomena is divided into two quite different constructs: selective decay and maximal entropy. Theoretical foundations of both of these principles are largely due to Montgomery and his collaborators. In this paper, selective decay and maximal entropy theories of turbulent relaxation of fluids are reviewed and experimental evidence is presented. Experimental evidence from both 2D fluids and from 3D magnetofluids is consistent with the selective decay hypothesis. However, high-resolution computational evidence strongly suggests that formation of large-scale structures is dictated by maximal-entropy principles rather than selective decay.

It is proposed that the differential rotation of the Earth's inner core deduced by Song and Richards is due to a combination of the deceleration of the Earth's rotation and the viscous drag between the Earth's inner and outer cores. If this model is correct then the dynamic viscosity in the outer core of the Earth can be estimated to be μ≈104 poise. Besides providing a novel way of determining the viscosity of the core, this simple model suggests some new tests and shows how astronomical effects can influence geological phenomena.