The cascade behavior of turbulent magnetohydrodynamics with a strong background magnetic field is examined and compared with direct numerical solutions at high Reynolds number. Resonant interactions give rise to qualitatively different behavior for modes below a characteristic wave number k L defined in terms of the background field. Modes with parallel wave number above k L are passively driven by the longer wavelength modes, even when the majority of the energy is contained in the passive wave numbers. The passive modes do not cascade to higher parallel wave numbers, so the parallel wave number spectrum is not a power law and does not extend to dissipation scales. Energy is cascaded normally to small perpendicular scales, but more rapidly in the case of the passive modes, so an anisotropic spectrum develops from isotropic initial conditions. For a finite system with minimum wave number Ͼk L , the only dynamically controlling mode is the vertical average, or mean mode. The mean mode evolves with two-dimensional dynamics, forming coherent current structures which are mirrored by the passive modes. Because of the differential decay rates, the mean mode dominates at long times. Quantitative comparisons are made to numerical solutions of reduced magnetohydrodynamics. ͓S1063-651X͑98͒06406-X͔

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Numerical solutions of decaying two-dimensional incompressible magnetohydrodynamic turbulence reach a long-lived self-similar state which is described in terms of a turbulent enstrophy cascade. The ratio of kinetic to magnetic enstrophy remains approximately constant, while the ratio of energies decreases steadily. Although the enstrophy is not an inviscid invariant, the rates of enstrophy production, dissipation, and conversion from magnetic to kinetic enstrophy are very evenly balanced, resulting in smooth power law decay. Energy spectra have a k−3/2 dependence at early times, but steepen to k−5/2. Local alignment of the intermediate and small-scale fields grows, but global correlation coefficients do not. The spatial kurtosis of current grows and is always greater than the vorticity kurtosis. Axisymmetric monopole patterns in the current (magnetic vortices) are dominant structures; they typically have a weaker concentric, nonmonotonic vorticity component. Fast reconnection or coalescence events occur on advective and Alfvén time scales between close vortices of like sign. Current sheets created during these coalescence events are local sites of enstrophy production, conversion, and dissipation. The number of vortices decreases until the fluid reaches a magnetic dipole as its nonlinear evolutionary end-state.

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We develop a filamentary construct of magnetohydrodynamical plasma dynamics based on the Elsasser variables. This approach is modeled after discrete vortex models of hydrodynamicai turbulence, which cannot be expected in general to produce results identical to ones based on a Fourier decomposition of the fields. La a highly intermittent plasma, the induction force is small compared to the convective motion, and when this force is neglected, the plasma vortex system is described by a Hamiltonian. For a system with many such vortices, we present a statistical treatment of a collection of discrete current-vorticity concentrations. Canonical and microcanonical statistical calculations show that both the vorticity and the current spectra are peaked at long wavelengths, and the expected states revert to known hydrodynamical states as the magnetic field vanishes. These results differ from previous Fourier-based statistical theories, but it is found that when the filament calculation is expanded to include the inductive force, the results approach the Fourier equilibria in the low-temperature limit, and the previous Hamiltonian plasma vortex results in the high-temperature limit. Numerical simulations of a large number of filaments are carried out and support the theory. A three-dimensional vortex model is outlined as weil, which is also Hamiltonian when the inductive force is neglected. A statistical calculi_tion in the canonical ensemble l lnstitute for Fusion Studies,

We present an alternative approach to statistical analysis of an intermittent ideal magnetohydrodynamics fluid in two dimensions, based on the hydrodynamic discrete vortex model applied to the Elsasser variables. The model contains negative temperature states which predict the formation of magnetic islands, but also includes a natural limit under which the equilibrium states revert to the familiar twin-vortex states predicted by hydrodynamic turbulence theories. Numerical dynamical calculations yield equilibrium spectra in agreement with the theoretical predictions.PACS numbers: 47.65.+a, 52.30.-q, 52.65.+Z Statistical theories of continuous fluids usually are based on some discrete representation of the fluid. Even though such fluids are not in thermodynamic equilibrium at the molecular level, one can expect real systems to tend towards the statistically favored states during time scales for which the model is valid. For numerical simulation, of course, some discretization of a continuous system is always necessary.Hydrodynamic turbulence has been discretized by two methods: a truncated Fourier representation, and a point vortex representation. An analytic statistical Fourier analysis has already been applied to two-dimensional magnetohydrodynamics (MHD) [1]. In this Letter, we show that a point-vortex discretization like that used in hydrodynamics (or the equivalent guiding-center plasma [2]) is also possible for 2D MHD, and we give results of statistical analysis as well as direct numerical simulation of the vortex system.Why is such an approach worth taking? It has been assented [3] that different approaches to discretization of functional integrations cannot in general be expected to yield equivalent results. Indeed, in the hydrodynamic studies, the two different discretization approaches, while both making similar qualitative predictions about a cascade of energy to low wave numbers, do not yield the same results [4]. A neutral 2D fluid with small dissipation is known to form intermediate-scale vorticity distributions, or coherent structures [5], which dominate the nonlinear evolution. Statistical theories based on inviscid equations [6,7] predict evolutionary tendencies suggestive of such structures, although they cannot complete the fully dissipative formation process. Vortices have nevertheless been taken as a starting point for a large body of work and many others). The end states predicted by such models have been observed in direct numerical simulation of the primitive fluid equations [13], and the dynamical approach »to the end state is well described by a modified vortex model [14]. These successes encourage the search for an analogous approach in 2D MHD. Computationally, discrete-vortex models can qualitatively reproduce the behavior of the primitive fluid equations at a lower cost than a spectral or grid point code [15], and allow the possibility of modeling more general large-scale filamentary structures [16,17]. Taking an analogous approach to MHD simulations could lead to similarly efficient n...

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.

This is the final report of a three-year, Laboratory Directed Research and Development (LDRD) project at Los Alamos National Laboratory (LANL). This is a fundamental research project whose aim is exploiting the last decades' progress in understanding the dynamics of nonlinear andor noisy systems in applications to a variety of problems in theoretical physics, chemistry and biology. The common denominator here is the fundamental role played by the combination of nonlinearity, noise and/or disorder in the dynamics of both simple and complex systems, and the underlying theoretical problems have much in common within the paradigms of nonlinear science. This project extends a technology base relevant to a variety of problems arising in applications of nonlinearity in science, and applies this technology to those problems. Thus, numerical simulations and experiments focused on nonlinear and stochastic processes provide important insights into nonlinear science, while nonlinear techniques help advance our understanding of the scientific principles underlying the control of complex behavior in systems with strong spatial and temporal internal variability.