von Kármán-Howarth equation for three-dimensional two-fluid plasmas.

We derive the von Kármán-Howarth equation for a full three-dimensional incompressible two-fluid plasma. In the long-time limit and for very large Reynolds numbers we obtain the equivalent of the hydrodynamic "four-fifths" law. This exact law predicts the scaling of the third-order two-point correlation functions, and puts a strong constraint on the plasma turbulent dynamics. Finally, we derive a simple expression for the 4/5 law in terms of third-order structure functions, which is appropriate for comparison with in situ measurements in the solar wind at different spatial ranges.

Intermittency, nonlinear dynamics and dissipation in the solar wind and astrophysical plasmas.

An overview is given of important properties of spatial and temporal intermittency, including evidence of its appearance in fluids, magnetofluids and plasmas, and its implications for understanding of heliospheric plasmas. Spatial intermittency is generally associated with formation of sharp gradients and coherent structures. The basic physics of structure generation is ideal, but when dissipation is present it is usually concentrated in regions of strong gradients. This essential feature of spatial intermittency in fluids has been shown recently to carry over to the realm of kinetic plasma, where the dissipation function is not known from first principles. Spatial structures produced in intermittent plasma influence dissipation, heating, and transport and acceleration of charged particles. Temporal intermittency can give rise to very long time correlations or a delayed approach to steady-state conditions, and has been associated with inverse cascade or quasi-inverse cascade systems, with possible implications for heliospheric prediction.

Magnetic field reversals and long-time memory in conducting flows.

Employing a simple ideal magnetohydrodynamic model in spherical geometry, we show that the presence of either rotation or finite magnetic helicity is sufficient to induce dynamical reversals of the magnetic dipole moment. The statistical character of the model is similar to that of terrestrial magnetic field reversals, with the similarity being stronger when rotation is present. The connection between long-time correlations, 1/f noise, and statistics of reversals is supported, consistent with earlier suggestions.

Long-term memory in experiments and numerical simulations of hydrodynamic and magnetohydrodynamic turbulence.

We analyze time series stemming from experiments and direct numerical simulations of hydrodynamic and magnetohydrodynamic turbulence. Simulations are done in periodic boxes, but with a volumetric forcing chosen to mimic the geometry of the flow in the experiments, the von Kármán swirling flow between two counterrotating impellers. Parameters in the simulations are chosen to (within computational limitations) allow comparisons between the experiments and the numerical results. Conducting fluids are considered in all cases. Two different configurations are considered: a case with a weak externally imposed magnetic field and a case with self-sustained magnetic fields. Evidence of long-term memory and 1/f noise is observed in experiments and simulations, in the case with weak magnetic field associated with the hydrodynamic behavior of the shear layer in the von Kármán flow, and in the dynamo case associated with slow magnetohydrodynamic behavior of the large-scale magnetic field.

Cancellation properties in Hall magnetohydrodynamics with a strong guide magnetic field.

We present a signed measure analysis of compressible Hall magnetohydrodynamic turbulence with an external guide field. Signed measure analysis allows us to characterize the scaling behavior of the sign-oscillating flow structures and their geometrical properties (fractal dimensions of structures). A reduced numerical model, valid when a strong guide magnetic field is present, is used here. In order to discuss the effect of the Hall term, different values for the ion skin depth are considered in the simulations. Results show that as the Hall term is increased, the fractal dimension of the current and vorticity sheets decreases. This observation, together with previous analysis of the same fields, provides a comprehensive description of the effect of the Hall force on the formation of structures. Two main processes are identified, namely, the widening and unraveling of the sheets.

Emergence of very long time fluctuations and 1/f noise in ideal flows.

This paper shows the connection between three previously observed but seemingly unrelated phenomena in hydrodynamic (HD) and magnetohydrodynamic (MHD) turbulent flows, involving the emergence of fluctuations occurring on very long time scales: the low-frequency 1/f noise in the power frequency spectrum, the delayed ergodicity of complex valued amplitude fluctuations in wave number space, and the spontaneous flippings or reversals of large-scale fields. Direct numerical simulations of ideal MHD and HD are employed in three space dimensions, at low resolution, for long periods of time, and with high accuracy to study several cases: different geometries, presence of rotation and/or a uniform magnetic field, and different values of the associated conserved global quantities. It is conjectured that the origin of all these long-time phenomena is rooted in the interaction of the longest wavelength fluctuations available to the system, with fluctuations at much smaller scales. The strength of this nonlocal interaction is controlled either by the existence of conserved global quantities with a back-transfer in Fourier space or by the presence of a slow manifold in the dynamics.

Large-scale behavior and statistical equilibria in rotating flows.

We examine long-time properties of the ideal dynamics of three-dimensional flows, in the presence or not of an imposed solid-body rotation and with or without helicity (velocity-vorticity correlation). In all cases, the results agree with the isotropic predictions stemming from statistical mechanics. No accumulation of excitation occurs in the large scales, although, in the dissipative rotating case, anisotropy and accumulation, in the form of an inverse cascade of energy, are known to occur. We attribute this latter discrepancy to the linearity of the term responsible for the emergence of inertial waves. At intermediate times, inertial energy spectra emerge that differ somewhat from classical wave-turbulence expectations and with a trace of large-scale excitation that goes away for long times. These results are discussed in the context of partial two dimensionalization of the flow undergoing strong rotation as advocated by several authors.

Waiting-time distributions of magnetic discontinuities: clustering or Poisson process?

Using solar wind data from the Advanced Composition Explorer spacecraft, with the support of Hall magnetohydrodynamic simulations, the waiting-time distributions of magnetic discontinuities have been analyzed. A possible phenomenon of clusterization of these discontinuities is studied in detail. We perform a local Poisson's analysis in order to establish if these intermittent events are randomly distributed or not. Possible implications about the nature of solar wind discontinuities are discussed.

Magnetic reconnection in two-dimensional magnetohydrodynamic turbulence.

Systematic analysis of numerical simulations of two-dimensional magnetohydrodynamic turbulence reveals the presence of a large number of X-type neutral points where magnetic reconnection occurs. We examine the statistical properties of this ensemble of reconnection events that are spontaneously generated by turbulence. The associated reconnection rates are distributed over a wide range of values and scales with the geometry of the diffusion region. Locally, these events can be described through a variant of the Sweet-Parker model, in which the parameters are externally controlled by turbulence. This new perspective on reconnection is relevant in space and astrophysical contexts, where plasma is generally in a fully turbulent regime.

Rapid alignment of velocity and magnetic field in magnetohydrodynamic turbulence.

We show that local directional alignment of the velocity and magnetic field fluctuations occurs rapidly in magnetohydrodynamics for a variety of parameters and is seen both in direct numerical simulations and in solar wind data. The phenomenon is due to an alignment between magnetic field and gradients of either pressure or kinetic energy, and is similar to alignment of velocity and vorticity in Navier-Stokes turbulence. This rapid and robust relaxation process leads to a local weakening of nonlinear terms.

Depression of nonlinearity in decaying isotropic MHD turbulence.

Spectral method simulations show that undriven magnetohydrodynamic turbulence spontaneously generates coherent spatial correlations of several types, associated with local Beltrami fields, directional alignment of velocity and magnetic fields, and antialignment of magnetic and fluid acceleration components. These correlations suppress nonlinearity to levels lower than what is obtained from Gaussian fields, and occur in spatial patches. We suggest that this rapid relaxation leads to non-Gaussian statistics and spatial intermittency.

Scaling Law for the Heating of Solar Coronal Loops.

We report preliminary results from a series of numerical simulations of the reduced magnetohydrodynamic equations used to describe the dynamics of magnetic loops in active regions of the solar corona. A stationary velocity field is applied at the photospheric boundaries to imitate the driving action of granule motions. A turbulent stationary regime is reached, characterized by a broadband power spectrum Ek approximately k-3&solm0;2 and heating rate levels compatible with the energy requirements of active region loops. A dimensional analysis of the equations indicates that their solutions are determined by two dimensionless parameters: the Reynolds number and the ratio between the Alfvén time and the photospheric turnover time. From a series of simulations for different values of this ratio, we determine how the heating rate scales with the physical parameters of the problem, which might be useful for an observational test of this model.