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Direct numerical simulations of magnetohydrodynamic flows with regular grids of up to 1536 3 points and at a unit magnetic Prandtl number allow for an investigation of the rate at which small scales develop. No forcing term is included and computations for both deterministic and random initial conditions are reported. Parallel current and vorticity sheets form at the same spatial locations, with a strong degree of correlation; these sheets further destabilize and fold or roll-up after an initial exponential growth phase. At high Reynolds numbers, a self-similar evolution of the current and vorticity maxima is found; these maxima grow as a cubic power of time within localized structures. The flow then reaches a finite dissipation rate independent of Reynolds number as was also found in MHD in two space dimensions. This evolution may be linked to the degree of nonlocality of nonlinear interactions in turbulent flows, to the amount of velocity-magnetic field correlation, and to the possibility of occurrence of non-universal behavior in MHD turbulence. [ABSTRACT FROM AUTHOR]

Direct numerical simulations of hydrodynamical turbulence are performed in the presence of a large-scale forcing up to Taylor-based Reynolds numbers of 800 for a Taylor-Green flow and 1000 for ABC forcing. Statistics on the triadic interactions responsible for the transfer of energy, and on their integrated counterparts are obtained from simulations with a turbulent steady state integrated for more than ten eddy turn-over times. The maximum resolution of the runs performed on regular grids are 10243 points. It is shown that the energy transfer is local but at the highest resolution as much as 20% of it comes from non-local interactions involving widely separated scales, with a particular emphasis on the forcing scale k0/-1. The scaling of the ratio of nonlocal to local energy flux with Reynolds number is found to be a power law. [ABSTRACT FROM AUTHOR]

It is often observed that when a wind of relatively modest speed blows over the surface of a large body of water (stably stratified), a large scale circulation consisting of a system of parallel wind-aligned rolls takes place. One of the most accepted models suggests that this circulation results from an instability caused by a forcing due to small scale surface gravity waves; We investigate the onset of the circulation by means of an initial value approach and show that only in particular cases is the model able to reproduce a circulation similar to that which is observed in lakes or oceans. [ABSTRACT FROM AUTHOR]

We derive a uniform system of equations for three-dimensional Alfvén waves in the long-wavelength limit, which generalizes the DNLS equation and remains valid when sonic and Alfvén waves have the same phase velocity. Depending on the longitudinal and transverse length scales, this system describes both Alfvén wave filamentation and shock formation for magnetosonic waves. [ABSTRACT FROM AUTHOR]

We present 21/2D simulations of the evolution of a vortex in the solar wind in the form of a comparison of three models: (1) MHD with dissipation, (2) MHD with the dispersive Hall term but no dissipation, and (3) hybrid simulations which treat ions as particles and electrons as a fluid. At large scales all three models predict that the vortex distorts due to a pressure imbalance and forms shock-like structures within which the current and vorticity grow. In the MHD-Hall and hybrid simulations, short wavelength dispersive waves are generated in these structures. [ABSTRACT FROM AUTHOR]

The solar corona must be built up by a large number of small scale current sheets where magnetic energy is efficiently dissipated. In this paper we discuss possible mechanisms responsible for the formation of such small scales and we support the idea that different aspects of solar activity can be understood within the unifying framework of MHD turbulence. [ABSTRACT FROM AUTHOR]

The magnetic shear instability appears to be a workable mechanism for generating turbulence in accretion discs. The magnetic field, in turn, is generated by a dynamo process that taps energy from the Keplerian shear flow. Large scale magnetic fields are generated, whose strength is comparable with, or in excess of, the turbulent kinetic energy. Such models enable us to investigate the detailed nature of turbulence in discs. We discuss in particular the possibility of generating convection, where the heat source is viscous and magnetic heating in the bulk of the disc. [ABSTRACT FROM AUTHOR]

The disordered motions of the interstellar medium exhibit some of the properties of incompressible turbulence at large Reynolds numbers. These properties, however, are at odds with the large compressibility of the gas, the multiplicity of its energy sources, and the major role played by self-gravity in its dynamical evolution. The detection of possible specific signatures of turbulence in the line profiles of interstellar clouds and of imprints of intermittency in their chemistry leads to the tentative conclusion that, despite the complexity of the medium, turbulence taken as a most general concept, generates velocity patterns which are present in the interstellar medium. [ABSTRACT FROM AUTHOR]

The formation of thin current sheets is believed to play an important role in many space and astrophysical plasma phenomena, including transport and conversion of magnetic to kinetic energy in stellar and magnetospheric activity. The Earth's magnetosphere is an appropriate environment for the in-situ study of these phenomena. Thin current sheets form typically when a smooth current sheet is perturbed by external forces. The result is a double structure with a thin current sheet embedded in a broader one. A simple example leading to a double structure is analyzed. Resistive instabilities typically involve thin current sheets also. When the Earth's magnetapause becomes resistivelly unstable due to localized resistive "patches", a fast unstable dynamical process occurs which leads to magnetic opening and complicated 3D magnetic structures involving thin current sheets. As magnetic flux is transferred to the magnetotail the plasma sheet compresses and the tail current density increases. However, a smoothly distributed current cannot explain the observed signatures of a resistive (or a corresponding kinetic) instability. Recently, observations have indicated that a double structure forms. That processes can be recovered in a simple model based on slow adiabatic evolutions, and the mechanism can be identified. Thin current sheet forming in the magnetotail before onset of the tail instability has played the role of a "missing link" in the theory of magnetospheric activity. [ABSTRACT FROM AUTHOR]

The nonlinear evolution of the flow field in a 1D (galaxy-)model is followed under the presence of the newly established γ-effect. The latter appears in the Reynolds equation as a non-diffusive part if an anisotropic turbulence is subject to a global rotation. The same part of the turbulence correlation tensor is reflected as the wellknown MHD α-effect. The resulting flow pattern is rotating with a period of a few Myr, it is antisymmetric with respect to the equator and has a maximal value of a few dozens of km/s. [ABSTRACT FROM AUTHOR]

All known fast dynamos where diffusion has been explicitly included exhibit eigenfunctions with fine structures whose characteristic sizes apparently scale as Rm−1/2, where Rm is the magnetic Reynolds number. Results for a number of such calculations are summarised, including cases with and without stagnation points, in Cartesian and spherical geometries. In all cases there is agreement with the conclusion of Moffatt and Proctor (1985) that fast dynamos can only occur where such fine structures are present. However, the fraction of space occupied by these structures tends to zero as Rm→∞, and the associated Lorentz force becomes infinite. There are thus paradoxes in considering the kinematic problem in this limit, and an astrophysically meaningful calculation must embody the back reaction of the magnetic field on the flow dynamics. [ABSTRACT FROM AUTHOR]

Reconnection of magnetic fluxtubes is an important energy conversion process in many solar coronal events. We here describe several recent advances that we have made in the numerical simulation of this process. The numerical simulations are carried out using a new version of our algorithm for solving the viscoresistive equations of compressible magnetohydrodynamics. The algorithm has been parallelized for the Connection Machine CM5. We present numerical simulations at a resolution of 1283 Fourier modes of the reconnection of initially orthogonal, uniform twist, force-free, magnetic fluxtubes. We describe the physical model and some preliminary simulation results. A discussion of parallelism issues related to our algorithm is also presented. [ABSTRACT FROM AUTHOR]

We discuss the selfsimilar solutions of MHD equations, when the Hall's effect is incorporated into the Ohm's law. These solutions describe current sheet formation in the vicinities of magnetic field zero points, zero lines and separatrix surfaces. We present the results of computer simulations of 2(1/2)D —MHD flows near the X- line of the magnetic field. We demonstrate that the Hall's effect makes the zero points to shift into the direction of electron component motion and leads to magnetic island formation. [ABSTRACT FROM AUTHOR]

Considerable controversy exists as to whether Petschek's solution for fast reconnection actually occurs in nature or even whether it is a valid solution of the MHD equations. This paper argues that Petschek's mechanism is a mathematically consistent solution, though not necessarily a stable one. Furthermore, Petschek's mechanism is not the only type of fast reconnection which can occur, and it may very well be that it does not typically occur in nature. Other types of reconnection such as flux-pile-up, where the field is strongly compressed by an external flow, may be more common. Even the slow type of reconnection originally proposed by Sweet and Parker may be fast if the effective electrical resistivity is determined by turbulent processes rather than laminar ones. [ABSTRACT FROM AUTHOR]

In two dimensions the theory of magnetic reconnection is now highly developed and fairly well understood. A general configuration will contain X-type neutral points and separatrix field lines which link to it. Reconnection occurs by the breaking and rejoining of field lines at the X-point and the transfer of flux across the separatrices from one topological region to another. In three dimensions the process is completely different! Several types of null point now exist but they have a common skeleton of field lines that link to it, consisting of an isolated spine curve and a fan surface. When a null point is present in a three-dimensional configuration, separatrix surfaces may be defined separating topologically distinct regions. However, two quite distinct types of reconnection are possible depending on the boundary conditions. "Spine reconnection" has a singular jetting flow along the spine curve and "fan reconnection" has a singular swirling flow at the fan surface. When there are no null points in the configuration, a difficulty arises since there are no separatrices and all field lines are topologically equivalent. It has been discovered, However, that reconnection can still take place, since the mapping of field lines from one part of the surface enclosing a finite volume to another reveals the presence of "quasi-separatrix layers". Here the mapping function has extremely steep gradients and the field lines can slip rapidly through the plasma by a process of "magnetic flipping". [ABSTRACT FROM AUTHOR]

The Hamiltonian structure of the two-fluid equations that describe nonlinear low-frequency phenomena in a plasma with large thermal ion gyroradius is investigated. When the system is energetically closed, the energy functional is the Hamiltonian and non-canonical Poisson brackets can be defined. The system possesses two infinite sets of invariants (Casimirs) that arise from the structure of the equations. They reflect the invariance of the topology of the configuration. The plasma dynamics in the neighbourhood of critical points (X- and O-points) of the magnetic configuration is investigated in terms of scale-invariant equations. Their solutions correspond to open systems which, in general, do not have well defined Casimirs. However, the scale-invariant members of the families of Casimirs of the closed system survive. These surviving elements are not related to simple power expansions in the fields. When the fields are analytical, they can be expressed as polynomials and the system has a finite number of degrees of freedom. This truncated system is Hamiltonian and integrable. Most of the initial structures lead to a collapse of the magnetic separatrices with a velocity that grows as (t−t0)−1 [ABSTRACT FROM AUTHOR]

Long-term self-similar behavior is exhibited in high-resolution numerical solutions of decaying turbulent two-dimensional magnetohydrodynamics. Random initial conditions produce coherent structures which dominate the fluid dynamics. During the self-similar evolution, current monopoles (magnetic vortices) with an accompanying vorticity distribution (which is axisymmetric but not necessarily monotonic) emerge spontaneously. Thin current and vorticity sheets are created as a result of close encounters between the vortices. The sheets are sites of current enstrophy production, conversion into kinetic enstrophy, and dissipation, all of which maintain constant ratios but which produce no net change in the total enstrophy. The chief mechanism for removal of enstrophy is the disappearance of magnetic vortices during coalescence. [ABSTRACT FROM AUTHOR]

Using direct numerical simulation results we discuss how the presence of a dc magnetic field (B0) in initially isotropic turbulent magnetohydrodynamic (MHD) flows leads to anisotropy in the small-scale velocity and magnetic fields. In such cases, the small-scale vorticity and current structures tend to elongate and align with B0. The incompressible behaviour is also compared to weakly compressible results (sonic Mach number <0.5). The simulations indicate that while density and longitudinal pressure fluctuations remain isotropic for the compressible systems, the v and b fluctuations behave quite similarly to their incompressible counterparts, exhibiting substantial anisotropies even at the modest Reynolds numbers employed here. [ABSTRACT FROM AUTHOR]

Recent work concerning magnetohydrodynamic (MHD) turbulence with net electric currents is reviewed. Most of the problems considered derive from those encountered in toroidal confinement devices. In the presence of net currents and externally imposed dc magnetic fields, the standard symmetries of "homogeneous turbulence" theory do not apply, and spatially periodic boundary conditions may not be invoked. The turbulence which results tends to be less than fully developed, and its properties are not controlled by Reynolds-like numbers alone. Its description requires occasional departures from the strict MHD framework. Recognizable structures are plentiful in unstable regimes, and include paired helical vortices and helical distortions of the current channel; these may be "large scale" or "small scale", depending upon the value of the on-axis Hartmann number at which the pinch ratio is raised above its critical value. Plasma rotation, due to departures from strict charge neutrality, may be used to suppress this MHD activity. Unsolved problems in microscopic plasma kinetic theory add uncertainty to the macroscopic MHD predictions, particularly in connection with the viscous stress tensor. [ABSTRACT FROM AUTHOR]

We propose an anisotropic modification to the dynamic Subgrid Scale Model for Large Eddy Simulations. The essential feature is that the principal axes of the SGS stress tensor that has to be modelled are not forced to be parallel to the resolved stress tensor's ones. In this way new degrees of freedom are introduced that reduce the isotropy requirements on the small scale structures. As a consequence coarser grids can be used to obtain the same accuracy of previous models. Numerical results for the plane channel flow using centered finite differences are presented. The computations are performed whithout averaging the model coefficients in space and time. This makes the results more accurate although the method is some-what less robust. We show that for the same numerical grid the new anisotropic model gives more accurate results compared to standard dynamic SGS models, especially near the walls, where the turbulence is highly anisotropic. We turn next to the modelling of the outlet boundary conditions. We present a new 3D development of boundary conditions that is an extension of a previous 2D model (Jin and Braza 1993). We show on numerical tests of a flow in an annulus that our boundary conditions are totally absorbing both for the velocity field and for a passive scalar. [ABSTRACT FROM AUTHOR]

The behavior of turbulent boundary layer over a flat bottom and a scour hole, in the presence of a cylindrical obstacle normal to the bottom has been investigated. This has been done through flow visualizations. The flow structures in the flat bottom and in the scour hole cases have been compared. The dominant features of the vortex structure in terms of the number of the principal vortices and critical lines have been taken as the main flow parameters. The flow fields, with different Reynolds numbers, have also been compared. The Poincare-Bendixon theorem, modified for a 3D body attached to a surface, has been verified by means of the flow visualizations. [ABSTRACT FROM AUTHOR]

Vertical transport is reduced in a fluid stratified along the vertical direction, and this effect is generally ascribed to suppression of vertical modes by stratification. An additional mechanism, discussed in this paper, consists in inhibition of vertical transport by horizontal homogeneization. Though this mechanism, three-dimensional modes which have not been suppressed are made ineffective for vertical transport. [ABSTRACT FROM AUTHOR]

We examine the effects of stratification on eddy—diffusion, and the distribution of pairs of particles released in the flow. DNS results are presented at a resolution of 1283 mesh points. We compare results for particle dispersion to simple analytic theories (such as that proposed by Csanady 1964, and Pearson et al., 1983) by adapting the basic Langevin model to decaying turbulence at low Reynolds numbers. Stable stratification arrests both single particle displacements and pair separation in the direction of stratification. With respect to the dynamics of stratified flows, we find that regions of strong viscous dissipation are intermittently spaced, and are associated with large horizontal vorticity, consistent with recent experimental results by Fincham et al. (1994). The small-scale structures of the flow are pancakes, not worms. As found in previous simulations (Métais et al 1994), vortex filaments develop only under the constraint of strong rotation. [ABSTRACT FROM AUTHOR]

The passive convection of Lagrangian points by a 2D compressible two-fluids flow is investigated numerically on a massively parallel computer. This numerical simulation concerns the Rayleigh-Taylor instability [1]. We compute the fractal dimension of this set of tracer particles located along the interface between the two fluids. A first result is that this dimension reaches a stationary value. Then this result is used to determine the effective opacity of the mixture. In the second part we study the morphology of the mixing layer via the wavelet transform of the density field. The multifractal analysis is discussed. [ABSTRACT FROM AUTHOR]

An experimental analysis of the longitudinal and transverse velocity components is conducted at moderate Reγ and in the homogenous and non-homogeneous region of a grid-generated turbulent flow. The scaling properties and the intermittency exponents (for p≤6) of the velocity structure functions are investigated by means of the Extended Self-Similarity method (ESS). A comparison of the longitudinal and transverse scaling exponents is then performed and discussed in addition to the analysis of the scaling transition at small scales. [ABSTRACT FROM AUTHOR]

We investigate the so-called inductive closure relation given by Reichardt for mean turbulent momentum transport in jets (1941). It is shown to be in good agreement with measurements in the axisymmetric jet by Panchapakesan and Lumley (1993). Despite these results, it is conjectured that there is a lack of account for intermittency effects which is hidden by the experimental procedure of Panchapakesan and Lumley. Intermittency corrections are then proposed, based on the classical concept of intermittency factor and the corrected model is compared with the results of Bradbury (1965) for the plane jet. The agreement with experimental measurements appears to be very good. The underlying picture of the Reichardt 1941 model is discussed, mainly the fact that it expresses the self-injection of kinetic energy by the jet and the conversion of longitudinal into lateral momentum thus providing entrainment of the surrounding fluid. [ABSTRACT FROM AUTHOR]

We construct a (chaotic) deterministic variant of random multiplicative cascade models of turbulence. It preserves the hierarchical tree structure, thanks to the addition of infinitesimal noise or finite-state Markov approximations of chaotic maps. The zero-noise limit can be handled by Perron-Frobenius theory, just as the zero-diffusivivity limit for the fast dynamo problem. We prove also the absence of phase transitions in conservative random multiplicative cascade models, corresponding to the non divergence of statistical moments. [ABSTRACT FROM AUTHOR]