H. Politano

Test particle study of minor ions in the solar wind

Using numerical simulations of test particles in a MHD turbulence model we investigate the influence of nonlinear effects in the interaction of MHD turbulence with minor ions. We conclude that non-linear interactions lead to an efficient heating of minor ions.

Intermittency in MHD Flows

Magnetic fields are ubiquitous in the Universe, often coupled to turbulent motions that are compressible as well. Most models do not take compressibility into account except for those relying on a Burgers—like approach; restricting the variations to one space dimension, several extensions to MHD of the Burgers equation have been proposed with various degrees of complexity. When retaining only one component of the velocity u x and of the magnetic field b y [1], one in fact may recover two Burgers equations for υ ± = u x ± b y with an extra dissipative term that couples them when the magnetic Prandtl number differs from unity.

Computer Simulation of Decaying Two-Dimensional Turbulence

It has early been realized that very high resolutions are required to simulate large Reynolds number turbulence, by direct numerical integration of the Navier-Stokes equation

Spiral small-scale structures in compressible turbulent flows

\begin{array}{*{20}{c}}{{\partial _t}V + V.\nabla V = - \nabla P + V\Delta V} \\ {\nabla .V = 0} \end{array}

A One-Dimensional MHD Model of Solar Flares: Statistics or Physics?

(1) Focussing on the internal dynamics rather than on the effects of special geometries, we assume periodic boundary conditions. We thus use spectral methods for the space variables. We concentrate here on the simulation of a turbulent flow at a resolution of (2048)2 collocation points, and especially on visualizations of the small scales of the flow. Computations at lower resolutions have been reported previously[1].

Vortex Tubes in Homogeneous Turbulence

A short review is given about the self‐consistent MHD model of solar coronal heating recently proposed by Bigot et al. (2008) in which the dynamical effect of the background magnetic field along a coronal structure is taken into account through exact results from Alfven wave turbulence. The main properties of the model are given as well as the heating rate and the microturbulent velocity obtained in the case of coronal loops. The conclusion is that Alfven wave turbulence may produce an efficient background heating for the solar corona.

Can Three-Dimensional Ideal Flows Become Singular in a Finite Time?

We extend the spiral vortex solution of Lundgren 1982 to compressible turbulent flows following a perfect gas law. Lundgren’s model links the dynamical and spectral properties of incompressible flows, providing a k −5/3 Kolmogorov spectrum. A similar compressible spatio-temporal transformation is now derived, reducing the dynamics of three-dimensional (3D) vortices stretched by an axisymmetric incompressible strain into a 2D compressible vortex dynamics. It enables to write the 3D spectra of the incompressible and compressible square velocities u s 2 and u d 2 in terms of, respectively, the 2D spectra of the enstrophy and of the square velocity divergence, by use of a temporal integration (Gomez a initially, the r.m.s. Mach number is 0.32, with local values up to 0.9, the Reynolds number is 1,400, and x=u s 2 /u d 2 =0.1. A k −5/3 inertial behaviour is seen to result from the dynamical evolution for both the compressible and incompressible three-dimensional kinetic energy spectra.

SMALL SCALE DYNAMICS OF AN INCOMPRESSIBLE MHD FLOW

In this paper the backreaction of a growing magnetic field in a nonlinear dynamo on the flow is investigated. The hypothesis that the magnetic field by the action of the Lorentz force supresses Lagrangian chaos of the flow is checked by direct numerical simulations of the MHD equations. As a measure of the level of chaos the Lyapunov exponent of a set of 128 × 128 trajectories of fluid particles is computed in the linear growth phase of the dynamo and in the saturated phase of the dynamo when the magnetic field has reached its final strength. The numerical code, based on a pseudospectral algorithm, is developed for parallel computation on a multiprocessor system (Cray-T3E). The trajectories for the computation of the Lyapunov exponent are advanced in a timestep parallel to the timestep of the MHD-solver. Magnetic Reynolds numbers up to 240 and scale separations between the wavelength of the hydrodynamical forcing and the scale of the computational domain up to four are reached. For the runs where the kinetic Reyold number is high enough that the hydrodynamical bifurcation sequence to a more chaotic flow already has taken place, the mean value of the Lyapunov exponent is noticeable diminished in the saturated phase compared to the growth phase of the dynamo.