Roland Grappin

Spectral Energy Dynamics in Magnetohydrodynamic Turbulence

Spectral direct numerical simulations of incompressible MHD turbulence at a resolution of up to 1024(3) collocation points are presented for a statistically isotropic system as well as for a setup with an imposed strong mean magnetic field. The spectra of residual energy, E(R)k=|E(M)k - E(K)k|, and total energy, Ek=E(K)k+E(M)k, are observed to scale self-similarly in the inertial range as E(R)k approximately k(-7/3), E(k)approximately k(-5/3) (isotropic case) and E(R)(k(perpendicular) approximately k(-2)(perpendicular), E(k(perpendicular))approximately k(-3/2)(perpendicular) (anisotropic case, perpendicular to the mean field direction). A model of dynamic equilibrium between kinetic and magnetic energy, based on the corresponding evolution equations of the eddy-damped quasinormal Markovian closure approximation, explains the findings. The assumed interplay of turbulent dynamo and Alfvén effect yields E(R)k approximately kE2(k), which is confirmed by the simulations.

Statistical anisotropy of magnetohydrodynamic turbulence.

Direct numerical simulations of decaying and forced magnetohydrodynamic (MHD) turbulence without and with mean magnetic field are analyzed by higher-order two-point statistics. The turbulence exhibits statistical anisotropy with respect to the direction of the local magnetic field even in the case of global isotropy. A mean magnetic field reduces the parallel-field dynamics while in the perpendicular direction a gradual transition towards two-dimensional MHD turbulence is observed with k(-3/2) inertial-range scaling of the perpendicular energy spectrum. An intermittency model based on the log-Poisson approach, zeta(p)=p/g(2)+1-(1/g)(p/g), is able to describe the observed structure function scalings.

Waves and streams in the expanding solar wind

The expanding box model (EBM) allows the simulation of the evolution of compressible MHD turbulence within the expanding solar wind, taking into account the basic properties of expansion. Using the EBM we follow the evolution of waves within a compressive stream shear and magnetic sector structure in the range of 0.1 to 1 AU from the Sun. We analyze the physical processes which lead in these simulations to the modulation and erosion of the wave component, combined with WKB and non-WKB processes due to expansion. A strong erosion by stream shear corresponds indeed to one of the observed regimes in the solar wind ; however, we are unable to reproduce the regime which holds during solar minimum, in which the correlation between large-scale stream structure and turbulence remains high independently from distance to the Sun. The main point of disagreement with observations concerns the energy spectrum (it is difficult to generate and sustain small-scale turbulence with an Alfvenic wave band present, and even more so in an expanding medium) ; the main point of agreement concerns the statistics of density fluctuations, which are independent of distance, and matches the observed amplitudes both within slow and fast wind. At the same time, small scales appear to be dominated in the simulations by compressible effects, which contradicts popular ideas on solar wind turbulence.

COUPLING THE SOLAR DYNAMO AND THE CORONA: WIND PROPERTIES, MASS, AND MOMENTUM LOSSES DURING AN ACTIVITY CYCLE

We study the connections between the Suns convection zone and the evolution of the solar wind and corona. We let the magnetic fields generated by a 2.5-dimensional (2.5D) axisymmetric kinematic dynamo code (STELEM) evolve in a 2.5D axisymmetric coronal isothermal magnetohydrodynamic code (DIP). The computations cover an 11 year activity cycle. The solar winds asymptotic velocity varies in latitude and in time in good agreement with the available observations. The magnetic polarity reversal happens at different paces at different coronal heights. Overall the Suns mass-loss rate, momentum flux, and magnetic braking torque vary considerably throughout the cycle. This cyclic modulation is determined by the latitudinal distribution of the sources of open flux and solar wind and the geometry of the Alfven surface. Wind sources and braking torque application zones also vary accordingly.

Hybrid simulations of the expanding solar wind: Temperatures and drift velocities

We study the evolution of the expanding solar wind using a onedimensional and a two-dimensional expanding box model [Grappin et al., 1993] implemented here within a hybrid code [Liewer et al., 2001]. We first consider a plasma with protons and 5 % of alpha particles, without drift between the protons and al phas, considering successively the low-beta and high-beta cases. Then we consider a strong drift between protons and alphas, again separately the low-beta and high-beta case. Without drift, the evolution of the low-beta plasma is adiabatic. In the high-beta pl asma without drift, the fire hose instabilities disrupt the adiab atic evolution. Finally, with a drift, the adiabatic evolution is stop ped by the

Hybrid simulations of the magnetosheath compression: Marginal stability path

This paper reports a two-dimensional hybrid simulation study which utilizes an expanding box model to represent the slow com- pression of the plasma as it flows through the magnetosheath. In the code we model the compression as an external force: The phys- ical sizes of the simulation box decrease with time. We present results of a simulation which starts in a parameter region of low beta where the plasma is stable with respect to both the Alfven ion cyclotron (AIC) and mirror instabilities. In this stable re gion the plasma behaves double-adiabatically and an important proton tem- perature anisotropy appears. When the plasma becomes unstable to AIC instability, the adiabatic behavior is broken and the AI C waves keep the system close to marginal stability, the theoretica l growth rate being about constant, small and positive. The AIC waves are continuously generated and the proton parallel beta increa ses with time. This marginal stability behavior is slightly disrupt ed for high proton parallel beta, where the mirror mode becomes unstable. The mirror waves rapidly grow and coexist with AIC wave, in later times the growth of AIC waves is inhibited and mirror waves be- come dominant. During the stages dominated by AIC and mirror waves, anticorrelation between anisotropy and proton para llel beta is observed. The hybrid expanding box simulation directly verifies the marginal stability evolution of the magnetosheath plasma.

Waves from the sun

Abstract Satellite observations of solar wind turbulence in the low frequency MHD domain show highly variable properties with respect to time and distance from the sun: one of the markers of this variability is the degree of “Alfvenicity”, which characterizes the relative level of quasi-incompressible waves propagating away from the sun. To answer the question of the origin and the evolution of this wave spectrum one must investigate the propagation of MHD fluctuations through the highly inhomogeneous and spherically expanding solar wind. Here we discuss some aspects both of the linear propagation before the critical point and of recent models for the evolution of the turbulence in the supersonic regions of the wind.

EVOLUTION OF TURBULENCE IN THE EXPANDING SOLAR WIND, A NUMERICAL STUDY

We study the evolution of turbulence in the solar wind by solving numerically the full 3D magneto-hydrodynamic (MHD) equations embedded in a radial mean wind. The corresponding equations (expanding box model or EBM) have been considered earlier but never integrated in 3D simulations. Here, we follow the development of turbulence from 0.2 AU up to about 1.5 AU. Starting with isotropic spectra scaling as

Scaling and anisotropy in magnetohydrodynamic turbulence in a strong mean magnetic field.

k^{-1}

Lyapunov exponents and the dimension of periodic incompressible Navier—Stokes flows: numerical measurements

, we observe a steepening toward a