Compressible magnetohydrodynamic turbulence: mode coupling, scaling relations, anisotropy, viscosity-damped regime and astrophysical implications

We present numerical simulations and explore scalings and anisotropy of compressible magnetohydrodynamic (MHD) turbulence. Our study covers both gas-pressure-dominated (high β) and magnetic-pressure-dominated (low β) plasmas at different Mach numbers. In addition, we present results for super-Alfvénic turbulence and discuss in what way it is similar to sub-Alfvénic turbulence. We describe a technique of separating different magnetohydrodynamic modes (slow, fast and Alfvén) and apply it to our simulations. We show that, for both high- and low-β cases, Alfvén and slow modes reveal a Kolmogorov   k ^−5/3  spectrum and scale-dependent Goldreich–Sridhar anisotropy, while fast modes exhibit a   k ^−3/2  spectrum and isotropy. We discuss the statistics of density fluctuations arising from MHD turbulence in different regimes. Our findings entail numerous astrophysical implications ranging from cosmic ray propagation to gamma ray bursts and star formation. In particular, we show that the rapid decay of turbulence reported by earlier researchers is not related to compressibility and mode coupling in MHD turbulence. In addition, we show that magnetic field enhancements and density enhancements are marginally correlated. Addressing the density structure of partially ionized interstellar gas on astronomical-unit scales, we show that the viscosity-damped regime of MHD turbulence that we reported earlier for incompressible flows persists for compressible turbulence and therefore may provide an explanation for these mysterious structures.     

Vorticity covariance in turbulence

In the Beltrami flow field, the rate of change of vorticity covariance has been discussed in the presence of magnetic field.     

A statistical description of astrophysical turbulence

The properties of the ISM indicate that it is turbulent. However, the ISM turbulence is radically different from that in incompressible fluids. That is why it is so important to study it through observations. The relevant study still poses a challenging problem. In the present paper recent results based on a statistical approach to the problem are surveyed. Although it was pointed out long ago (see Kaplanet al., 1970) that random 3D motions of the ISM gas result in fluctuations of the observed electromagnetic emission, it is only recently that the problem of recovering statistical properties of the ISM turbulence from the line integrated data was given an adequate mathematical treatment. Here by the example of studying turbulence in HI, it is shown that the inverse problem can be solved uniquely using a realistic model of the ISM. The application of theoretical conclusions to existing data explains some facts which used to be considered inconsistent with turbulent behaviour and reveals unexpected features of the ISM turbulence.     

Compressible turbulence in Hall Magnetohydrodynamics

By direct numerical simulations we investigate the nonlinear dynamics of a compressible Hall Magnetohydrodynamic (MHD) plasma. At small scales, where the Hall effect dominates, we found an increase of the compressibility of the system and the breakdown of the strong link between velocity and magnetic fields, typical of usual MHD. Moreover, we find that small-scale fluctuations are characterized by an anti-correlation between density and magnetic field intensity. These features characterize the excitation of a quasi-perpendicular magnetosonic turbulence that can be interpreted as the small-scale signature of the break-down of the MHD nonlinear energy cascade due to Hall effect. Fluctuations with the same properties, based on measurements by Cluster spacecraft in space plasma turbulence during different magnetopause crossings, have been recently observed.     

Coronal heating by prominence turbulence

The generation of magnetohydrodynamic waves in the corona by the observed random motions in prominences is considered. The associated energy input into the corona may be a significant source of heating for the coronal loops overlying prominences, especially during the onset of flares. Some relevant observations are discussed.     

Stellar turbulence and mode physics

An overview of selected topical problems on modelling oscillation properties in solar-like stars is presented. High-quality oscillation data from both space-borne intensity observations and ground-based spectroscopic measurements provide first tests of the still-ill-understood superficial layers in distant stars. Emphasis will be given to modelling the pulsation dynamics of the stellar surface layers, the stochastic excitation processes and the associated dynamics of the turbulent fluxes of heat and momentum.     

Three-wave turbulence in pulsar winds

Three-wave interactions can modify the very bright radio waves propagating through dense, magnetized pulsar winds and prevent radiation from escaping, or severely alter the resulting spectrum. Absence of the signatures of such effects in the very bright radio emission from pulsars implies constraints on the structure of their winds, especially for a spherically-symmetric wind which should block the radiation unless that Lorentz factor of the pairs is 8 × 10².Presented at the Cosmic Winds and the Heliosphere conference in Tucson, Arizona, U.S.A., October 18–22, 1993.     

Plasma acceleration by ion-acoustic turbulence

An energetic proton beam passing through a stationary ionized medium, excites ion-acoustic turbulence. The ion-acoustic instability saturates due to the non-linear indirect wave-particle scattering. The electric field associated with the ion-acoustic waves accelerates the plasma particles. Applicability of the results to cometary tails is discussed.     

Hydromagnetic turbulence in cometary plasmas

An instability associated with the magnetosonic wave driven unstable due to coupling with electron and ion drift modes has been considered as a potential source for driving the hydromagnetic turbulence observed in Giacobini-Zinner (G-Z) Cometary plasma. The instability has good growth rate for propagation perpendicular to plasma inhomogeneities and exists for all wave numbers. The wave period for waves propagating perpendicular to the gradients is about a few times ion-gyroperiod and higher values of plasma beta ( _e lead to stronger instability.     

Flux expulsion by inhomogeneous turbulence

Flux expulsion is an important consequence of the interaction of magnetic fields with fluid convection and has been well studied for particular cases of steady, single-cell flows. Here we examine a related phenomenon in inhomogeneous turbulence using direct numerical simulations. To understand our numerical results, we analyse average properties of our model, and obtain mean transport coefficients which can be used to describe the approach of the system to its final state. For the kinematic problem these transport coefficients give an excellent prediction of the expulsion process; however, the enhanced transport is suppressed by dynamical back-reaction of the Lorentz force. Finally, we discuss the astrophysical implications for magnetic fields in stellar convection zones. Segregation of magnetic fields from turbulent motion not only allows strong toroidal fields to accumulate in regions of convective overshoot but also permits significant poloidal fields to be maintained by dynamo action in stars like the Sun.     

Primeval turbulence from matter-antimatter annihilation

In a previous work by two of us, the main difficulties of the theory of galaxy formation from universal primordial cosmic turbulence were focussed; it was mainly found that the decay of the turbulence was so strong during the plasma era that turbulence should have been almost completely washed out before recombination, unless, and only for low-density universes, unlikely large turbulent velocities were postulated at the largest scale of the turbulence at the end of the radiation era. It was suggested that a possibility to turn around such a difficulty should consist in finding en adequate physical energy source feeding the turbulence during at least the whole plasma phase. The present work is intended to test whether matter-antimatter annihilation theory at the origin of the universe, as it is developed by Omnès and his collaborators, may be considered to yield the required energy source of the turbulence. To this aim, the main results of the work of Stecker and Puget concerning the behaviour of the most important quantities of the matter- antimatter annihilation theory are used, in order to describe the properties of the energy source for the turbulence down to recombination time, and extended to take a somewhat more detailed account of theirz and mean matter density dependences. The energy feeding source thus obtained is then introduced into the general framework of the galaxy formation theory from cosmic turbulence taking account of energy dissipation as developed in our previous works. The results obtained concerning the comparison of the main parameters of galaxies derived from the theory with the experimental data are much more satisfactory than in the previous approach, and show that, inside the errors of the present day values, sufficiently good fits are possible in a range of mean universe densities between 0.4 to 1 times the critical density.     

Unified approach to weak turbulence

A unifield formulation of weak homogeneous turbulence has been developed by introducing Bogoliubov's expansion method, known from the dynamical theory in statistical mechanics. It enables to close the hierarchy of the associated wave-correlation functions as well as to derive dynamical equations which statistically describe the nonlinear interaction of the different modes. The latter modes may have complex frequencies, connected with the linearized problem, corresponding to either stable or unstable modes, although the non-linearity has to be weak. For this model, some general properties such as energy conservation as well as special cases — e.g., resonant three-wave interaction, etc. — are discussed.     

Solar models with strong turbulence

A series of evolutionary models for the Sun were constructed using the strong turbulence model of the variable mixing-length theory (AMLT) of Canuto (1990). The present values of the solar model were obtained by an initial compositionX = 0.754,Z = 0.019, and(x) = 1.1. The physical variables which were obtained by applying the strong turbulence case of AMLT were similar to those of weak turbulence model (Kzlolu and Civelek, 1992) if we focused on the fitting of present solar radius and luminosity.     

Two spectra of turbulence of the sun

Observations obtained at the 70-cm vacuum tower telescope (VTT) at Izaña (Tenerife, Spain) are analyzed to show that turbulent processes in the solar photosphere have two distinct spectra of turbulence. The first is the well-known Kolmogorov spectrum, which describes plasmas with a zero mean magnetic field, and the second is the Kraichnan spectrum with a nonzero mean magnetic field. The transition from one spectrum type to another is found to occur at a scale of 3 Mm. This scale is consistent with the typical size of mesogranular structures, which indicates a transition to large-scale self-organizing magnetic structures.     

Effects of turbulence development in solar surges

Several authors have claimed for correlations between surges (dark features) and various kinds of solar emissions (radio, microwave, X-ray). In this paper we propose a model to explain such correlations, in particular presenting the properties of the instabilities resulting from the coupling between material flow, connected to the appearance of a surge, and magnetic field topology. As a consequence of such instability a turbulent energy cascade to small characteristic lengths grows up. Depending of the relevant parameters of the surge (dark feature), different regimes can be found, producing different levels of electrons acceleration and mass motion deceleration. We try then to correlate the different developments of the instability with the behavior observed in type I and type III radio bursts related to surges.Proceedings of the Second CERSA Workshop on Particle Acceleration and Trapping in Solar Flares, held at Aubigny-sur-Nère (France), 23–26 June, 1986.     

Simulations of multiphase turbulence in jet cocoons

The interaction of optically emitting clouds with warm X-ray gas and hot, tenuous radio plasma in radio jet cocoons is modelled by 2D compressible hydrodynamic simulations. The initial setup is the Kelvin–Helmholtz instability at a contact surface of density contrast 10⁴. The denser medium contains clouds of higher density. Optically thin radiation is realized via a cooling source term. The cool phase effectively extracts energy from the other gas which is both, radiated away and used for acceleration of the cold phase. This increases the system's cooling rate substantially and leads to a massively amplified cold mass dropout. We show that it is feasible, given small seed clouds of the order of  100 M_⊙  , that all of the optically emitting gas in a radio jet cocoon may be produced by this mechanism on the propagation time-scale of the jet. The mass is generally distributed as   T ^−1/2  with temperature, with a prominent peak at 14 000 K. This peak is likely to be related to the counteracting effects of shock heating and a strong rise in the cooling function. The volume filling factor of cold gas in this peak is of the order of  10⁻⁵–10⁻³  and generally increases during the simulation time.
The simulations tend towards an isotropic scale-free Kolmogorov-type energy spectrum over the simulation time-scale. We find the same Mach-number density relation as Kritsuk & Norman and show that this relation may explain the velocity widths of emission lines associated with high-redshift radio galaxies, if the environmental temperature is lower, or the jet-ambient density ratio is less extreme than in their low-redshift counterparts.     

Generation of atmospheric turbulence by solar radiation

A statistical framework of weak turbulence is applied to investigate the maintenance of atmospheric turbulence during a long period, even after the external energy supply from solar radiations has stopped. Thus, the problem of hydrodynamical turbulence without any mean motion is dealt with. Main attention is drawn to one-dimensional Burgers equation, together with a discussion devoted mainly to Millionshtchikov's hypothesis, which may be applied as a consequence of the assumed weak turbulence. Remarkably, this leads to an explicit proof of the existence of the cascade process in turbulence. The results are illustrated by numerical calculations.On study leave from the Department of Physics, M.S. College, Subaranpur, U.P., India.