Long-time properties of MHD turbulence and the role of symmetries

We investigate long-time properties of three-dimensional MHD turbulence in the absence of forcing and examine in particular the role played by the quadratic invariants of the system and by the symmetries of the initial configurations. We observe that, when sufficient accuracy is used, initial conditions with a high degree of symmetries, as in the absence of helicity, do not travel through parameter space over time whereas by perturbing these solutions either explicitly or implicitly using for example single precision for long times, the flows depart from their original behavior and can become either strongly helical, or have a strong alignment between the velocity and the magnetic field. When the symmetries are broken, the flows evolve towards different end states, as predicted by statistical arguments for non-dissipative systems with the addition of an energy minimization principle, as already analyzed in \cite{stribling_90} for random initial conditions using a moderate number of Fourier modes. Furthermore, the alignment properties of these flows, between velocity, vorticity, magnetic potential, induction and current, correspond to the dominance of two main regimes, one helically dominated and one in quasi-equipartition of kinetic and magnetic energy. We also contrast the scaling of the ratio of magnetic energy to kinetic energy as a function of wavenumber to the ratio of eddy turn-over time to Alfv\'en time as a function of wavenumber. We find that the former ratio is constant with an approximate equipartition for scales smaller than the largest scale of the flow whereas the ratio of time scales increases with increasing wavenumber.Comment: 14 pages, 6 figure

Inverse cascade behavior in freely decaying two-dimensional fluid turbulence

We present results from an ensemble of 50 runs of two-dimensional hydrodynamic turbulence with spatial resolution of 2048^2 grid points, and from an ensemble of 10 runs with 4096^2 grid points. All runs in each ensemble have random initial conditions with same initial integral scale, energy, enstrophy, and Reynolds number. When both ensemble- and time-averaged, inverse energy cascade behavior is observed, even in the absence of external mechanical forcing: the energy spectrum at scales larger than the characteristic scale of the flow follows a k^(-5/3) law, with negative flux, together with a k^(-3) law at smaller scales, and a positive flux of enstrophy. The source of energy for this behavior comes from the modal energy around the energy containing scale at t=0. The results shed some light into connections between decaying and forced turbulence, and into recent controversies in experimental studies of two-dimensional and magnetohydrodynamic turbulent flows.Comment: 7 pages, 6 figure

A Turbulent Model for the Interstellar Medium. II. Magnetic Fields and Rotation

We present results from two-dimensional numerical simulations of a supersonic turbulent flow in the plane of the galactic disk, incorporating shear, thresholded and discrete star formation (SF), self-gravity, rotation and magnetic fields. A test of the model in the linear regime supports the results of the linear theory of Elmegreen (1991). In the fully nonlinear turbulent regime, while some results of the linear theory persist, new effects also emerge. Some exclusively nonlinear effects are: a) Even though there is no dynamo in 2D, the simulations are able to maintain or increase their net magnetic energy in the presence of a seed uniform azimuthal component. b) A well-defined power-law magnetic spectrum and an inverse magnetic cascade are observed in the simulations, indicating full MHD turbulence. Thus, magnetic field energy is generated in regions of SF and cascades up to the largest scales. c) The field has a slight but noticeable tendency to be aligned with density features. d) The magnetic field prevents HII regions from expanding freely, as in the recent results of Slavin \& Cox (1993). e) A tendency to exhibit {\it less} filamentary structures at stronger values of the uniform component of the magnetic field is present in several magnetic runs. f) For fiducial values of the parameters, the flow in general appears to be in rough equipartition between magnetic and kinetic energy. There is no clear domination of either the magnetic or the inertial forces. g) A median value of the magnetic field strength within clouds is $\sim 12\mu$G, while for the intercloud medium a value of $\sim 3\mu$G is found. Maximum contrasts of up to a factor of $\sim 10$ are observed.Comment: Plain TeX file, 25 pages. Gzipped, tarred set of Tex file plus 17 figures and 3 tables (Postscript) available at ftp://kepler.astroscu.unam.mx/incoming/enro/papers/mhdgturb.tar.g

Turbulence comes in bursts in stably stratified flows

There is a clear distinction between simple laminar and complex turbulent fluids. But in some cases, as for the nocturnal planetary boundary layer, a stable and well-ordered flow can develop intense and sporadic bursts of turbulent activity which disappear slowly in time. This phenomenon is ill-understood and poorly modeled; and yet, it is central to our understanding of weather and climate dynamics. We present here a simple model which shows that in stably stratified turbulence, the stronger bursts can occur when the flow is expected to be more stable. The bursts are generated by a rapid non-linear amplification of energy stored in waves, and are associated with energetic interchanges between vertical velocity and temperature (or density) fluctuations. Direct numerical simulations on grids of 2048^3 points confirm this somewhat paradoxical result of measurably stronger events for more stable flows, displayed not only in the temperature and vertical velocity derivatives, but also in the amplitude of the fields themselves

Generation of turbulence through frontogenesis in sheared stratified flows

The large-scale structures in the ocean and the atmosphere are in geostrophic balance, and a conduit must be found to channel the energy to the small scales where it can be dissipated. In turbulence this takes the form of an energy cascade, whereas one possible mechanism in a balanced flow at large scales is through the formation of fronts, a common occurrence in geophysical dynamics. We show in this paper that an iconic configuration in laboratory and numerical experiments for the study of turbulence, that of the Taylor-Green or von K\'arm\'an swirling flow, can be suitably adapted to the case of fluids with large aspect ratios, leading to the creation of an imposed large-scale vertical shear. To this effect we use direct numerical simulations of the Boussinesq equations without net rotation and with no small-scale modeling, and with this idealized Taylor-Green set-up. Various grid spacings are used, up to $2048^2\times 256$ spatial points. The grids are always isotropic, with box aspect ratios of either $1:4$ or $1:8$. We find that when shear and stratification are comparable, the imposed shear layer resulting from the forcing leads to the formation of multiple fronts and filaments which destabilize and further evolve into a turbulent flow in the bulk, with a sizable amount of dissipation and mixing, and with a cycle of front creation, instability, and development of turbulence. The results depend on the vertical length scales for shear and for stratification, with stronger large-scale gradients being generated when the two length scales are comparable.Comment: 19 pages, 15 figures, several simulations added in this new versio

Highly Compressible MHD Turbulence and Gravitational Collapse

We investigate the properties of highly compressible turbulence and its ability to produce self-gravitating structures. The compressibility is parameterized by an effective polytropic exponent gama-eff. In the limit of small gama-eff, the density jump at shocks is shown to be of the order of e^{M^2}, and the production of vorticity by the nonlinear terms appears to be negligible. In the presence of self-gravity, we suggest that turbulence can produce bound structures for gama-eff < 2(1-1/n), where 'n' is the typical dimensionality of the turbulent compressions. We show, by means of numerical simulations, that, for sufficiently small gama-eff, small-scale turbulent density fluctuations eventually collapse even though the medium is globally stable. This result is preserved in the presence of a magnetic field for supercritical mass-to-flux ratios.Comment: 4 pages, 3 postscript figures. Latex, uses aipproc.sty Contribution to the Conference Proc. of the 7th Annual Astrophysics Conference in Maryland, STAR FORMATION, NEAR AND FAR, eds. Stephen S. Holt and Lee G. Mund