Landau-fluid simulations of Alfvén-wave instabilities in a warm collisionless plasma

A dispersive Landau-fluid model is used to study the decay and modulational instabilities of circularly-polarized Alfvén waves in a collisionless plasma, as well as their nonlinear developments. Comparisons are presented with the drift-kinetic approximation for the dispersionless regime and with hybrid simulations in more general conditions. The effect of the nature of the instability on particle heating is discussed, together with the formation of coherent structures or the development of an inverse cascade

Cross-Newell equations for hexagons and triangles

The Cross-Newell equations for hexagons and triangles are derived for general real gradient systems, and are found to be in flux-divergence form. Specific examples of complex governing equations that give rise to hexagons and triangles and which have Lyapunov functionals are also considered, and explicit forms of the Cross-Newell equations are found in these cases. The general nongradient case is also discussed; in contrast with the gradient case, the equations are not flux-divergent. In all cases, the phase stability boundaries and modes of instability for general distorted hexagons and triangles can be recovered from the Cross-Newell equations.Comment: 24 pages, 1 figur

The Statistics of Supersonic Isothermal Turbulence

We present results of large-scale three-dimensional simulations of supersonic Euler turbulence with the piecewise parabolic method and multiple grid resolutions up to 2048^3 points. Our numerical experiments describe non-magnetized driven turbulent flows with an isothermal equation of state and an rms Mach number of 6. We discuss numerical resolution issues and demonstrate convergence, in a statistical sense, of the inertial range dynamics in simulations on grids larger than 512^3 points. The simulations allowed us to measure the absolute velocity scaling exponents for the first time. The inertial range velocity scaling in this strongly compressible regime deviates substantially from the incompressible Kolmogorov laws. The slope of the velocity power spectrum, for instance, is -1.95 compared to -5/3 in the incompressible case. The exponent of the third-order velocity structure function is 1.28, while in incompressible turbulence it is known to be unity. We propose a natural extension of Kolmogorov's phenomenology that takes into account compressibility by mixing the velocity and density statistics and preserves the Kolmogorov scaling of the power spectrum and structure functions of the density-weighted velocity v=\rho^{1/3}u. The low-order statistics of v appear to be invariant with respect to changes in the Mach number. For instance, at Mach 6 the slope of the power spectrum of v is -1.69, and the exponent of the third-order structure function of v is unity. We also directly measure the mass dimension of the "fractal" density distribution in the inertial subrange, D_m = 2.4, which is similar to the observed fractal dimension of molecular clouds and agrees well with the cascade phenomenology.Comment: 15 pages, 19 figures, ApJ v665, n2, 200

Turbulent dissipation in the ISM: the coexistence of forced and decaying regimes and implications for galaxy formation and evolution

We discuss the dissipation of turbulent kinetic energy Ek in the global ISM by means of 2-D, MHD, non-isothermal simulations in the presence of model radiative heating and cooling. We argue that dissipation in 2D is representative of that in three dimensions as long as it is dominated by shocks rather than by a turbulent cascade. Energy is injected at a few isolated sites in space, over relatively small scales, and over short time periods. This leads to the coexistence of forced and decaying regimes in the same flow. We find that the ISM-like flow dissipates its turbulent energy rapidly. In simulations with forcing, the input parameters are the radius l_f of the forcing region, the total kinetic energy e_k each source deposits into the flow, and the rate of formation of those regions, sfr_OB. The global dissipation time t_d depends mainly on l_f. In terms of measurable properties of the ISM, t_d >= Sigma_g u_rms^2/(e_k sfr_OB), where Sigma_g is the average gas surface density and u_rms is the rms velocity dispersion. For the solar neighborhood, t_d >= 1.5x10^7 yr. The global dissipation time is consistently smaller than the crossing time of the largest energy-containing scales. In decaying simulations, Ek decreases with time as t^-n, where n~0.8-0.9. This suggests a decay with distance d as Ek\propto d^{-2n/(2-n)} in the mixed forced+decaying case. If applicable to the vertical direction, our results support models of galaxy evolution in which stellar energy injection provides significant support for the gas disk thickness, but not models of galaxy formation in which this energy injection is supposed to reheat an intra-halo medium at distances of up to 10-20 times the optical galaxy size, as the dissipation occurs on distances comparable to the disk height.Comment: 23 pages, including figures. To appear in ApJ. Abstract abridge

A Super-Alfvenic Model of Dark Clouds

Supersonic random motions are observed in dark clouds and are traditionally interpreted as Alfven waves, but the possibility that these motions are super-Alfvenic has not been ruled out. In this work we report the results of numerical experiments in two opposite regimes; M_a ~ 1 and M_a >> 1, where M_a is the initial Alfvenic Mach number --the ratio of the rms velocity to the Alfven speed. Our results show that models with M_a >> 1 are consistent with the observed properties of molecular clouds that we have tested --statistics of extinction measurements, Zeeman splitting measurements of magnetic field strength, line width versus integrated antenna temperature of molecular emission line spectra, statistical B-n relation, and scatter in that relation-- while models with M_a ~ 1 have properties that are in conflict with the observations. We find that both the density and the magnetic field in molecular clouds may be very intermittent. The statistical distributions of magnetic field and gas density are related by a power law, with an index that decreases with time in experiments with decaying turbulence. After about one dynamical time it stabilizes at B ~ n^{0.4}. Magnetically dominated cores form early in the evolution, while later on the intermittency in the density field wins out, and also cores with weak field can be generated, by mass accretion along magnetic field lines.Comment: 10 figures, 2 tables include

Nonlinear theory of mirror instability near threshold

An asymptotic model based on a reductive perturbative expansion of the drift kinetic and the Maxwell equations is used to demonstrate that, near the instability threshold, the nonlinear dynamics of mirror modes in a magnetized plasma with anisotropic ion temperatures involves a subcritical bifurcation,leading to the formation of small-scale structures with amplitudes comparable with the ambient magnetic field

Statistics of Dissipation and Enstrophy Induced by a Set of Burgers Vortices

Dissipation and enstropy statistics are calculated for an ensemble of modified Burgers vortices in equilibrium under uniform straining. Different best-fit, finite-range scaling exponents are found for locally-averaged dissipation and enstrophy, in agreement with existing numerical simulations and experiments. However, the ratios of dissipation and enstropy moments supported by axisymmetric vortices of any profile are finite. Therefore the asymptotic scaling exponents for dissipation and enstrophy induced by such vortices are equal in the limit of infinite Reynolds number.Comment: Revtex (4 pages) with 4 postscript figures included via psfi

Vorticity alignment results for the three-dimensional Euler and Navier-Stokes equations

We address the problem in Navier-Stokes isotropic turbulence of why the vorticity accumulates on thin sets such as quasi-one-dimensional tubes and quasi-two-dimensional sheets. Taking our motivation from the work of Ashurst, Kerstein, Kerr and Gibson, who observed that the vorticity vector {\boldmath\omega} aligns with the intermediate eigenvector of the strain matrix $S$, we study this problem in the context of both the three-dimensional Euler and Navier-Stokes equations using the variables \alpha = \hat{{\boldmath\xi}}\cdot S\hat{{\boldmath\xi}} and {\boldmath\chi} = \hat{{\boldmath\xi}}\times S\hat{{\boldmath\xi}} where \hat{{\boldmath\xi}} = {\boldmath\omega}/\omega. This introduces the dynamic angle $\phi (x,t) = \arctan(\frac{\chi}{\alpha})$, which lies between {\boldmath\omega} and S{\boldmath\omega}. For the Euler equations a closed set of differential equations for $\alpha$ and {\boldmath\chi} is derived in terms of the Hessian matrix of the pressure $P = \{p_{,ij}\}$. For the Navier-Stokes equations, the Burgers vortex and shear layer solutions turn out to be the Lagrangian fixed point solutions of the equivalent (\alpha,{\boldmath\chi}) equations with a corresponding angle $\phi = 0$. Under certain assumptions for more general flows it is shown that there is an attracting fixed point of the (\alpha,\bchi) equations which corresponds to positive vortex stretching and for which the cosine of the corresponding angle is close to unity. This indicates that near alignment is an attracting state of the system and is consistent with the formation of Burgers-like structures.Comment: To appear in Nonlinearity Nov. 199

Turbulent Control of the Star Formation Efficiency

Supersonic turbulence plays a dual role in molecular clouds: On one hand, it contributes to the global support of the clouds, while on the other it promotes the formation of small-scale density fluctuations, identifiable with clumps and cores. Within these, the local Jeans length \Ljc is reduced, and collapse ensues if \Ljc becomes smaller than the clump size and the magnetic support is insufficient (i.e., the core is ``magnetically supercritical''); otherwise, the clumps do not collapse and are expected to re-expand and disperse on a few free-fall times. This case may correspond to a fraction of the observed starless cores. The star formation efficiency (SFE, the fraction of the cloud's mass that ends up in collapsed objects) is smaller than unity because the mass contained in collapsing clumps is smaller than the total cloud mass. However, in non-magnetic numerical simulations with realistic Mach numbers and turbulence driving scales, the SFE is still larger than observational estimates. The presence of a magnetic field, even if magnetically supercritical, appears to further reduce the SFE, but by reducing the probability of core formation rather than by delaying the collapse of individual cores, as was formerly thought. Precise quantification of these effects as a function of global cloud parameters is still needed.Comment: Invited review for the conference "IMF@50: the Initial Mass Function 50 Years Later", to be published by Kluwer Academic Publishers, eds. E. Corbelli, F. Palla, and H. Zinnecke

A Simple Perspective on the Mass-Area Relationship in Molecular Clouds

Despite over 30 years of study, the mass-area relationship within and among clouds is still poorly understood both observationally and theoretically. Modern extinction datasets should have sufficient resolution and dynamic range to characterize this relationship for nearby molecular clouds, although recent papers using extinction data seem to yield different interpretations regarding the nature and universality of this aspect of cloud structure. In this paper we try to unify these various results and interpretations by accounting for the different ways cloud properties are measured and analyzed. We interpret the mass-area relationship in terms of the column density distribution function and its possible variation within and among clouds. We quantitatively characterize regional variations in the column density PDF. We show that structures both within and among clouds possess the same degree of "universality", in that their PDF means do not systematically scale with structure size. Because of this, mass scales linearly with area.Comment: 10 pages, 8 figures, MNRAS in pres