Subcritical dynamos in shear flows

Identifying generic physical mechanisms responsible for the generation of magnetic fields and turbulence in differentially rotating flows is fundamental to understand the dynamics of astrophysical objects such as accretion disks and stars. In this paper, we discuss the concept of subcritical dynamo action and its hydrodynamic analogue exemplified by the process of nonlinear transition to turbulence in non‐rotating wall‐bounded shear flows. To illustrate this idea, we describe some recent results on nonlinear hydrodynamic transition to turbulence and nonlinear dynamo action in rotating shear flows pertaining to the problem of turbulent angular momentum transport in accretion disks. We argue that this concept is very generic and should be applicable to many astrophysical problems involving a shear flow and non‐axisymmetric instabilities of shearinduced axisymmetric toroidal velocity or magnetic fields, such as Kelvin‐Helmholtz, magnetorotational, Tayler or global magnetoshear instabilities. In the light of several recent numerical results, we finally suggest that, similarly to a standard linear instability, subcritical MHD dynamo processes in high‐Reynolds number shear flows could act as a large‐scale driving mechanism of turbulent flows that would in turn generate an independent small‐scale dynamo. (© 2008 WILEY‐VCH Verlag GmbH & Co. KGaA, Weinheim)     

Hydrodynamic processes of angular momentum transport in the interior of a rotating massive hydrogen-burning star

The evolution of a rotating star with a mass of 16M _⊙ at the hydrogen burning phase is considered together with the hydrodynamic processes of angular momentum transport in its interior. Shear turbulence is shown to limit the amplitude of the latitudinal variations in mean molecular weight on a surface of constant pressure in a layer with variable chemical composition. The resulting nonuniformity in the mean molecular weight distribution and the turbulent energy transport along the surface of constant pressure reduce the absolute value of the meridional circulation velocity. Nevertheless, meridional circulation remains the main mechanism of angular momentum transport in the radial direction in a layer with variable chemical composition. The intensity of the processes of angular momentum transport by meridional circulation and shear turbulence is determined by the angular momentum of the star. At a fairly high angular momentum, more specifically, at J = 3.69 × 10⁵² g cm² s^?1, the star during the second half of the hydrogen-burning phase in its convective core has characteristics typical of classical early Be stars.     

Effect of partial mixing of matter on the hydrodynamic angular momentum transport processes in massive main-sequence stars

We consider the evolution of a rotating star with a mass of 16M _⊙ and an angular momentum of 3.25 × 10⁵² g cm² s^?1, along with the hydrodynamic transport of angular momentum and chemical elements in its interiors. When the partial mixing of matter of the turbulent radiative envelope and the convective core is taken into account, the efficiency of the angular momentum transport by meridional circulation in the stellar interiors and the duration of the hydrogen burning phase increase. Depending on the Schmidt number in the turbulent radiative stellar envelope, the ratio of the equatorial rotational velocity to the circular one increases with time in the process of stellar evolution and can become typical of early-type Be stars during an additional evolution time of the star on the main sequence. Partial mixing of matter is a necessary condition under which the hydrodynamic transport processes can increase the angular momentum of the outer stellar layer to an extent that the equatorial rotational velocity begins to increase during the second half of the evolutionary phase of the star on the main sequence, as shown by observations of the brightest stars in open star clusters with ages of 10–25 Myr. When the turbulent Schmidt number is 0.4, the equatorial rotational velocity of the star increases during the second half of the hydrogen burning phase in the convective core from 330 to 450 km s^?1.     

Swirling hydrodynamic jets in viscous accretion flows

A study is made of axisymmetric, low sonic-Mach-number flows of a viscous fluid with angular momentum outside of a black-hole. The viscosity is an eddy viscosity due to turbulence in the sheared flows. Self-similar solutions arise naturally, reducing the Navier-Stokes equations to a set of nonlinear ordinary differential equations. These equations are solved analytically for flows of constant specific angular momentum and numerically for more general flows. For flows with non-constant specific angular momentum, the momentum flux density includes a planar discontinuity which is interpreted as an accretion disc. In general, two flow regions appear on each side of the disk, corresponding to accretion onto the disk and jet-like outflows along the ±z-axes. Physical interpretations of the solutions show that these flows arise in response to point sources of axial momentum at the origin directed in the ±z-directions. The power needed to maintain this momentum input is assumed to come from the mass accretion onto the black hole.The hydrodynamic flows are generalized to include a magnetic field. In the limit of infinite electrical conductivity, the possible types of flow patterns are the same as in hydrodynamic case. The magnetic field alters the relative amounts of reversible and irreversible momentum and angular momentum transport by the flow. For a flow with turbulent viscosity, the magnetic field acts to reduce the level of the turbulence and the effective value of the eddy viscosity.     

Hypersonic Swizzle Sticks: Protostellar Turbulence, Outflows and Fossil Outflow Cavities

The expected lifetimes for molecular clouds has become a topic of considerable debate as numerical simulations have shown that MHD turbulence, the nominal means of support for clouds against self-gravity, will decay on short timescales. Thus it appears that either molecular clouds are transient features or they are resupplied with turbulent energy through some means. Jets and molecular outflows are recognized as a ubiquitous phenomena associated with star formation. Stars however form not isolation but in clusters of different density and composion. The ubiquity and high density of outflows from young stars in clusters make them an intriguing candidate for the source of turbulence energy in molecular clouds. In this contribution we present new studies, both observational and theoretical, which address the issue of jet/outflow interactions and their abilityto drive turbulent flows in molecular clouds. Our studies focus on scales associated with young star forming clusters. In particular we first show that direct collisions between active outflows are not effective at stirring the ambient medium. We then show that fossil cavities from “extinct” outflows may provide the missing link in terms of transferring momentum and energy to the cloud.     

Progress Toward the Study of Laboratory Scale, Astrophysically Relevant, Turbulent Plasmas

Recent results from an ongoing series of Rayleigh-Taylor instability experiments being conducted on the Omega Laser are described. The goal of these experiments is to study, in a controlled laboratory setting, the mixing that occurs at an unstable interface subjected to an acceleration history similar to the explosion phase of a core-collapse supernova. In a supernova, the Reynolds number characterizing this mixing is extremely large (Re > 10¹⁰) and is more than sufficient to produce a turbulent flow at the interface. In the laboratory experiment, by contrast, the spatial scales are much smaller, but are still sufficiently large (Re > 10⁵) to support a turbulent flow and therefore recreate the conditions relevant to the supernova problem. The data from these experiments will be used to validate astrophysical codes as well as to better understand the transition to turbulence in such high energy density systems. The experimental results to date using two-dimensional initial perturbations demonstrate a clear visual transition from a well-ordered perturbation structure consisting of only a few modes to one with considerable modal content. Analysis of these results, however, indicates that while a turbulent spectrum visually appears to be forming, the layer has not yet reached the asymptotic growth rate characteristic of a fully turbulent layer. Recent advances in both target fabrication and diagnostic techniques are discussed as well. These advances will allow for the study of well-controlled 3D perturbations, increasing our ability to recreate the conditions occurring in the supernova.     

The angular momentum transport in rotating turbulent convection

The angular momentum transport in rotating turbulent convection is simulated with the NIRVANA code for Taylor numbers up to 10⁶. The box consists of an unstable layer embedded in two stable overshoot layers. We find the expected anisotropies in the rotating anisotropic turbulence field: 〈u^′2_r〉 exceeds 〈u^′2_ϕ〉, and 〈u^′2_ϕ〉 exceeds 〈u^′2_θ〉. The resulting radial angular momentum transport is directed inwards and peaks in the middle of the convective layer. The resulting latitudinal angular momentum transport is equatorwards, peaks at the surface and is highly concentrated to the equatorial region. Apart from a factor of 2–3 the total amplitudes of the cross‐correlations are of the same order of magnitude. In the lower overshoot region (‘tachocline’) the cross‐correlations are negative. It is argued that the concentration of the latitudinal angular momentum transport towards the surface and towards the equator does not too strongly reduce its potential to produce rotation laws with accelerated equators. (© 2005 WILEY‐VCH Verlag GmbH & Co. KGaA, Weinheim)     

The generation and dissipation of solar and galactic magnetic fields

Turbulent diffusion of magnetic field plays an essential role in the generation of magnetic field in most astrophysical bodies. This paper reviews what can be proved, and what can be believed, about the turbulent diffusion of magnetic field. Observations indicate the dissipation of magnetic field at rates that can be understood only in terms of turbulent diffusion. Theory shows that a largescale weak magnetic field diffuses in a turbulent flow in the same way that smoke is mixed throughout the fluid by the turbulence. The small-scale fields (produced from the large-scale field by the turbulence) are limited in their growth by reconnection of field lines at neutral points, so that the turbulent mixing of field and fluid is not halted by them.Altogether, it appears that the mixing of field and fluid in the observed turbulent motions in the Sun and in the Galaxy is unavoidable. Turbulent diffusion causes decay of the general solar fields in a decade or so, and of the galactic field in 10⁸–10⁹ yr. We conclude that continual dynamo action is implied by the observed existence of the fields.This work was supported in part by the National Aeronautics and Space Administration under Grant NGL 14-001-001.     

A theory of differntial rotation based on the discussion of turbulent transport of angular momentum

This paper deals with the theory of the solar rotational law. We assume the turbulence to be of the largest influence compared with the momentum flux caused by molecular viscosity and meridional circulation. Firstly we use heuristical forms for the needed cross correlations Qrφ (turbulent radial momentum flux) and Qνφ (turbulent latitudinal momentum flux): Qrφ = −α₀r ϑΩ/ϑr · sin ν + Q₀ sin ν + Q₂ sin³ ν, Qνφ = −δ₀ ϑΩ/ϑν· sin ν + P₂ sin²θ cos θ. It is shown that a radial dependence of the angular velocity Ω is given by Q₀. Furthermore, the observed equatorial acceleration occurs in the case of non-negativity of Q₂ and/or P₂. Because of the spatial dependence of the solar angular velocity the coefficients of Q and P are unfortunately not to be measured. Secondly, we determine the coefficients with a theory founded upon the hypothesis that a rotating stochastical force field — independent from Ω — maintains an anisotropic turbulence. The global fast rotation produces, indeed, finite cross correlations Q₂ and P₂. It is suggested that horizontally directed turbulent motions with not too small radial correlations lengths and time scales of about 2 weeks could be responsible for the solar differential rotation. Finally, we show that also short-living turbulent horizontal modes provide the observed equatorial acceleration if they occur preferably at the equatorial region.     

A Consistent one-Dimensional Model for the Turbulent Tachocline

The first consistent model for the turbulent tachocline is presented, with the turbulent diffusivity computed within the model instead of being specified arbitrarily. For the origin of the 3D turbulence a new mechanism is proposed. Owing to the strongly stable stratification, the mean radial shear is stable, while the horizontal shear is expected to drive predominantly horizontal, quasi-2D motions in thin slabs. Here I suggest that a major source of 3D overturning turbulent motions in the tachocline is the secondary shear instability due to the strong, random vertical shear arising between the uncorrelated horizontal flows in neighboring slabs. A formula for the vertical diffusivity due to this turbulence, Equation (9), is derived and applied in a simplified 1D model of the tachocline. It is found that Maxwell stresses due to an oscillatory poloidal magnetic field of a few hundred gauss are able to confine the tachocline to a thickness less than 5 Mm. The integral scale of the 3D overturning turbulence is the buoyancy scale, on the order of 10 km, and its velocity amplitude is a few m s^–1, yielding a vertical turbulent diffusivity on the order of 10⁸ cm² s^–1.     

Hydrodynamic Aspects of Modeling of the Mass Transfer and Coagulation Processes in Turbulent Accretion Disks

This paper considers, in the context of modeling the evolution of a protoplanetary cloud, the hydrodynamic aspects of the theory of concurrent processes of mass transfer and coagulation in a two-phase medium in the presence of shear turbulence in a differentially rotating gas–dust disk and of polydisperse solid particles suspended in a carrying flow of solid particles. The defining relations are derived for diffuse fluxes of particles of different sizes in the equations of turbulent diffusion in the gravitational field, which describe the convective transfer, turbulent mixing, and sedimentation of disperse dust grains onto the central plane of the disk, as well as their coagulation growth. A semiempirical method is developed for calculating the coefficients of turbulent viscosity and turbulent diffusion for particles of different kinds. This method takes into account the inverse effects of dust transfer on the turbulence evolution in the disk and the inertial differences between disperse solid particles. To solve rigorously the problem of the mutual influence of the turbulent mixing and coagulation kinetics in forming the gas–dust subdisk, the possible mechanisms of gravitational, turbulent, and electric coagulation in a protoplanetary disk are explored and the parametric method of moments for solving the Smoluchowski integro-differential coagulation equation for the particles' size distribution function is considered. This method takes into account the fact that this distribution belongs to a definite parametric class of distributions.     

Turbulence and its parameterization in accretion discs

Accretion disc turbulence is investigated in the framework of the shearing box approximation. The turbulence is either driven by the magneto‐rotational instability or, in the non‐magnetic case, by an explicit and artificial forcing term in the momentum equation. Unlike the magnetic case, where most of the dissipation occurs in the disc corona, in the forced hydrodynamic case most of the dissipation occurs near the midplane. In the hydrodynamic case evidence is presented for the stochastic excitation of epicycles. When the vertical and radial epicyclic frequencies are different (modeling the properties around rotating black holes), the beat frequency between these two frequencies appear to show up as a peak in the temporal power spectrum in some cases. Finally, the full turbulent resistivity tensor is determined and it is found that, if the turbulence is driven by a forcing term, the signs of its off‐diagonal components are such that this effect would not be capable of dynamo action by the shear–current effect. (© 2005 WILEY‐VCH Verlag GmbH & Co. KGaA, Weinheim)     

Meridional circulation in the radiation zones of rotating stars: Origins,behaviors and consequences on stellar evolution

Stellar radiation zones are the seat of meridional currents. This circulation has a strong impact on the transport of angular momentum and the mixing of chemicals that modify the evolution of stars. First, we recall in details the dynamical processes that are taking place in differentially rotating stellar radiation zones and the assumptions which are adopted for their modelling in stellar evolution. Then, we present our new results of numerical simulations which allow us to follow in 2D the secular hydrodynamics of rotating stars, assuming that anisotropic turbulence enforces a shellular rotation law and taking into account the transport of angular momentum by internal gravity waves. The different behaviors of the meridional circulation in function of the type of stars which is studied are discussed with their physical origin and their consequences on the transport of angular momentum and of chemicals. Finally, we show how this work is leading to a dynamical vision of the evolution of rotating stars from their birth to their death. (© 2007 WILEY-VCH Verlag GmbH & Co. KGaA, Weinheim)     

Transport of angular momentum and chemical species by anisotropic mixing in stellar radiative interiors

Small levels of turbulence can be present in stellar radiative interiors due to, e.g., the instability of rotational shear. In this paper we estimate turbulent transport coefficients for stably stratified rotating stellar radiation zones. Stable stratification induces strong anisotropy with a very small ratio of radial‐to‐horizontal turbulence intensities. Angular momentum is transported mainly due to the correlation between azimuthal and radial turbulent motions induced by the Coriolis force. This non‐diffusive transport known as the Λ‐effect has outward direction in radius and is much more efficient compared to the effect of radial eddy viscosity. Chemical species are transported by small radial diffusion only. This result is confirmed using direct numerical simulations combined with the test‐scalar method. As a consequence of the non‐diffusive transport of angular momentum, the estimated characteristic time of rotational coupling (≲100 Myr) between radiative core and convective envelope in young solar‐type stars is much shorter compared to the time‐scale of Lithium depletion (∼1 Gyr) (© 2011 WILEY‐VCH Verlag GmbH & Co. KGaA, Weinheim)     

Turbulence,convection, and mixing in red giant stars: Some empirical approaches based on high resolution spectroscopy

The differential velocity field in cool stars can be measured effectively on photographic plates by the use of a PDS micro-densitometer, from which it is shown that radial velocity gradients are larger for stars with larger turbulent velocities, which are determined from the high resolution echellograms. This indicates that the stellar turbulence may have something to do with the differential velocity field in stellar atmospheres. As an observational probe of the mixing processes in red giant stars, stellar abundances that are sensitive to mixing are determined on the basis of high resolution Fourier Transform spectroscopy. For example, the¹²C/¹³C ratio has now been determined for large number of red giant stars and shows characteristic changes through the first red giant branch to the asymptotic giant branch, including both the pre-thermal pulsing and the thermal pulsing phases. This information, together with additional information on the¹⁶O/¹⁷O ratio and on CNO abundances, provides useful constraints on the theory of mixing in red giant stars.Paper presented at the IAU Third Asian-Pacific Regional Meeting, held in Kyoto, Japan, between 30 September-6 October, 1984.     

Simulation of turbulent convection in a slowly rotating red giant star

The first 3-D non-linear hydrodynamical simulation of the inner convective envelope of a rotating low mass red giant star is presented. This simulation, computed with the ASH code, aims at understanding the redistribution of angular momentum and heat in extended convection zones. The convection patterns achieved in the simulation consist of few broad and warm upflows surrounded by a network of cool downflows. This asymmetry between up and downflows leads to a strong downward kinetic energy flux, that must be compensated by an overluminous enthalpy flux in order to carry outward the total luminosity of the star. The influence of rotation on turbulent convection results in the establishment of largescale mean flows: a strong radial differential rotation and a single cell poleward meridional circulation per hemisphere. A detailed analysis of angular momentum redistribution reveals that the meridional circulation transports angular momentum outward in the radial direction and poleward in the latitudinal direction, with the Reynolds stresses acting in the opposite direction. This simulation indicates that the classical hypothesis of mixing length theory and solid-body rotation in the envelope of red giants assumed in 1-D stellar evolution models are unlikely to be realized and thus should be reconsidered. (© 2007 WILEY-VCH Verlag GmbH & Co. KGaA, Weinheim)     

Particles in the nebular midplane: Collective effects and relative velocities

Abstract– In the absence of global turbulence, solid particles in the solar nebula tend to settle toward the midplane, forming a layer with enhanced solids/gas ratio. Shear relative to the surrounding pressure‐supported gas generates turbulence within the layer, inhibiting further settling and preventing gravitational instability. Turbulence and size‐dependent drift velocities cause collisions between particles. Relative velocities between small grains and meter‐sized bodies are typically about 50 m s^?1 for isolated particles; however, in a dense particle layer, collective effects alter the motion of the gas near the midplane. Here, we develop a numerical model for the coupled motions of gas and particles of arbitrary size, based on the assumption that turbulent viscosity transfers momentum on the scale of the Ekman length. The vertical distribution of particles is determined by a balance between settling and turbulent diffusion. Self‐consistent distributions of density, turbulent velocities, and radial fluxes of gas and particles of different sizes are determined. Collective effects generate turbulence that increases relative velocities between small particles, but reduce velocities between small grains and bodies of decimeter size or larger by bringing the layer’s motion closer to Keplerian. This effect may alleviate the “meter‐size barrier” to collisional growth of planetesimals.     

A semi-analytic solution for the radial and vertical structure of accretion discs with a magnetic wind

A semi-analytic method is presented for solving for the radial and vertical structures of an accretion disc, with a magnetically channelled wind flowing from its surfaces. Both magnetic and turbulent viscous effects are taken into account, and the essential wind properties are related to the disc structure. The angular momentum removed by the wind plays a major part in driving the inflow through the disc, with photospheric temperatures being sufficient to generate the required wind mass flux. The magnetic field is generated by an αω-dynamo, but the method of solution should have application with other magnetic field sources. Self-consistent disc-wind solutions result, with rms turbulent Mach numbers which are in good agreement with those found in simulations of turbulence generated from magnetic shearing instabilities.     

Diffusion of a passive scalar in a rotating medium with anisotropic turbulence

We investigate the influence of turbulence anisotropy and rotation on the diffusion of a low-concentration passive scalar in a turbulent medium. Using the renormalization the diffusion tensor over the spectrum of turbulent fluctuations, we show that enhanced horizontal mixing reduces the vertical diffusion transport of a passive scalar. Allowance for rotation results in two effects, which have not been noted previously: (1) under the influence of Coriolis forces, horizontal turbulence also produces a vertical diffusion flux, with the horizontal and vertical diffusions being of the same order of magnitude for rapidly rotating stars and (2) in the case of rapid rotation, all diffusion fluxes of a passive scalar decrease in inverse proportion to the square root of the Coriolis number.     

Observational Magnetogasdynamics: 21 Years of HI Zeeman Splitting Measurements... and More

We review observations of the physical properties of the diffuse ISM HI components, namely the Cold and Warm Neutral Media (CNM and WNM). There is somewhat more WNM than CNM, and at least half of the WNM is not thermally stable. The CNM has typical turbulent Mach number 3. Magnetic fields in the CNM are not as large as expected from the classical flux-freezing argument; neither are magnetic fields always strong enough for the Alfven velocity to equal the turbulent velocity. Nevertheless, they are usually strong enough to put CNM clouds in the magnetically subcritical regime. We identify a probable new source of turbulence for the diffuse ISM. We discuss one very cold cloud that has considerable internal turbulence and, because of its extreme thinness ～0.05 pc, a turbulent crossing time of only ～5 × 10⁴ yr.