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We use three-dimensional direct numerical simulations of the helically forced magnetohydrodynamic equations in spherical shell segments in order to study the effects of changes in the geometrical shape and size of the domain on the growth and saturation of large-scale magnetic fields. We inject kinetic energy along with kinetic helicity in spherical domains via helical forcing using Chandrasekhar-Kendall functions. We take perfect conductor boundary conditions for the magnetic field to ensure that no magnetic helicity escapes the domain boundaries. We find dynamo action giving rise to magnetic fields at scales larger than the characteristic scale of the forcing. The magnetic energy exceeds the kinetic energy over dissipative time scales, similar to that seen earlier in Cartesian simulations in periodic boxes. As we increase the size of the domain in the azimuthal direction we find that the nonlinearly saturated magnetic field organizes itself in long-lived cellular structures with aspect ratios close to unity. These structures tile the domain along the azimuthal direction, thus resulting in very small longitudinally averaged magnetic fields for large domain sizes. The scales of these structures are determined by the smallest scales of the domain, which in our simulations is usually the radial scale. We also find that increasing the meridional extent of the domains produces little qualitative change, except a marginal increase in the large-scale field. We obtain qualitatively similar results in Cartesian domains with similar aspect ratios., Comment: Updated with minor changes to be consistent with the published version

In the mean-field theory of magnetic fields, turbulent transport, i.e. the turbulent electromotive force, is described by a combination of the alpha effect and turbulent magnetic diffusion, which are usually assumed to be proportional respectively to the mean field and its spatial derivatives. For a passive scalar there is just turbulent diffusion, where the mean flux of concentration depends on the gradient of the mean concentration. However, these proportionalities are approximations that are valid only if the mean field or the mean concentration vary slowly in time. Examples are presented where turbulent transport possesses memory, i.e. where it depends crucially on the past history of the mean field. Such effects are captured by replacing turbulent transport coefficients with time integral kernels, resulting in transport coefficients that depend effectively on the frequency or the growth rate of the mean field itself. In this paper we perform numerical experiments to find the characteristic timescale (or memory length) of this effect as well as simple analytical models of the integral kernels in the case of passive scalar concentrations and kinematic dynamos. The integral kernels can then be used to find self-consistent growth or decay rates of the mean fields. In mean-field dynamos the growth rates and cycle periods based on steady state values of alpha effect and turbulent diffusivity can be quite different from the actual values., Comment: 16 pages, 16 figures, published version

Simulations of stochastically forced shear-flow turbulence in a shearing-periodic domain are used to study the spontaneous generation of large-scale flow patterns in the direction perpendicular to the plane of the shear. Based on an analysis of the resulting large-scale velocity correlations it is argued that the mechanism behind this phenomenon could be the mean-vorticity dynamo effect pioneered by Elperin, Kleeorin, and Rogachevskii in 2003 (Phys. Rev. E 68, 016311). This effect is based on the anisotropy of the eddy viscosity tensor. One of its components may be able to replenish cross-stream mean flows by acting upon the streamwise component of the mean flow. Shear, in turn, closes the loop by acting upon the cross-stream mean flow to produce stronger streamwise mean flows. The diagonal component of the eddy viscosity is found to be of the order of the rms turbulent velocity divided by the wavenumber of the energy-carrying eddies., Comment: 8 pages, 11 figures, Phys. Rev. E (in press)

The coefficients defining the mean electromotive force in a Galloway-Proctor flow are determined. This flow shows a two-dimensional pattern and is helical. The pattern wobbles in its plane. Apart from one exception a circular motion of the flow pattern is assumed. This corresponds to one of the cases considered recently by Courvoisier, Hughes and Tobias (2006, Phys. Rev. Lett., 96, 034503). An analytic theory of the alpha effect and related effects in this flow is developed within the second-order correlation approximation and a corresponding fourth-order approximation. In the validity range of these approximations there is an alpha effect but no gamma effect, or pumping effect. Numerical results obtained with the test-field method, which are independent of these approximations, confirm the results for alpha and show that gamma is in general nonzero. Both alpha and gamma show a complex dependency on the magnetic Reynolds number and other parameters that define the flow, that is, amplitude and frequency of the wobbling motion. Some results for the magnetic diffusivity eta_t and a related quantity are given, too. Finally a result for alpha in the case of a randomly varying flow without the aforementioned circular motion is presented. This flow may be a more appropriate model for studying the alpha effect and related effects in flows that are statistical isotropic in a plane., Comment: 12 pages, 14 figures, submitted to MNRAS

Several aspects of mathematical astrobiology are discussed. It is argued that around the time of the origin of life the handedness of biomolecules must have established itself through an instability. Possible pathways of producing a certain handedness include mechanisms involving either autocatalysis or, alternatively, epimerization as governing effects. Concepts for establishing hereditary information are discussed in terms of the theory of hypercycles. Instabilities toward parasites and possible remedies by invoking spatial extent are reviewed. Finally, some effects of early life are discussed that contributed to modifying and regulating atmosphere and climate of the Earth, and that could have contributed to the highly oxidized state of its crust., Comment: 32 pages, 16 figures, to appear in Encyclopedia of Complexity and System Science

Using direct simulations, weakly nonlinear theory and nonlinear mean-field theory, it is shown that the quenched velocity field of a saturated nonlinear dynamo can itself act as a kinematic dynamo. The flow is driven by a forcing function that would produce a Roberts flow in the absence of a magnetic field. This result confirms an analogous finding by F. Cattaneo & S. M. Tobias (arXiv:0809.1801) for the more complicated case of turbulent convection, suggesting that this may be a common property of nonlinear dynamos; see also the talk given also online at the Kavli Institute for Theoretical Physics (http://online.kitp.ucsb.edu/online/dynamo_c08/cattaneo). It is argued that this property can be used to test nonlinear mean-field dynamo theories., Comment: 5 pages, 2 figures, accepted by MNRAS

Using direct simulations of hydromagnetic turbulence driven by random polarized waves it is shown that dynamo action is possible over a wide range of magnetic Prandtl numbers from 10^-3 to 1. Triply periodic boundary conditions are being used. In the final saturated state the resulting magnetic field has a large-scale component of Beltrami type. For the kinematic phase, growth rates have been determined for magnetic Prandtl numbers between 0.01 and 1, but only the case with the smallest magnetic Prandtl number shows large-scale magnetic fields. It is less organized than in the nonlinear stage. For small magnetic Prandtl numbers the growth rates are comparable to those calculated from an alpha squared mean-field dynamo. In the linear regime the magnetic helicity spectrum has a short inertial range compatible with a -5/3 power law, while in the nonlinear regime it is the current helicity whose spectrum may be compatible with such a law. In the saturated case, the spectral magnetic energy in the inertial range is in slight excess over the spectral kinetic energy, although for small magnetic Prandtl numbers the magnetic energy spectrum reaches its resistive cut off wavenumber more quickly. The viscous energy dissipation declines with the square root of the magnetic Prandtl number, which implies that most of the energy is dissipated via Joule heat., Comment: 8 pages, 12 figures, Astrophys. J. (in press)

Aspects of turbulence in protostellar accretion discs are being reviewed. The emergence of dead zones due to poor ionization and alternatives to the magneto-rotational instability are discussed. The coupling between dust and gas in protostellar accretion discs is explained and turbulent drag is compared with laminar drag in the Stokes and Epstein regimes. Finally, the significance of magnetic field generation in turbulent discs is emphasized in connection with driving outflows and with star-disc coupling., Comment: 16 pages, 7 figures, proceedings of Nobel Symposium 135: Physics of Planetary Systems

The role of shear in alleviating catastrophic quenching by shedding small-scale magnetic helicity through fluxes along contours of constant shear is discussed. The level of quenching of the dynamo effect depends on the quenched value of the turbulent magnetic diffusivity. Earlier estimates that might have suffered from the force-free degeneracy of Beltrami fields are now confirmed for shear flows where this degeneracy is lifted. For a dynamo that is saturated near equipartition field strength those estimates result in a 5-fold decrease of the magnetic diffusivity as the magnetic Reynolds number based on the wavenumber of the energy-carrying eddies is increased from 2 to 600. Finally, the role of shear in driving turbulence and large-scale fields by the magneto-rotational instability is emphasized. New simulations are presented and the 3pi/4 phase shift between poloidal and toroidal fields is confirmed. It is suggested that this phase shift might be a useful diagnostic tool in identifying mean-field dynamo action in simulations and to distinguish this from other scenarios invoking magnetic buoyancy as a means to explain migration away from the midplane., Comment: 7 pages, 10 figures, proceedings of the workshop on MHD Laboratory Experiments for Geophysics and Astrophysics

We study the dependence of turbulent transport coefficients, such as the components of the $\alpha$ tensor ($\alpha_{ij}$) and the turbulent magnetic diffusivity tensor ($\eta_{ij}$), on shear and magnetic Reynolds number in the presence of helical forcing. We use three-dimensional direct numerical simulations with periodic boundary conditions and measure the turbulent transport coefficients using the kinematic test field method. In all cases the magnetic Prandtl number is taken as unity. We find that with increasing shear the diagonal components of $\alpha_{ij}$ quench, whereas those of $\eta_{ij}$ increase. The antisymmetric parts of both tensors increase with increasing shear. We also propose a simple expression for the turbulent pumping velocity (or $\gamma$ effect). This pumping velocity is proportional to the kinetic helicity of the turbulence and the vorticity of the mean flow. For negative helicity, i.e. for a positive trace of $\alpha_{ij}$, it points in the direction of the mean vorticity, i.e. perpendicular to the plane of the shear flow. Our simulations support this expression for low shear and magnetic Reynolds number. The transport coefficients depend on the wavenumber of the mean flow in a Lorentzian fashion, just as for non-shearing turbulence., Comment: A&A, in press

We analyze the mass distribution of cores formed in an isothermal, magnetized, turbulent, and self-gravitating nearly critical molecular cloud model. Cores are identified at two density threshold levels. Our main results are that the presence of self-gravity modifies the slopes of the core mass function (CMF) at the high mass end. At low thresholds, the slope is shallower than the one predicted by pure turbulent fragmentation. The shallowness of the slope is due to the effects of core coalescence and gas accretion. Most importantly, the slope of the CMF at the high mass end steepens when cores are selected at higher density thresholds, or alternatively, if the CMF is fitted with a log-normal function, the width of the lognormal distribution decreases with increasing threshold. This is due to the fact that gravity plays a more important role in denser structures selected at higher density threshold and leads to the conclusion that the role of gravity is essential in generating a CMF that bears more resemblance with the IMF when cores are selected with an increasing density threshold in the observations., Comment: 13 pages, 4 figures, accepted to ApJ Letters. An additional simulation has been added. The sign of the beta values in Fig. 1 changed to fit their definition in the text. The main conclusions, however unchanged, are better clarified

A simple explicit example of a Roberts-type dynamo is given in which the alpha-effect of mean-field electrodynamics exists in spite of point-wise vanishing kinetic helicity of the fluid flow. In this way it is shown that alpha-effect dynamos do not necessarily require non-zero kinetic helicity. A mean-field theory of Roberts-type dynamos is established within the framework of the second-order correlation approximation. In addition numerical solutions of the original dynamo equations are given, that are independent of any approximation of that kind. Both theory and numerical results demonstrate the possibility of dynamo action in the absence of kinetic helicity., Comment: 6 pages, 3 figures, accepted for PRE

Using numerical simulations at moderate magnetic Reynolds numbers up to 220 it is shown that in the kinematic regime, isotropic helical turbulence leads to an alpha effect and a turbulent diffusivity whose values are independent of the magnetic Reynolds number, $\Rm$, provided $\Rm$ exceeds unity. These turbulent coefficients are also consistent with expectations from the first order smoothing approximation. For small values of $\Rm$, alpha and turbulent diffusivity are proportional to $\Rm$. Over finite time intervals meaningful values of alpha and turbulent diffusivity can be obtained even when there is small-scale dynamo action that produces strong magnetic fluctuations. This suggests that small-scale dynamo-generated fields do not make a correlated contribution to the mean electromotive force., Comment: Accepted for publication in MNRAS Letters

Some basic properties of the solar convection zone are considered and the use of helioseismology as an observational tool to determine its depth and internal angular velocity is discussed. Aspects of solar magnetism are described and explained in the framework of dynamo theory. The main focus is on mean field theories for the Sun's magnetic field and its differential rotation., Comment: 45 pages, 17 figures, to appear in Handbook of Solar-Terrestrial Environment, eds. Y. Kamide & A. C.-L. Chian, Springer

The outer surface layers of the sun show a clear deceleration at low latitudes. This is generally thought to be the result of a strong dominance of vertical turbulent motions associated with strong downdrafts. This strong negative radial shear should not only contribute to amplifying the toroidal field locally and to expelling magnetic helicity, but it may also be responsible for producing a strong prograde pattern speed in the supergranulation layer. Using simulations of rotating stratified convection in cartesian boxes located at low latitudes around the equator it is shown that in the surface layers patterns move in the prograde direction on top of a retrograde mean background flow. These patterns may also be associated with magnetic tracers and even sunspot proper motions that are known to be prograde relative to the much slower surface plasma., Comment: 11 pages, 8 figures, to appear in Highlights of Astronomy, ed. F. Kupka, I.W. Roxburgh, and K.L. Chan, Astron. Soc. Pac. Conf. Ser

Large scale dynamo-generated fields are a combination of interlocked poloidal and toroidal fields. Such fields possess magnetic helicity that needs to be regenerated and destroyed during each cycle. A number of numerical experiments now suggests that stars may do this by shedding magnetic helicity. In addition to plain bulk motions, a favorite mechanism involves magnetic helicity flux along lines of constant rotation. We also know that the sun does shed the required amount of magnetic helicity mostly in the form of coronal mass ejections. Solar-like stars without cycles do not face such strong constraints imposed by magnetic helicity evolution and may not display coronal activity to that same extent. I discuss the evidence leading to this line of argument. In particular, I discuss simulations showing the generation of strong mean toroidal fields provided the outer boundary condition is left open so as to allow magnetic helicity to escape. Control experiments with closed boundaries do not produce strong mean fields., Comment: 2 pages, 2 figures, to appear in Highlights of Astronomy, ed. K. G. Strassmeier & A. Kosovichev, Astron. Soc. Pac. Conf. Ser

The backreaction of the Lorentz force on the alpha-effect is studied in the limit of small magnetic and fluid Reynolds numbers, using the first order smoothing approximation (FOSA) to solve both the induction and momentum equations. Both steady and time dependent forcings are considered. In the low Reynolds number limit, the velocity and magnetic fields can be expressed explicitly in terms of the forcing function. The nonlinear alpha-effect is then shown to be expressible in several equivalent forms in agreement with formalisms that are used in various closure schemes. On the one hand, one can express alpha completely in terms of the helical properties of the velocity field as in traditional FOSA, or, alternatively, as the sum of two terms, a so-called kinetic alpha-effect and an oppositely signed term proportional to the helical part of the small scale magnetic field. These results hold for both steady and time dependent forcing at arbitary strength of the mean field (abridged)., Comment: Accepted for publication in MNRAS

The thermal instability with a piecewise power law cooling function is investigated using one- and three-dimensional simulations with periodic and shearing-periodic boundary conditions in the presence of constant thermal diffusion and kinematic viscosity coefficients. Consistent with earlier findings, the flow behavior depends on the average density, . When $\bra{\rho}$ is in the range 1-5 x 10^{-24} g cm^{-3} the system is unstable and segregates into cool and warm phases with temperatures of roughly 100 and 10^4 K, respectively. However, in all cases the resulting average pressure is independent of and just a little above the minimum value. For a constant heating rate of 0.015 erg g^{-1} s^{-1}, the mean pressure is around 24 x 10^{-14} dyn (corresponding to p/k_B ~ K cm^{-3}). Cool patches tend to coalesce into bigger ones. In all cases investigated there is no sustained turbulence, which is in agreement with earlier results. Simulations in which turbulence is driven by a body force show that when rms velocities of between 10 and 30 km/s are obtained, the resulting dissipation rates rates are comparable to the thermal energy input rate. The resulting mean pressures are then about 30 x 10^{-14} dyn, corresponding to p/k_B ~ 2170 K cm^{-3}. This is comparable to the value expected for the Galaxy. Differential rotation tends to make the flow two-dimensional, that is, uniform in the streamwise direction, but this does not lead to instability., Comment: 10 pages, 13 figures

We review advances in the theoretical and computational studies of disk winds, jets and outflows including: the connection between accretion and jets, the launch of jets from magnetized disks, the coupled evolution of jets and disks, the interaction of magnetized young stellar objects with their surrounding disks and the relevance to outflows, and finally, the link between jet formation and gravitational collapse. We also address the predictions that the theory makes about jet kinematics, collimation, and rotation, that have recently been confirmed by high spatial and spectral resolution observations. Disk winds have a universal character that may account for jets and outflows during the formation of massive stars as well as brown dwarfs., Comment: 18 pages, 5 figures, review to appear in Protostars and Planets V, B. Reipurth, D. Jewitt, and K. Keil (eds.), University of Arizona Press, Tucson, 2006

In an attempt to determine the outer scale of turbulence driven by localized sources, such as supernova explosions in the interstellar medium, we consider a forcing function given by the gradient of gaussian profiles localized at random positions. Different coherence times of the forcing function are considered. In order to isolate the effects specific to the nature of the forcing function we consider the case of a polytropic equation of state and restrict ourselves to forcing amplitudes such that the flow remains subsonic. When the coherence time is short, the outer scale agrees with the half-width of the gaussian. Longer coherence times can cause extra power at large scales, but this would not yield power law behavior at scales larger than that of the expansion waves. At scales smaller than the scale of the expansion waves the spectrum is close to power law with a spectral exponent of -2. The resulting flow is virtually free of vorticity. Viscous driving of vorticity turns out to be weak and self-amplification through the nonlinear term is found to be insignificant. No evidence for small scale dynamo action is found in cases where the magnetic induction equation is solved simultaneously with the other equations., Comment: 5 pages, 7 figures, MNRAS

Some common properties of helical magnetic fields in decaying and driven turbulence are discussed. These include mainly the inverse cascade that produces fields on progressively larger scales. Magnetic helicity also restricts the evolution of the large scale field: the field decays less rapidly than a non-helical field, but it also saturates more slowly, i.e. on a resistive time scale if there are no magnetic helicity fluxes. The former effect is utilized in primordial field scenarios, while the latter is important for successfully explaining astrophysical dynamos that saturate faster than resistively. Dynamo action is argued to be important not only in the galactic dynamo, but also in accretion discs in active galactic nuclei and around protostars, both of which contribute to producing a strong enough seed magnetic field. Although primordial magnetic fields may be too weak to compete with these astrophysical mechanisms, such fields could perhaps still be important in producing polarization effects in the cosmic background radiation., Comment: 8 pages, 5 figures, talk given in Bologna, August 2006, proceedings of "The Origin and Evolution of Cosmic Magnetism", Astron. Nachr. (in press)

Arguments are presented in favor of the idea that the solar dynamo may operate not just at the bottom of the convection zone, i.e. in the tachocline, but it may operate in a more distributed fashion in the entire convection zone. The near-surface shear layer is likely to play an important role in this scenario., Comment: 4 pages, 2 figures, in Solar activity: exploration, understanding and prediction, ed: H. Lundstedt, ESA, ESTEC Noordwijk

The location of the solar dynamo is discussed in the context of new insights into the theory of nonlinear turbulent dynamos. It is argued that, from a dynamo-theoretic point of view, the bottom of the convection zone is not a likely location and that the solar dynamo may be distributed over the convection zone. The near surface shear layer produces not only east-west field alignment, but it also helps the dynamo disposing of its excess small scale magnetic helicity., Comment: 6 pages, 3 figures, in Solar MHD: Theory and Observations, eds: J. W. Leibacher, H. Uitenbroek, & R. F. Stein, Astron. Soc. Pac. Conf. Ser

Nonlinear behaviour of galactic dynamos is studied, allowing for magnetic helicity removal by the galactic fountain flow. A suitable advection speed is estimated, and a one-dimensional mean-field dynamo model with dynamic alpha-effect is explored. It is shown that the galactic fountain flow is efficient in removing magnetic helicity from galactic discs. This alleviates the constraint on the galactic mean-field dynamo resulting from magnetic helicity conservation and thereby allows the mean magnetic field to saturate at a strength comparable to equipartition with the turbulent kinetic energy., Comment: 4 pages, 2 figures, accepted by A&A Letters

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., Comment: 11 pages, 11 figures

A gauge invariant and hence physically meaningful definition of magnetic helicity density for random fields is proposed, using the Gauss linking formula, as the density of correlated field line linkages. This definition is applied to the random small scale field in weakly inhomogeneous turbulence, whose correlation length is small compared with the scale on which the turbulence varies. For inhomogeneous systems, with or without boundaries, our technique then allows one to study the local magnetic helicity density evolution in a gauge independent fashion, which was not possible earlier. This evolution equation is governed by local sources (owing to the mean field) and by the divergence of a magnetic helicity flux density. The role of magnetic helicity fluxes in alleviating catastrophic quenching of mean field dynamos is discussed., Comment: 4 pages, accepted by ApJ

The macroscopic behaviour of cosmic rays in turbulent magnetic fields is discussed. An implementation of anisotropic diffusion of cosmic rays with respect to the magnetic field in a non-conservative, high-order, finite-difference magnetohydrodynamic code is discussed. It is shown that the standard implementation fails near singular X-points of the magnetic field, which are common if the field is random. A modification to the diffusion model for cosmic rays is described and the resulting telegraph equation (implemented by solving a dynamic equation for the diffusive flux of cosmic rays) is used; it is argued that this modification may better describe the physics of cosmic ray diffusion. The present model reproduces several processes important for the propagation and local confinement of cosmic rays, including spreading perpendicular to the local large-scale magnetic field, controlled by the random-to-total magnetic field ratio, and the balance between cosmic ray pressure and magnetic tension. Cosmic ray diffusion is discussed in the context of a random magnetic field produced by turbulent dynamo action. It is argued that energy equipartition between cosmic rays and other constituents of the interstellar medium do not necessarily imply that cosmic rays play a significant role in the balance of forces., Comment: 11 pages, 12 figures, a major revision; accepted for publication in MNRAS

Several one and two dimensional mean field models are analyzed where the effects of current helicity fluxes and boundaries are included within the framework of the dynamical quenching model. In contrast to the case with periodic boundary conditions, the final saturation energy of the mean field decreases inversely proportional to the magnetic Reynolds number. If a nondimensional scaling factor in the current helicity flux exceeds a certain critical value, the dynamo can operate even without kinetic helicity, i.e. it is based only on shear and current helicity fluxes, as first suggested by Vishniac & Cho (2001, ApJ 550, 752). Only above this threshold is the current helicity flux also able to alleviate catastrophic quenching. The fact that certain turbulence simulations have now shown apparently non-resistively limited mean field saturation amplitudes may be suggestive of the current helicity flux having exceeded this critical value. Even below this critical value the field still reaches appreciable strength at the end of the kinematic phase, which is in qualitative agreement with dynamos in periodic domains. However, for large magnetic Reynolds numbers the field undergoes subsequent variations on a resistive time scale when, for long periods, the field can be extremely weak., Comment: 9 pages, 9 figures, accepted by Astron. Nachr

Star-disc coupling is considered in numerical models where the stellar field is not an imposed perfect dipole, but instead a more irregular self-adjusting dynamo-generated field. Using axisymmetric simulations of the hydromagnetic mean-field equations, it is shown that the resulting stellar field configuration is more complex, but significantly better suited for driving a stellar wind. In agreement with recent findings by a number of people, star-disc coupling is less efficient in braking the star than previously thought. Moreover, stellar wind braking becomes equally important. In contrast to a perfect stellar dipole field, dynamo-generated stellar fields favor field-aligned accretion with considerably higher velocity at low latitudes, where the field is weaker and originating in the disc. Accretion is no longer nearly periodic (as it is in the case of a stellar dipole), but it is more irregular and episodic., Comment: 19 pages, 15 figures, some errors corrected, Astron. Nach. (submitted). For higher quality images, see http://www.nordita.dk/~brandenb/papers/stellardyn/

Arguments for and against the widely accepted picture of a solar dynamo being seated in the tachocline are reviewed and alternative ideas concerning dynamos operating in the bulk of the convection zone, or perhaps even in the near-surface shear layer, are discussed. Based on the angular velocities of magnetic tracers it is argued that the observations are compatible with a distributed dynamo that may be strongly shaped by the near-surface shear layer. Direct simulations of dynamo action in a slab with turbulence and shear are presented to discuss filling factor and tilt angles of bipolar regions in such a model., Comment: 10 pages, 6 figures, Astrophys. J. 625 (scheduled for the 1 June 2005 issue)

Large scale dynamos produce small scale current helicity as a waste product that quenches the large scale dynamo process (alpha effect). This quenching can be catastrophic (i.e.intensify with magnetic Reynolds number) unless one has fluxes of small scale magnetic (or current) helicity out of the system. We derive the form of helicity fluxes in turbulent dynamos, taking also into account the nonlinear effects of Lorentz forces due to fluctuating fields. We confirm the form of an earlier derived magnetic helicity flux term, and also show that it is not renormalized by the small scale magnetic field, just like turbulent diffusion. Additional nonlinear fluxes are identified, which are driven by the anisotropic and antisymmetric parts of the magnetic correlations. These could provide further ways for turbulent dynamos to transport out small scale magnetic helicity, so as to avoid catastrophic quenching., Comment: 4 pages, Minor revisions to match version accepted in Physical Review Letters

The standard theory of the solar cycle in terms of an alpha-Omega dynamo hinges on a proper understanding of the nonlinear alpha effect. Boundary conditions play a surprisingly important role in determining the magnitude of alpha. For closed boundaries, the total magnetic helicity is conserved, and since the alpha effect produces magnetic helicity of one sign in the large scale field, it must simultaneously produce magnetic helicity of the opposite sign. It is this secondary magnetic helicity that suppresses the dynamo in a potentially catastrophic fashion. Open boundaries allow magnetic helicity to be lost. Simulations are presented that allow an estimate of alpha in the presence of open or closed boundaries, either with or without solar-like differential rotation. In all cases the sign of the magnetic helicity agrees with that observed at the solar surface (negative in the north, positive in the south), where significant amounts of magnetic helicity can be ejected via coronal mass ejections. It is shown that open boundaries tend to alleviate catastrophic alpha quenching. The importance of looking at current helicity instead of magnetic helicity is emphasized and the conceptual advantages are discussed., Comment: 8 pages, 7 figs, IAU Symp. 223, In: Multi-Wavelength Investigations of Solar Activity. Eds: A.V. Stepanov, E.E. Benevolenskaya & A.G. Kosovichev

Reaction-diffusion equations based on a polymerization model are solved to simulate the spreading of hypothetic left and right handed life forms on the Earth's surface. The equations exhibit front-like behavior as is familiar from the theory of the spreading of epidemics. It is shown that the relevant time scale for achieving global homochirality is not, however, the time scale of front propagation, but the much longer global diffusion time. The process can be sped up by turbulence and large scale flows. It is speculated that, if the deep layers of the early ocean were sufficiently quiescent, there may have been the possibility of competing early life forms with opposite handedness., Comment: submitted to Int. J. Astrobiol., 15 pages, 10 figs. submitted to Int. J. Astrobiol., 15 pages, 10 figs

The effect of compressibility on the onset of nonhelical turbulent dynamo action is investigated using both direct simulations as well as simulations with shock-capturing viscosities, keeping however the regular magnetic diffusivity. It is found that the critical magnetic Reynolds number increases from about 35 in the subsonic regime to about 70 in the supersonic regime. In the high resolution direct simulations the shock structures are much sharper than in the low resolution shock-capturing simulations. Nevertheless, the magnetic field looks roughly similar in both cases and does not show shock structures. Similarly, the onset of dynamo action is not significantly affected by the shock-capturing viscosity., Comment: 6 pages

The current understanding of astrophysical magnetic fields is reviewed, focusing on their generation and maintenance by turbulence. In the astrophysical context this generation is usually explained by a self-excited dynamo, which involves flows that can amplify a weak 'seed' magnetic field exponentially fast. Particular emphasis is placed on the nonlinear saturation of the dynamo. Analytic and numerical results are discussed both for small scale dynamos, which are completely isotropic, and for large scale dynamos, where some form of parity breaking is crucial. Central to the discussion of large scale dynamos is the so-called alpha effect which explains the generation of a mean field if the turbulence lacks mirror symmetry, i.e. if the flow has kinetic helicity. Large scale dynamos produce small scale helical fields as a waste product that quench the large scale dynamo and hence the alpha effect. With this in mind, the microscopic theory of the alpha effect is revisited in full detail and recent results for the loss of helical magnetic fields are reviewed., Comment: 285 pages, 72 figures, accepted by Phys. Rep

The dimensionless kinetic energy dissipation rate C_epsilon is estimated from numerical simulations of statistically stationary isotropic box turbulence that is slightly compressible. The Taylor microscale Reynolds number Re_lambda range is 20 < Re_lambda < 220 and the statistical stationarity is achieved with a random phase forcing method. The strong Re_lambda dependence of C_epsilon abates when Re_lambda approx. 100 after which C_epsilon slowly approaches approx 0.5 a value slightly different to previously reported simulations but in good agreement with experimental results. If C_epsilon is estimated at a specific time step from the time series of the quantities involved it is necessary to account for the time lag between energy injection and energy dissipation. Also, the resulting value can differ from the ensemble averaged value by up to +-30%. This may explain the spread in results from previously published estimates of C_epsilon., Comment: 7 pages, 7 figures. Submitted to Phys. Rev. E

The excitation of gravity waves by penetrative convective plumes is investigated using 2D direct simulations of compressible convection. The oscillation field is measured by a new technique based on the projection of our simulation data onto the theoretical g-modes solutions of the associated linear eigenvalue problem. This allows us to determine both the excited modes and their corresponding amplitudes accurately., Comment: 4 pages, 2 figures, proceeding of the Porto conference "Asteroseismology Across the HR Diagram", edited by M.J. Thompson, M.S Cunha & M.J.P.G. Monteiro, Kluwer Academic Publishers (also in Ap&SS, 284, 237)

Numerical turbulence with hyperviscosity is studied and compared with direct simulations using ordinary viscosity and data from wind tunnel experiments. It is shown that the inertial range scaling is similar in all three cases. Furthermore, the bottleneck effect is approximately equally broad (about one order of magnitude) in these cases and only its height is increased in the hyperviscous case--presumably as a consequence of the steeper decent of the spectrum in the hyperviscous subrange. The mean normalized dissipation rate is found to be in agreement with both wind tunnel experiments and direct simulations. The structure function exponents agree with the She-Leveque model. Decaying turbulence with hyperviscosity still gives the usual t^{-1.25} decay law for the kinetic energy, and also the bottleneck effect is still present and about equally strong., Comment: Final version (7 pages)

Non-helical hydromagnetic turbulence with an externally imposed magnetic field is investigated using direct numerical simulations. It is shown that the imposed magnetic field lowers the spectral magnetic energy in the inertial range. This is explained by a suppression of the small scale dynamo. At large scales, however, the spectral magnetic energy increases with increasing imposed field strength for moderately strong fields, and decreases only slightly for even stronger fields. The presence of Alfven waves is explicitly confirmed by monitoring the evolution of magnetic field and velocity at one point. The frequency omega agrees with vA k1, where vA is the Alfven speed and k1 is the smallest wavenumber in the box., Comment: Final version (7 pages)

A new simulation set-up is proposed for studying mean field dynamo action. The model combines the computational advantages of local cartesian geometry with the ability to include a shear profile that resembles the sun's differential rotation at low latitudes. It is shown that in a two-dimensional mean field model this geometry produces cyclic solutions with dynamo waves traveling away from the equator -- as expected for a positive alpha effect in the northern hemisphere. In three dimensions with turbulence driven by a helical forcing function, an alpha effect is self-consistently generated in the presence of a finite imposed toroidal magnetic field. The results suggest that, due to a finite flux of current helicity out of the domain, alpha quenching appears to be non-catastrophic -- at least for intermediate values of the magnetic Reynolds number. For larger values of the magnetic Reynolds number, however, there is evidence for a reversal of the trend and that $\alpha$ may decrease with increasing magnetic Reynolds number. Control experiments with closed boundaries confirm that in the absence of a current helicity flux, but with shear as before, alpha quenching is always catastrophic and alpha decreases inversely proportional to the magnetic Reynolds number. For solar parameters, our results suggest a current helicity flux of about 0.001 G^2/s. This corresponds to a magnetic helicity flux, integrated over the northern hemisphere and over the 11 year solar cycle, of about 10^{46}Mx^2., Comment: 9 pages, 10 figures, A&A (in press)

Decaying turbulence is studied numerically using as initial condition a random flow whose shell-integrated energy spectrum increases with wavenumber k like k^q. Alternatively, initial conditions are generated from a driven turbulence simulation by simply stopping the driving. It is known that the dependence of the decaying energy spectrum on wavenumber, time, and viscosity can be collapsed onto a unique scaling function that depends only on two parameters. This is confirmed using three-dimensional simulations and the dependence of the scaling function on its two arguments is determined., Comment: 8 pages, 9 figures. Published in PRE

The excitation of internal gravity waves by an entropy bubble oscillating in an isothermal atmosphere is investigated using direct two-dimensional numerical simulations. The oscillation field is measured by a projection of the simulated velocity field onto the anelastic solutions of the linear eigenvalue problem for the perturbations. This facilitates a quantitative study of both the spectrum and the amplitudes of excited g-modes., Comment: 12 pages, 11 figures, Appendices only available online

Considerable progress has been made in understanding the hydrodynamics, but only to a certain extent the magnetohydrodynamics, of shaping bipolar outflows forming protoplanetary nebulae (PPNs) and planetary nebulae (PNs). In particular, Blackman et al. (2001b,2001a) point out two problems related to the formation of PNs and PPNs, regarding the formation of multipolar structures and the origin of the nebulae. They propose a solution by giving a semi-quantitative physical model which should be investigated by numerical simulations., Comment: 4 pages, 6 figures, APN3 conference proceedings

Local three-dimensional shearing box simulations of the compressible coupled dust-gas equations are used in the fluid approximation to study the evolution of different initial vortex configurations in a protoplanetary disc and their dust-trapping capabilities. The initial conditions for the gas are derived from an analytic solution to the compressible Euler equation and the continuity equation. The solution is valid if there is a vacuum outside the vortex. In the simulations the vortex is either embedded in a hot corona, or it is extended in a cylindrical fashion in the vertical direction. Both configurations are found to survive for at least one orbit and lead to accumulation of dust inside the vortex. This confirms earlier findings that dust accumulates in anticyclonic vortices, indicating that this is a viable mechanism for planetesimal formation., Comment: 15 pages, 13 figures, accepted for publication in A&A

The interaction between a protostellar magnetosphere and a surrounding dynamo-active accretion disc is investigated using an axisymmetric mean-field model. In all models investigated, the dynamo-generated magnetic field in the disc arranges itself such that in the corona, the field threading the disc is anti-aligned with the central dipole so that no X-point forms. When the magnetospheric field is strong enough (stellar surface field strength around 2 kG or larger), accretion happens in a recurrent fashion with periods of around 15 to 30 days, which is somewhat longer than the stellar rotation period of around 10 days. In the case of a stellar surface field strength of at least a few 100 G, the star is being spun up by the magnetic torque exerted on the star. The stellar accretion rates are always reduced by the presence of a magnetosphere which tends to divert a much larger fraction of the disc material into the wind. Both, a pressure-driven stellar wind and a disc wind form. In all our models with disc dynamo, the disc wind is structured and driven by magneto-centrifugal as well as pressure forces., Comment: 16 pages, 22 figures, accepted for publication in A&A

Nonhelical hydromagnetic forced turbulence is investigated using large scale simulations on up to 256 processors and $1024^3$ meshpoints. The magnetic Prandtl number is varied between 1/8 and 30, although in most cases it is unity. When the magnetic Reynolds number is based on the inverse forcing wavenumber, the critical value for dynamo action is shown to be around 35 for magnetic Prandtl number of unity. For small magnetic Prandtl numbers we find the critical magnetic Reynolds number to increase with decreasing magnetic Prandtl number. The Kazantsev $k^{3/2}$ spectrum for magnetic energy is confirmed for the kinematic regime, i.e. when nonlinear effects are still unimportant and when the magnetic Prandtl number is unity. In the nonlinear regime, the energy budget converges for large Reynolds numbers (around 1000) such that for our parameters about 70% is in kinetic energy and about 30% is in magnetic energy. The energy dissipation rates are converged to 30% viscous dissipation and 70% resistive dissipation. Second order structure functions of the Elsasser variables give evidence for a $k^{-5/3}$ spectrum. Nevertheless, the three-dimensional spectrum is close to $k^{-3/2}$, but we argue that this is due to the bottleneck effect. The bottleneck effect is shown to be equally strong both for magnetic and nonmagnetic turbulence, but it is far weaker in one-dimensional spectra that are normally studied in laboratory turbulence. Structure function exponents for other orders are well described by the She-Leveque formula, but the velocity field is significantly less intermittent and the magnetic field is more intermittent than the Elsasser variables., Comment: Final version

Numerical simulations of the multi-phase interstellar medium have been carried out, using a 3D, nonlinear, magnetohydrodynamic, shearing-box model, with random motions driven by supernova explosions. These calculations incorporate the effects of magnetic fields and rotation in 3D; these play important dynamical roles in the galaxy, but are neglected in many other simulations. The supernovae driving the motions are not arbitrarily imposed, but occur where gas accumulates into cold, dense clouds; their implementation uses a physically motivated model for the evolution of such clouds. The process is self-regulating, and produces mean supernova rates as part of the solution. Simulations with differing mean density show a power law relation between the supernova rate and density, with exponent 1.7; this value is within the range suggested from observations (taking star formation rate as a proxy for supernova rate). The global structure of the supernova driven medium is strongly affected by the presence of magnetic fields; e.g. for one solution the filling factor of hot gas is found to vary from 0.19 (with no field) to 0.12 (with initial mid-plane field B_0=6 muG)., Comment: 6 pages, 4 figures, v2: minor revisions, now accepted for publication in: Magnetic fields and star formation: theory versus observations, eds: A. I. Gomez de Castro et al., Kluwer Acad. Publ., Dordrecht

An axisymmetric model of a cool, dynamo-active accretion disc is applied to protostellar discs. Thermally and magnetically driven outflows develop that are not collimated within 0.1 AU. In the presence of a central magnetic field from the protostar, accretion onto the protostar is highly episodic, which is in agreement with earlier work., Comment: 8 pages, 9 figures, to be published in: Magnetic fields and star formation: theory versus observations, eds: A. I. Gomez de Castro et al., Kluwer Acad. Publ., Dordrech

Evidence for non-Fickian diffusion of a passive scalar is presented using direct simulations of homogeneous isotropic turbulence. The results compare favorably with an explicitly time-dependent closure model based on the tau approximation. In the numerical experiments three different cases are considered: (i) zero mean concentration with finite initial concentration flux, (ii) an initial top hat profile for the concentration, and (iii) an imposed background concentration gradient. All cases agree in the resulting relaxation time in the tau approximation relating the triple correlation to the concentration flux. The first order smoothing approximation is shown to be inapplicable., Comment: 10 pages, 7 figs, Physics of Fluids (final version)

According to the kinematic theory of nonhelical dynamo action the magnetic energy spectrum increases with wavenumber and peaks at the resistive cutoff wavenumber. It has previously been argued that even in the dynamical case the magnetic energy peaks at the resistive scale. Using high resolution simulations (up to 1024^3 meshpoints) with no large scale imposed field we show that the magnetic energy peaks at a wavenumber that is independent of the magnetic Reynolds number and about 5 times larger than the forcing wavenumber. Throughout the inertial range the spectral magnetic energy exceeds the kinetic energy by a factor of 2 to 3. Both spectra are approximately parallel. The total energy spectrum seems to be close to k^{-3/2}, but there is a strong bottleneck effect and it is suggested that the asymptotic spectrum is instead k^{-5/3}. This is supported by the value of the second order structure function exponent that is found to be zeta_2=0.70, suggesting a k^{-1.70} spectrum. The third order structure function scaling exponent is very close to unity, in agreement with Goldreich-Sridhar theory. Adding an imposed field tends to suppress the small scale magnetic field. We find that at large scales the magnetic power spectrum follows then a k^{-1} slope. When the strength of the imposed field is of the same order as the dynamo generated field, we find almost equipartition between the magnetic and kinetic power spectra., Comment: 8 pages