Search

Angular momentum transport due to hydrodynamic turbulent convection is studied using local three-dimensional numerical simulations employing the shearing box approximation. We determine the turbulent viscosity from non-rotating runs over a range of values of the shear parameter and use a simple analytical model in order to extract the non-diffusive contribution (L-effect) to the stress in runs where rotation is included. Our results suggest that the turbulent viscosity is on the order of the mixing length estimate and weakly affected by rotation. The L-effect is non-zero and a factor of 2-4 smaller than the turbulent viscosity in the slow rotation regime. We demonstrate that for Keplerian shear, the angular momentum transport can change sign and be outward when the rotation period is greater than the turnover time, i.e., when the Coriolis number is below unity. This result seems to be relatively independent of the value of the Rayleigh number.

In the mean-field theory of magnetic fields, turbulent transport, i.e., the turbulent electromotive force is described by a combination of the a 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 a effect, and turbulent diffusivity can be quite different from the actual values.

Dynamo action owing to helically forced turbulence and large-scale shear is studied using direct numerical simulations. The resulting magnetic field displays propagating wave-like behavior. This behavior can be modeled in terms of an aO dynamo. In most cases super-equipartition fields are generated. By varying the fraction of helicity of the turbulence the regeneration of poloidal fields via the helicity effect (corresponding to the a-effect) is regulated. The saturation level of the magnetic field in the numerical models is consistent with a linear dependence on the ratio of the fractional helicities of the small and large-scale fields, as predicted by a simple nonlinear mean-field model. As the magnetic Reynolds number (Re M ) based on the wavenumber of the energy-carrying eddies is increased from 1 to 180, the cycle frequency of the large-scale field is found to decrease by a factor of about 6 in cases where the turbulence is fully helical. This is interpreted in terms of the turbulent magnetic diffusivity, which is found to be only weakly dependent on the Re M .

The existence of large-scale dynamos in rigidly rotating turbulent convection without shear is studied using three-dimensional numerical simulations of penetrative rotating compressible convection. We demonstrate that rotating convection in a Cartesian domain can drive a large-scale dynamo even in the absence of shear. The large-scale field contains a significant fraction of the total field in the saturated state. The simulation results are compared with one-dimensional mean-field dynamo models where turbulent transport coefficients, as determined using the test field method, are used. The reason for the absence of large-scale dynamo action in earlier studies is shown to be due to the rotation being too slow: whereas the a-effect can change sign, its magnitude stays approximately constant as a function of rotation, and the turbulent diffusivity decreases monotonically with increasing rotation. Only when rotation is rapid enough a large-scale dynamo can be excited. The one-dimensional mean-field model with dynamo coefficients from the test-field results predicts reasonably well the dynamo excitation in the direct simulations. This result further validates the test field procedure and reinforces the interpretation that the observed dynamo is driven by a turbulent a-effect. This result demonstrates the existence of an a-effect and an a2-dynamo with natural forcing.

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.

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 timescales, 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.

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, [?]r[?]. When [?]r[?] 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 104 K, respectively. However, in all cases the resulting average pressure [?]p[?] is independent of [?]r[?] and just a little above the minimum value. For a constant heating rate of 0.015 ergs g-1 s-1, the mean pressure is around 24 x 10-14 dyn (corresponding to p/kB [?] 1750 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-1 are obtained, the resulting dissipation rates are comparable to the thermal energy input rate. The resulting mean pressures are then about 30 x 10-14 dyn, corresponding to p/kB [?] 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.

Magnetohydrodynamic simulations of fully convective, rotating spheres with volume heating near the center and cooling at the surface are presented. The dynamo-generated magnetic field saturates at equipartition field strength near the surface. In the interior, the field is dominated by small-scale structures, but outside the sphere, by the global scale. Azimuthal averages of the field reveal a large-scale field of smaller amplitude also inside the star. The internal angular velocity shows some tendency to be constant along cylinders and is "antisolar" (fastest at the poles and slowest at the equator).

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.

The emergence and spread of chirality on the early Earth is considered by studying a set of reaction-diffusion equations based on a polymerization model. It is found that effective mixing of the early oceans is necessary to reach the present homochiral state. The possibility of introducing mass extinctions and modifying the emergence rate of life are discussed.

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.

We supplement the mean field dynamo growth equation with the total magnetic helicity evolution equation. This provides an explicitly time-dependent model for a-quenching in dynamo theory. For dynamos without shear, this approach accounts for the observed large-scale field growth and saturation in numerical simulations. After a significant kinematic phase, the dynamo is resistively quenched, i.e., the saturation time depends on the microscopic resistivity. This is independent of whether or not the turbulent diffusivity is resistively quenched. We find that the approach is also successful for dynamos that include shear and exhibit migratory waves (cycles). In this case, however, whether or not the cycle period remains of the order of the dynamical timescale at large magnetic Reynolds numbers does depend on how the turbulent magnetic diffusivity quenches. Since this is unconstrained by magnetic helicity conservation, the diffusivity is currently an input parameter. Comparison with current numerical experiments suggests a turbulent diffusivity that depends only weakly on the magnetic Reynolds number, but higher resolution simulations are needed.

Various approaches to estimate turbulent transport coefficients from numerical simulations of hydromagnetic turbulence are discussed. A quantitative comparison between the averaged magnetic field obtained from a specific three-dimensional simulation of a rotating turbulent shear flow in a slab and a simple one-dimensional alpha-omega dynamo model is given. A direct determination of transport coefficients is attempted by calculating the correlation matrix of different components of the field and its derivatives. This matrix relates the electromotive force to physically relevant parameters like the tensor components of the f -effect and the turbulent diffusivity. The f -effect operating on the toroidal field is found to be negative and of similar magnitude as the value obtained in previous work by correlating the electromotive force with the mean magnetic field. The turbulent diffusion of the toroidal field is comparable to the kinematic viscosity that was determined earlier by comparing the stress with the shear. However, the turbulent diffusion of the radial field component is smaller and can even be formally negative. The method is then modified to obtain the spectral dependence of the turbulent transport coefficients on the wavenumber. There is evidence for nonlocal behaviour in that most of the response comes from the smallest wavenumbers corresponding to the largest scale possible in the simulation. Again, the turbulent diffusion coefficient for the radial field component is small, or even negative, which is considered unphysical. However, when the diffusion tensor is assumed to be diagonal the radial component of the diffusion tensor is positive, supporting thus the relevance of a nonlocal approach. Finally, model calculations are presented using nonlocal prescriptions of the f -effect and the turbulent diffusion. We emphasize that in all cases the electromotive force exhibits a strong stochastic component which make the f -effect and the turbulent diffusion intrinsically noisy.

A numerical model of isotropic homogeneous turbulence with helical forcing is investigated. The resulting flow, which is essentially the prototype of the a2 dynamo of mean field dynamo theory, produces strong dynamo action with an additional large-scale field on the scale of the box (at wavenumber k = 1; forcing is at k = 5). This large-scale field is nearly force free and exceeds the equipartition value. As the magnetic Reynolds number Rm increases, the saturation field strength and the growth rate of the dynamo increase. However, the time it takes to build up the large-scale field from equipartition to its final superequipartition value increases with magnetic Reynolds number. The large-scale field generation can be identified as being due to nonlocal interactions originating from the forcing scale, which is characteristic of the a-effect. Both a and turbulent magnetic diffusivity et are determined simultaneously using numerical experiments where the mean field is modified artificially. Both quantities are quenched in an Rm-dependent fashion. The evolution of the energy of the mean field matches that predicted by an a2 dynamo model with similar a and et quenchings. For this model an analytic solution is given that matches the results of the simulations. The simulations are numerically robust in that the shape of the spectrum at large scales is unchanged when changing the resolution from 303 to 1203 mesh points, or when increasing the magnetic Prandtl number (viscosity/magnetic diffusivity) from 1 to 100. Increasing the forcing wavenumber to 30 (i.e., increasing the scale separation) makes the inverse cascade effect more pronounced, although it remains otherwise qualitatively unchanged.

Local hydromagnetic simulations of accretion–disc turbulence currently provide the most convincing evidence that the origin of turbulence in discs could be the Balbus–Hawley magnetorotational instability. The main results of such calculations are highlighted with particular emphasis on the generation of large–scale magnetic fields. Comparison with mean–field dynamo theory is made. This theory is then used to address the question of the launching and collimation of winds emanating from the disc surfaces.

We further explore nondimensional relationships between the magnetic dynamo cycle period Pcyc, the rotational period Prot, the activity level (as observed in Ca II HK), and other stellar properties by expanding the stellar sample studied in the first paper in this series. We do this by adding photometric and other cycles seen in active stars and the secondaries of CV systems and by selectively adding less certain cycles from the Mount Wilson HK survey; evolved stars, long-term HK trends and secondary Pcyc are also considered. We confirm that most stars with age t [?] 0.1 Gyr occupy two roughly parallel branches, separated by a factor of ~6 in Pcyc, with the ratio of cycle and rotational frequencies ocyc/O [?] Ro-0.5, where Ro is the Rossby number. Using the model of the first paper in this series, this result implies that the a effect increases with mean magnetic field (contrary to the traditional a-quenching concept) and that a and ocyc decrease with t. Stars are not strictly segregated onto one or the other branch by activity level, though the high-ocyc/O branch is primarily composed of inactive stars. The expanded data set suggests that for t [?] 1 Gyr, stars can have cycles on one or both branches, though among older stars, those with higher (lower) mass tend to have their primary Pcyc on the lower (upper) ocyc/O branch. The Sun's ~80 yr Gleissberg cycle agrees with this scenario, suggesting that long-term activity "trends" in many stars may be segments of long (Pcyc ~ 50-100 yr) cycles not yet resolved by the data. Most very active stars (Prot < 3 days) appear to occupy a new, third branch with ocyc/O [?] Ro0.4. Many RS CVn variables lie in a transition region between the two most active branches. We compare our results with various models, discuss their implications for dynamo theory and evolution, and use them to predict Pcyc for three groups: stars with long-term HK trends, stars in young open clusters, and stars that may be in Maunder-like magnetic minima.

There is phenomenological evidence that magnetic reconnection operates in the interstellar medium, and magnetic reconnection is also necessary for the operation of a galactic dynamo. The extremely long ohmic diffusion times of magnetic fields in typical interstellar structures suggest that reconnection occurs in two stages, with thin current layers that have relatively short resistive decay times forming by magnetohydrodynamical processes first, followed by reconnection of the fields in the layers. We propose that ambipolar drift can lead to the formation of these thin sheets in weakly ionized interstellar gas and can delineate the parameter regime in which this occurs by means of a numerical model: we find that the magnetic field cannot be too large and the medium cannot be too diffusive. Both limits are imposed by the requirement that the field be wound up about 1 time by the eddy.

In a recent work (Covas et al., 1996), the behaviour and the robustness of truncated α Ω dynamos with a dynamic α were studied with respect to a number of changes in the driving term of the dynamic α equation, which was considered previously by Schmalz and Stix (1991) to be of the form ∼ AΦBΦ. Here we review and extend our previous work and consider the effect of adding a quadratic quenching term of the form α|B|2. We find that, as before, such a change can have significant effects on the dynamics of the related truncated systems. We also find intervals of (negative) dynamo numbers, in the system considered by Schmalz and Stix (1991), for which there is sensitivity with respect to small changes in the dynamo number and the initial conditions, similar to what was found in our previous work. This latter behaviour may be of importance in producing the intermittent type of behaviour observed in the Sun.

Axisymmetric mean‐field dynamo models in spherical shells are shown to be capable of producing temporally intermittent behaviour. This is of potential importance since (i) it is, as far as we are aware, the first time such behaviour has been produced internally by a mean‐field dynamo model in a spherical shell, without requiring any additional assumptions or truncations, and (ii) it may be characteristic of the type of behaviour observed in the long‐term record of solar activity, such as Maunder minima. We also show that these types of behaviour persist when the functional form of the alpha quenching is altered and also occur over intervals of the shell thickness and the dynamo number.

We use the mean-field dynamo equations to show that spatially and temporally incoherent fluctuations in the helicity in mirror-symmetric turbulence in a shearing flow can generate a large-scale, coherent magnetic field. We illustrate this effect with simulations of a few simple systems. For statistically homogeneous turbulence, we find that the dynamo growth rate is roughly ?eddy?1/3?shear?2/3Neddy?1/3(?eddy/LB)2/3, where ?eddyis the eddy turnover time, ?shear?1is the local shearing rate, Neddyis the number of eddies per magnetic domain, ?eddyis the size of an eddy, and LBis the extent of a magnetic domain perpendicular to the mean flow direction. Even in the presence of turbulence and shear the dynamo can be stopped by turbulent dissipation if (for example) the eddy scale is close to the magnetic domain scale and ?shear> ?eddy. We also identify a related incoherent dynamo in a system with a stationary distribution of helicity with a high-spatial frequency and an average value of zero. In accretion disks, the incoherent dynamo can lead to axisymmetric magnetic domains the radial and vertical dimensions of which will be comparable to the disk height. This process may be responsible for dynamo activity seen in simulations of dynamo-generated turbulence involving, for example, the Balbus-Hawley instability. However, although it explains the generation of a magnetic field in numerical simulations without significant large-scale average helicity and the occasional field reversals, it also predicts that the dimensionless viscosity will scale as ~(h/r)2, which is not seen in the simulations. On the other hand, this result is consistent with phenomenological models of accretion disks, although these suggest a slightly shallower dependence on h/r. We discuss some possible resolutions to these contradictions.

The radial structure of a thin accretion disc is calculated in the presence of a central dipole magnetic field aligned with the rotation axis. The problem is treated using a modified expression for the turbulent magnetic diffusion, which allows the angular momentum equation to be integrated analytically. The governing algebraic equations are solved iteratively between 1 and 104stellar radii. An analytic approximation is provided that is valid near the disruption radius at about 100 stellar radii. At that point, which is approximately 60 per cent of the Alfvén radius and typically about 30 per cent of the corotation radius, the disc becomes viscously unstable. This instability results from the fact that both radiation pressure and opacity caused by electron scattering become important. This in turn is a consequence of the magnetic field which leads to an enhanced temperature in the inner parts. This is because the magnetic field gives rise to a strongly enhanced vertically integrated viscosity, so that the viscous torque can balance the magnetic torque.

Astrobiology harbours a number of rather diverse disciplines combining expertise in astronomy and astrophysics, biophysics and biology, chemistry and biochemistry, geophysics and geology, as well as mathematics. The need to foster advances in astrobiology are two-fold. On the one hand, there are many scientific reasons: the discoveries of extra-solar planets which contribute to our understanding of the Solar System and the formation of Earth-like planets, the realization that life can thrive under rather extreme conditions making it more probable for life to exist elsewhere in the Solar System and beyond, and the fact that major resources are being spent in developing the technology to produce artificial life, which helps us to appreciate the range of possibilities that nature may have utilized on Earth or elsewhere. On the other hand, astrobiology touches upon some fundamental questions regarding our very existence, and it is perhaps this that attracts the broad interest of scientists and the public alike. As a result, astrobiology networks and astrobiology centres have been emerging all over the world.

Magnetic helicity has risen to be a major player in dynamo theory, with the helicity of the small-scale field being linked to the dynamo saturation process for the large-scale field. It is a nearly conserved quantity, which allows its evolution equation to be written in terms of production and flux terms. The flux term can be decomposed in a variety of fashions. One particular contribution that has been expected to play a significant role in dynamos in the presence of mean shear was isolated by Vishniac & Cho. Magnetic helicity fluxes are explicitly gauge dependent however, and the correlations that have come to be called the Vishniac-Cho flux were determined in the Coulomb gauge, which turns out to be fraught with complications in shearing systems. While the fluxes of small-scale helicity are explicitly gauge dependent, their divergences can be gauge independent. We use this property to investigate magnetic helicity fluxes of the small-scale field through direct numerical simulations in a shearing-box system and find that in a numerically usable gauge the divergence of the small-scale helicity flux vanishes, while the divergence of the Vishniac-Cho flux remains finite. We attribute this seeming contradiction to the existence of horizontal fluxes of small-scale magnetic helicity with finite divergences.