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The short time evolution of three dimensional small perturbations is studied. Exhibiting spectral asymptotic stability, thin discs are nonetheless shown to host intensive hydrodynamical activity in the shape of non modal growth of initial small perturbations. Two mechanisms that lead to such behavior are identified and studied, namely, non-resonant excitation of vertically confined sound waves by stable planar inertia-coriolis modes that results in linear growth with time, as well as resonant coupling of those two modes that leads to a quadratic growth of the initial perturbations. It is further speculated that the non modal growth can give rise to secondary strato-rotational instabilities and thus lead to a new route to turbulence generation in thin discs.

The short time evolution of three dimensional small perturbations is studied. Exhibiting spectral asymptotic stability, thin discs are nonetheless shown to host intensive hydrodynamical activity in the shape of non modal growth of initial small perturbations. Two mechanisms that lead to such behavior are identified and studied, namely, non-resonant excitation of vertically confined sound waves by stable planar inertia-coriolis modes that results in linear growth with time, as well as resonant coupling of those two modes that leads to a quadratic growth of the initial perturbations. It is further speculated that the non modal growth can give rise to secondary strato-rotational instabilities and thus lead to a new route to turbulence generation in thin discs.

We consider the flow of an electrically conducting fluid between differentially rotating cylinders, in the presence of an externally imposed toroidal field B_0 (r_i/r) e_phi. It is known that the classical, axisymmetric magnetorotational instability does not exist for such a purely toroidal imposed field. We show here that a non-axisymmetric magnetorotational instability does exist, having properties very similar to the axisymmetric magnetorotational instability in the presence of an axial field.

We consider the flow of an electrically conducting fluid between differentially rotating cylinders, in the presence of an externally imposed toroidal field B_0 (r_i/r) e_phi. It is known that the classical, axisymmetric magnetorotational instability does not exist for such a purely toroidal imposed field. We show here that a non-axisymmetric magnetorotational instability does exist, having properties very similar to the axisymmetric magnetorotational instability in the presence of an axial field.

A geodynamo-model based on an \alpha-effect which has been computed under conditions suitable for the geodynamo is constructed. For a highly restricted class of radial \alpha-profiles the linear \alpha2-model exhibits oscillating solutions on a timescale given by the turbulent diffusion time. The basic properties of the periodic solutions are presented and the influence of the inner core size on the characteristics of the critical range that allows for oscillating solutions is shown. Reversals are interpreted as half of such an oscillation. They are rather seldom events because they can only occur if the \alpha-profile exists long enough within the small critical range that allows for periodic solutions. Due to strong fluctuations on the convective timescale the probability of such a reversal is very small. Finally, a simple non-linear mean-field model with reasonable input parameters based on simulations of Giesecke et al. (2005) demonstrates the plausibility of the presented theory with a long-time series of a (geo-)dynamo reversal sequence., Comment: 8 pages, 9 figures, Astron. Nachr. 326, No. 8, 693-700 (2005)

A geodynamo-model based on an \alpha-effect which has been computed under conditions suitable for the geodynamo is constructed. For a highly restricted class of radial \alpha-profiles the linear \alpha2-model exhibits oscillating solutions on a timescale given by the turbulent diffusion time. The basic properties of the periodic solutions are presented and the influence of the inner core size on the characteristics of the critical range that allows for oscillating solutions is shown. Reversals are interpreted as half of such an oscillation. They are rather seldom events because they can only occur if the \alpha-profile exists long enough within the small critical range that allows for periodic solutions. Due to strong fluctuations on the convective timescale the probability of such a reversal is very small. Finally, a simple non-linear mean-field model with reasonable input parameters based on simulations of Giesecke et al. (2005) demonstrates the plausibility of the presented theory with a long-time series of a (geo-)dynamo reversal sequence., Comment: 8 pages, 9 figures, Astron. Nachr. 326, No. 8, 693-700 (2005)

We measure the eddy viscosity in the outermost layers of the solar convection zone by comparing the rotation law computed with the Reynolds stress resulting from f-plane simulations of the angular momentum transport in rotating convection with the observed differential rotation pattern. The simulations lead to a negative vertical and a positive horizontal angular momentum transport. The consequence is a subrotation of the outermost layers, as it is indeed indicated both by helioseismology and the observed rotation rates of sunspots. In order to reproduce the observed gradient of the rotation rate, a value of about 1.5 x 10(13) cm(2)/s for the eddy viscosity is necessary. Comparison with the magnetic eddy diffusivity derived from the sunspot decay yields a surprisingly large magnetic Prandtl number of 150 for the supergranulation layer. The negative gradient of the rotation rate also drives a surface meridional flow towards the poles, in agreement with the results from Doppler measurements. The successful reproduction of the abnormally positive horizontal cross correlation (on the northern hemisphere) observed for bipolar groups then provides an independent test of the resulting eddy viscosity.

We measure the eddy viscosity in the outermost layers of the solar convection zone by comparing the rotation law computed with the Reynolds stress resulting from f-plane simulations of the angular momentum transport in rotating convection with the observed differential rotation pattern. The simulations lead to a negative vertical and a positive horizontal angular momentum transport. The consequence is a subrotation of the outermost layers, as it is indeed indicated both by helioseismology and the observed rotation rates of sunspots. In order to reproduce the observed gradient of the rotation rate, a value of about 1.5 x 10(13) cm(2)/s for the eddy viscosity is necessary. Comparison with the magnetic eddy diffusivity derived from the sunspot decay yields a surprisingly large magnetic Prandtl number of 150 for the supergranulation layer. The negative gradient of the rotation rate also drives a surface meridional flow towards the poles, in agreement with the results from Doppler measurements. The successful reproduction of the abnormally positive horizontal cross correlation (on the northern hemisphere) observed for bipolar groups then provides an independent test of the resulting eddy viscosity.

The velocity fluctuations in a spherical shell arising from sinusoidal perturbations of a Keplerian shear flow with a free amplitude parameter \epsilon are studied numerically by means of fully 3D nonlinear simulations. The investigations are performed at high Reynolds numbers, i.e. 3000 < Re < 5000. We find Taylor-Proudman columns of large eddies parallel to the rotation axis for sufficiently strong perturbations. An instability sets in at critical amplitudes with \epsilon_crit \propto Re^-1. The whole flow turns out to be almost axisymmetric and nonturbulent exhibiting, however, a very rich radial and latitudinal structure. The Reynolds stress is positive in the entire computational domain, from its Gaussian radial profile a positive viscosity-alpha of about 10^-4 is derived. The kinetic energy of the turbulent state is dominated by the azimuthal component whereas the other components are smaller by two orders of magnitude. Our simulations reveal, however, that these structures disappear as soon as the perturbations are switched off. We did not find an ``effective'' perturbation whose amplitude is such that the disturbance is sustained for large times (cf. Dauchot & Daviaud 1995) which is due to the effective violation of the Rayleigh stability criterion. The fluctuations rapidly smooth the original profile towards to pure Kepler flow which, therefore, proves to be stable in that sense., Comment: 9 pages, 9 figures, Astron. Nachr., in press

The rotational influence on the eddy-diffusivity tensor D_ij for anisotropic turbulence fields is considered in order to explain the lithium decay law during the spin-down process of solar-type stars. Rotation proves to be highly effective in the transfer of chemicals through the solar tachocline (beneath the convection zone) which is assumed to contain only turbulence with horizontal motions. The effect is so strong that the tachocline turbulence must not exceed a limit of ~10^-(3...4) of the rms velocity in the convection zone in order to let the lithium survive after Gigayears. Such long depletion times can also be explained by a very small rotational influence upon the eddy-diffusion tensor if it is realized with correlation times shorter than 15 min. It is argued that such slow and/or short-living turbulence beneath the convection zone could hardly drive the solar dynamo. In our theory the diffusion remains small for rapid rotation due to the rotational quenching of the turbulence. In young stellar clusters like Pleiades, there should be a (positive) correlation between rotation rate and lithium abundance, where the fastest stars should have maximal lithium. First inspections of the data seem to confirm this finding., Comment: 6 pages, 9 figures, aa.cls

The presence of an imposed external magnetic field may drastically influence the structure of thin accretion discs. The magnetic field energy is here assumed to be in balance with the thermal energy of the accretion flow. The vertical magnetic field, its toroidal component B^tor at the disc surface (due to different rotation rates between disc and its magnetosphere), the turbulent magnetic Prandtl number and the viscosity-alpha are the key parameters of our model. Inside the corotation radius for rather small B^tor the resulting inclination angle i of the magnetic field lines to the disc surface normal can exceed the critical value 30^\circ (required to launch cold jets) even for small magnetic Prandtl numbers of order unity. The self-consistent consideration of both magnetic field and accretion flow demonstrates a weak dependence of the inclination (``dragging'') angle on the magnetic Prandtl number for given surface density but a strong dependence on the toroidal field component at the disc surface. A magnetic disc is thicker than a nonmagnetic one for typical parameter values. The accretion rate can be strongly amplified by large B^tor and small magnetic Prandtl number. On the other hand, for given accretion rate the magnetised disc is less massive than the standard-alpha disc. The surface values of the toroidal magnetic fields which are necessary to induce considerably high values for the inclination angle are much smaller than expected and are of order 10^-3 of the imposed vertical field. As the innermost part of the disc produces the largest B^tor, the largest radial inclination can be expected also there. The idea is therefore supported that the cold jets are launched only in the central disc area., Comment: 8 pages, 6 figures, Submitted to MNRAS

We perform global three-dimensional simulations of accretion disks integrating the compressible, non-viscous, but diffusive MHD equations. The disk is supposed to be isothermal. We make use of the ZEUS-3D code integrating the MHD equations and added magnetic diffusivity. We measure the efficiency of the angular-momentum transport. Various model simulations delivered transport parameters of alpha_SS=0.01 to 0.05 which are consistent with several local numerical investigations. Two of the models reach a highly turbulent state at which alpha_SS is of the order of 0.1. After a certain stage of saturating of the turbulence, Reynolds stress is found to be negative (inward transport) in many of the models, whereas Maxwell stresses dominate and deliver a positive (outward) total transport. Several of the models yield strongly fluctuating Reynolds stresses, while Maxwell stresses are smooth and always transport outwards. Dynamo action is found in the accretion disk simulations. A positive dynamo-alpha is indicated in the northern hemisphere of the most prominent run, coming along with negative kinetic and current helicities (all having the opposite sign on the southern side). The dipolar structure of the magnetic field is maintained throughout the simulations, although indication for a decay of antisymmetry is found. The simulations covered relatively thick disks, and results of thin-disk dynamo models showing quadrupolar fields may not be compatible with the results presented here., Comment: 13 pages, LaTeX, submitted to A&A

The rotational influence on the eddy-diffusivity tensor D_ij for anisotropic turbulence fields is considered in order to explain the lithium decay law during the spin-down process of solar-type stars. Rotation proves to be highly effective in the transfer of chemicals through the solar tachocline (beneath the convection zone) which is assumed to contain only turbulence with horizontal motions. The effect is so strong that the tachocline turbulence must not exceed a limit of ~10^-(3...4) of the rms velocity in the convection zone in order to let the lithium survive after Gigayears. Such long depletion times can also be explained by a very small rotational influence upon the eddy-diffusion tensor if it is realized with correlation times shorter than 15 min. It is argued that such slow and/or short-living turbulence beneath the convection zone could hardly drive the solar dynamo. In our theory the diffusion remains small for rapid rotation due to the rotational quenching of the turbulence. In young stellar clusters like Pleiades, there should be a (positive) correlation between rotation rate and lithium abundance, where the fastest stars should have maximal lithium. First inspections of the data seem to confirm this finding., Comment: 6 pages, 9 figures, aa.cls

The presence of an imposed external magnetic field may drastically influence the structure of thin accretion discs. The magnetic field energy is here assumed to be in balance with the thermal energy of the accretion flow. The vertical magnetic field, its toroidal component B^tor at the disc surface (due to different rotation rates between disc and its magnetosphere), the turbulent magnetic Prandtl number and the viscosity-alpha are the key parameters of our model. Inside the corotation radius for rather small B^tor the resulting inclination angle i of the magnetic field lines to the disc surface normal can exceed the critical value 30^\circ (required to launch cold jets) even for small magnetic Prandtl numbers of order unity. The self-consistent consideration of both magnetic field and accretion flow demonstrates a weak dependence of the inclination (``dragging'') angle on the magnetic Prandtl number for given surface density but a strong dependence on the toroidal field component at the disc surface. A magnetic disc is thicker than a nonmagnetic one for typical parameter values. The accretion rate can be strongly amplified by large B^tor and small magnetic Prandtl number. On the other hand, for given accretion rate the magnetised disc is less massive than the standard-alpha disc. The surface values of the toroidal magnetic fields which are necessary to induce considerably high values for the inclination angle are much smaller than expected and are of order 10^-3 of the imposed vertical field. As the innermost part of the disc produces the largest B^tor, the largest radial inclination can be expected also there. The idea is therefore supported that the cold jets are launched only in the central disc area., Comment: 8 pages, 6 figures, Submitted to MNRAS

The velocity fluctuations in a spherical shell arising from sinusoidal perturbations of a Keplerian shear flow with a free amplitude parameter \epsilon are studied numerically by means of fully 3D nonlinear simulations. The investigations are performed at high Reynolds numbers, i.e. 3000 < Re < 5000. We find Taylor-Proudman columns of large eddies parallel to the rotation axis for sufficiently strong perturbations. An instability sets in at critical amplitudes with \epsilon_crit \propto Re^-1. The whole flow turns out to be almost axisymmetric and nonturbulent exhibiting, however, a very rich radial and latitudinal structure. The Reynolds stress is positive in the entire computational domain, from its Gaussian radial profile a positive viscosity-alpha of about 10^-4 is derived. The kinetic energy of the turbulent state is dominated by the azimuthal component whereas the other components are smaller by two orders of magnitude. Our simulations reveal, however, that these structures disappear as soon as the perturbations are switched off. We did not find an ``effective'' perturbation whose amplitude is such that the disturbance is sustained for large times (cf. Dauchot & Daviaud 1995) which is due to the effective violation of the Rayleigh stability criterion. The fluctuations rapidly smooth the original profile towards to pure Kepler flow which, therefore, proves to be stable in that sense., Comment: 9 pages, 9 figures, Astron. Nachr., in press

We perform global three-dimensional simulations of accretion disks integrating the compressible, non-viscous, but diffusive MHD equations. The disk is supposed to be isothermal. We make use of the ZEUS-3D code integrating the MHD equations and added magnetic diffusivity. We measure the efficiency of the angular-momentum transport. Various model simulations delivered transport parameters of alpha_SS=0.01 to 0.05 which are consistent with several local numerical investigations. Two of the models reach a highly turbulent state at which alpha_SS is of the order of 0.1. After a certain stage of saturating of the turbulence, Reynolds stress is found to be negative (inward transport) in many of the models, whereas Maxwell stresses dominate and deliver a positive (outward) total transport. Several of the models yield strongly fluctuating Reynolds stresses, while Maxwell stresses are smooth and always transport outwards. Dynamo action is found in the accretion disk simulations. A positive dynamo-alpha is indicated in the northern hemisphere of the most prominent run, coming along with negative kinetic and current helicities (all having the opposite sign on the southern side). The dipolar structure of the magnetic field is maintained throughout the simulations, although indication for a decay of antisymmetry is found. The simulations covered relatively thick disks, and results of thin-disk dynamo models showing quadrupolar fields may not be compatible with the results presented here., Comment: 13 pages, LaTeX, submitted to A&A