Problems of astrophysical turbulent convection: thermal convection in a layer without boundaries

Thermal convection in fluid layers heated from below are usually realized experimentally as well as treated theoretically with fixed boundaries on which conditions for the temperature and the velocity field are prescribed. The thermal and velocity boundary layers attached to the upper and lower boundaries determine to a large extent the properties of turbulent convection at high Rayleigh numbers. Fixed boundaries are often absent in natural realizations of thermal convection. This paper studies the properties of convection driven by a planar heat source below a cooling source of equal size immersed in an otherwise stably stratified fluid layer are studied in this paper. Unavoidable boundaries do not influence the convection flow since they are separated from the active convection layer by nearly motionless stably stratified regions. The onset of convection occurs in an inner unstably stratified region where the mean temperature gradient is reversed. But the region of a reversed horizontally averaged temperature gradient disappears at higher amplitudes of convection such that the vertical derivative of the mean temperature no longer changes its sig

Inertial convection in rotating fluid spheres

The onset of convection in the form of inertial waves in a rotating fluid sphere is studied through a perturbation analysis in an extension of earlier work by Zhang (1994). Explicit expressions for the dependence of the Rayleigh number on the azimuthal wavenumber are derived and new results for the case of a nearly thermally insulating boundary are obtained

Prandtl-number dependence of convection-driven dynamos in rotating spherical fluid shells

The value of the Prandtl number P exerts a strong influence on convection-driven dynamos in rotating spherical shells filled with electrically conducting fluids. Low Prandtl numbers promote dynamo action through the shear provided by differential rotation, while the generation of magnetic fields is more difficult to sustain in high-Prandtl-number fluids where higher values of the magnetic Prandtl number Pm are required. The magnetostrophic approximation often used in dynamo theory appears to be valid only for relatively high values of P and Pm. Dynamos with a minimum value of Pm seem to be most readily realizable in the presence of convection columns at moderately low values of P. The structure of the magnetic field varies strongly with P in that dynamos with a strong axial dipole field are found for high values of P while the energy of this component is exceeded by that of the axisymmetric toroidal field and by that of the non-axisymmetric components at low values of P. Some conclusions are discussed in relation to the problem of the generation of planetary magnetic fields by motions in their electrically conducting liquid cores

Asymptotic theory of wall-attached convection in a horizontal fluid layer with a vertical magnetic field

A horizontal fluid layer heated from below in the presence of a vertical magnetic field is considered. A simple asymptotic analysis is presented which demonstrates that a convection mode attached to the side walls of the layer sets in at Rayleigh numbers much below those required for the onset of convection in the bulk of the layer. The analysis complements an earlier analysis by Houchens [J. Fluid Mech. 469, 189 (2002)] which derived expressions for the critical Rayleigh number for the onset of convection in a vertical cylinder with an axial magnetic field in the cases of two aspect ratios

Turbulent 3D MHD dynamo model in spherical shells: regular oscillations of the dipolar field

We report the results of three-dimensional numerical simulations of convection-driven dynamos in relatively thin rotating spherical shells that show a transition from an strong non-oscillatory dipolar magnetic field to a weaker regularly oscillating dipolar field. The transition is induced primarily by the effects a stress-free boundary condition. The variation of the inner to outer radius ratio is found to have a less important effect

Tertiary and Quaternary States in the Taylor-Couette System

The analysis of the Taylor-Couette problem in the small gap limit is extended to the cases of tertiary and quaternary solutions. The theoretical results are compared with experimental observations. Although in the latter the small-gap approximation is not always well approximated, the comparison of theoretical results and observations yields reasonable agreements. The absence of the wavy twist mode in the observed patterns is explained by the presence of no-slip boundary conditions in the axial direction of the experimental apparatus, which differ from the periodic conditions imposed in the theoretical analysis. Quaternary solutions bifurcating from the tertiary ones through subharmonic instabilities are presented and compared with experimental observations. Reasonable agreement has been found

Asymmetric Squares as Standing Waves in Rayleigh-Benard Convection

Possibility of asymmetric square convection is investigated numerically using a few mode Lorenz-like model for thermal convection in Boussinesq fluids confined between two stress free and conducting flat boundaries. For relatively large value of Rayleigh number, the stationary rolls become unstable and asymmetric squares appear as standing waves at the onset of secondary instability. Asymmetric squares, two dimensional rolls and again asymmetric squares with their corners shifted by half a wavelength form a stable limit cycle.Comment: 8 pages, 7 figure

Some Unusual Properties of Turbulent Convection and Dynamos in Rotating Spherical Shells

The dynamics of convecting fluids in rotating spherical shells is governed at Prandtl numbers of the order unity by the interaction between differential rotation and roll-like convection eddies. While the differential rotation is driven by the Reynolds stresses of the eddies, its shearing action inhibits convection and causes phenomena such as localized convection and turbulent relaxation oscillations. The response of the system is enriched in the case of dynamo action. Lorentz forces may brake either entirely or partially the geostrophic differential rotation and give rise to two rather different dynamo states. Bistability of turbulent dynamos exists for magnetic Prandtl numbers of the order unity. While the ratios between mean magnetic and kinetic energies differ by a factor of 5 or more for the two dynamo states, the mean convective heat transports are nearly the same. They are much larger than in the absence of a magnetic field.Comment: To appear in Procs. IUTAM Symposium on Turbulence in the Atmosphere and Oceans, 08-7 = GA.06-0

Toroidal flux oscillation as possible cause of geomagnetic excursions and reversals

It is proposed that convection driven dynamos operating in planetary cores could be oscillatory even when the oscillations are not directly noticeable from the outside. Examples of dynamo simulations are pointed out that exhibit oscillations in the structure of the azimuthally averaged toroidal magnetic flux while the mean poloidal field shows only variations in its amplitude. In the case of the geomagnetic field, global excursions may be associated with these oscillations. Long period dynamo simulations indicate that the oscillations may cause reversals once in a while. No special attempt has been made to use most realistic parameter values. Nevertheless some similarities between the simulations and the paleomagnetic record can be pointed out.Comment: Published in PEP