Double-diffusive convection in a rotating cylindrical annulus with conical caps

Double-diffusive convection driven by both thermal and compositional buoyancy in a rotating cylindrical annulus with conical caps is considered with the aim to establish whether a small fraction of compositional buoyancy added to the thermal buoyancy (or vice versa) can significantly reduce the critical Rayleigh number and amplify convection in planetary cores. It is shown that the neutral surface describing the onset of convection in the double-buoyancy case is essentially different from that of the well-studied purely thermal case, and does indeed allow the possibility of low-Rayleigh number convection. In particular, isolated islands of instability are formed by an additional "double-diffusive" eigenmode in certain regions of the parameter space. However, the amplitude of such low-Rayleigh number convection is relatively weak. At similar flow amplitudes purely compositional and double-diffusive cases are characterized by a stronger time dependence compared to purely thermal cases, and by a prograde mean zonal flow near the inner cylindrical surface. Implications of the results for planetary core convection are briefly discussed.Comment: Accepted for publication in Physics of the Earth and Planetary Interiors on 20 April 201

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

How far can minimal models explain the solar cycle?

A physically consistent model of magnetic field generation by convection in a rotating spherical shell with a minimum of parameters is applied to the Sun. Despite its unrealistic features the model exhibits a number of properties resembling those observed on the Sun. The model suggests that the large scale solar dynamo is dominated by a non-axisymmetric $m=1$ component of the magnetic field.Comment: Accepted for publication in the Astrophysical Journal on 2012/01/3

Asymptotics of conduction velocity restitution in models of electrical excitation in the heart

We extend a non-Tikhonov asymptotic embedding, proposed earlier, for calculation of conduction velocity restitution curves in ionic models of cardiac excitability. Conduction velocity restitution is the simplest non-trivial spatially extended problem in excitable media, and in the case of cardiac tissue it is an important tool for prediction of cardiac arrhythmias and fibrillation. An idealized conduction velocity restitution curve requires solving a non-linear eigenvalue problem with periodic boundary conditions, which in the cardiac case is very stiff and calls for the use of asymptotic methods. We compare asymptotics of restitution curves in four examples, two generic excitable media models, and two ionic cardiac models. The generic models include the classical FitzHugh–Nagumo model and its variation by Barkley. They are treated with standard singular perturbation techniques. The ionic models include a simplified “caricature” of Noble (J. Physiol. Lond. 160:317–352, 1962) model and Beeler and Reuter (J. Physiol. Lond. 268:177–210, 1977) model, which lead to non-Tikhonov problems where known asymptotic results do not apply. The Caricature Noble model is considered with particular care to demonstrate the well-posedness of the corresponding boundary-value problem. The developed method for calculation of conduction velocity restitution is then applied to the Beeler–Reuter model. We discuss new mathematical features appearing in cardiac ionic models and possible applications of the developed method

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

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

Quasi-geostrophic approximation of anelastic convection

The onset of convection in a rotating cylindrical annulus with parallel ends filled with a compressible fluid is studied in the anelastic approximation. Thermal Rossby waves propagating in the azimuthal direction are found as solutions. The analogy to the case of Boussinesq convection in the presence of conical end surfaces of the annular region is emphasised. As in the latter case, the results can be applied as an approximation for the description of the onset of anelastic convection in rotating spherical fluid shells. Reasonable agreement with three-dimensional numerical results published by Jones, Kuzanyan & Mitchell (J. Fluid Mech., vol. 634, 2009, pp. 291–319) for the latter problem is found. As in those results, the location of the onset of convection shifts outwards from the tangent cylinder with increasing number Nρof density scale heights until it reaches the equatorial boundary. A new result is that at a much higher number Nρ the onset location returns to the interior of the fluid shell

Baroclinically-driven flows and dynamo action in rotating spherical fluid shells

The dynamics of stably stratified stellar radiative zones is of considerable interest due to the availability of increasingly detailed observations of Solar and stellar interiors. This article reports the first non-axisymmetric and time-dependent simulations of flows of anelastic fluids driven by baroclinic torques in stably stratified rotating spherical shells – a system serving as an elemental model of a stellar radiative zone. With increasing baroclinicity a sequence of bifurcations from simpler to more complex flows is found in which some of the available symmetries of the problem are broken subsequently. The poloidal component of the flow grows relative to the dominant toroidal component with increasing baroclinicity. The possibility of magnetic field generation thus arises and this paper proceeds to provide some indications for self-sustained dynamo action in baroclinically-driven flows. We speculate that magnetic fields in stably stratified stellar interiors are thus not necessarily of fossil origin as it is often assumed

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

Magneto-inertial convection in rotating fluid spheres

The onset of convection in the form of magneto-inertial waves in a rotating fluid sphere permeated by a constant axial electric current is studied through a perturbation analysis. Explicit expressions for the dependence of the Rayleigh number on the azimuthal wavenumber are derived in the limit of high thermal diffusivity. Results for the cases of thermally infinitely conducting and of nearly thermally insulating boundaries are obtained.Comment: 10 pages, 5 figures, to be submitted for publicatio