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

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

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

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

Asymptotic properties of mathematical models of excitability

We analyse small parameters in selected models of biological excitability, including Hodgkin-Huxley (1952) model of nerve axon, Noble (1962) model of heart Purkinje fibres, and Courtemanche et al. (1998) model of human atrial cells. Some of the small parameters are responsible for differences in the characteristic timescales of dynamic variables, as in the traditional singular perturbation approaches. Others appear in a way which makes the standard approaches inapplicable. We apply this analysis to study the behaviour of fronts of excitation waves in spatially-extended cardiac models. Suppressing the excitability of the tissue leads to a decrease in the propagation speed, but only to a certain limit; further suppression blocks active propagation and leads to a passive diffusive spread of voltage. Such a dissipation may happen if a front propagates into a tissue recovering after a previous wave, e.g. re-entry. A dissipated front does not recover even when the excitability restores. This has no analogy in FitzHugh-Nagumo model and its variants, where fronts can stop and then start again. In two spatial dimensions, dissipation accounts for break-ups and self-termination of re-entrant waves in excitable media with Courtemanche et al. (1998) kinetics.Comment: 15 pages, 8 figures, to appear in Phil Trans Roy Soc London

Non-symmetric magnetohydrostatic equilibria:a multigrid approach

Aims. Linear magnetohydrostatic (MHS) models of solar magnetic fields balance plasma pressure gradients, gravity and Lorentz forces where the current density is composed of a linear force-free component and a cross-field component that depends on gravitational stratification. In this paper, we investigate an efficient numerical procedure for calculating such equilibria.Methods. The MHS equations are reduced to two scalar elliptic equations – one on the lower boundary and the other within the interior of the computational domain. The normal component of the magnetic field is prescribed on the lower boundary and a multigrid method is applied on both this boundary and within the domain to find the poloidal scalar potential. Once solved to a desired accuracy, the magnetic field, plasma pressure and density are found using a finite difference method.Results. We investigate the effects of the cross-field currents on the linear MHS equilibria. Force-free and non-force-free examples are given to demonstrate the numerical scheme and an analysis of speed-up due to parallelization on a graphics processing unit (GPU) is presented. It is shown that speed-ups of ×30 are readily achievable

Kinetic energy cascades in quasi-geostrophic convection in a spherical shell

We consider triadic nonlinear interaction in the Navier-Stokes equation for quasi-geostrophic convection in a spherical shell. This approach helps understanding the origin of kinetic energy transport in the system and the particular scheme of mode interaction, as well as the locality of the energy transfer. The peculiarity of convection in the sphere, concerned with excitation of Rossby waves, is considered. The obtained results are compared with our previous study in Cartesian geometry

Bistability and hysteresis of dipolar dynamos generated by turbulent convection in rotating spherical shells

Bistability and hysteresis of magnetohydrodynamic dipolar dynamos generated by turbulent convection in rotating spherical fluid shells is demonstrated. Hysteresis appears as a transition between two distinct regimes of dipolar dynamos with rather different properties including a pronounced difference in the amplitude of the axisymmetric poloidal field component and in the form of the differential rotation. The bistability occurs from the onset of dynamo action up to about 9 times the critical value of the Rayleigh number for onset of convection and over a wide range of values of the ordinary and the magnetic Prandtl numbers including the value unity