Ján Šimkanin

Convection in rotating non-uniformly stratified spherical fluid shells: a systematic parameter study

Convection in rotating non-uniformly stratified spherical fluid shells: a systematic parameter study A systematic parameter study of rotating convection in non-uniformly stratified spherical shells in dependence on the Prandtl number, Ekman number and Rayleigh number is presented. Attention is focused on the case, in which the thickness of both sublayers (stable and unstable) is the same (which was not investigated before). In our case the convection is not suppressed in the stably stratified region but, it is developed in both sublayers. Cases of small and large Prandtl numbers are characterized by the creation of multilayer convective structures. Convective motions take place simultaneously in the stable and unstable layers and form a multilayer structure. On the other hand, it is not possible to observe any multilayer convection for Prandtl number equal to one but it is possible to observe the small-scale structures. A conclusion is that our case is similar to the case in which the thickness of unstable sublayer is greater than that of stable one.

Hydromagnetic dynamos at the low Ekman and magnetic Prandtl numbers

Abstract Hydromagnetic dynamos are numerically investigated at low Prandtl, Ekman and magnetic Prandtl numbers using the PARODY dynamo code. In all the investigated cases, the generated magnetic fields are dominantly-dipolar. Convection is small-scale and columnar, while the magnetic field maintains its large-scale structure. In this study the generated magnetic field never becomes weak in the polar regions, neither at large magnetic Prandtl numbers (when the magnetic diffusion is weak), nor at low magnetic Prandtl numbers (when the magnetic diffusion is strong), which is a completely different situation to that observed in previous studies. As magnetic fields never become weak in the polar regions, then the magnetic field is always regenerated in the tangent cylinder. At both values of the magnetic Prandtl number, strong polar magnetic upwellings and weaker equatorial upwellings are observed. An occurrence of polar magnetic upwellings is coupled with a regenaration of magnetic fields inside the tangent cylinder and then with a not weakened intensity of magnetic fields in the polar regions. These new results indicate that inertia and viscosity are probably negligible at low Ekman numbers.

Polarity reversals in dependence on the Prandtl number and density stratification

Dependence of polarity reversals on the Prandtl number and density stratification using the MAG dynamo code was investigated. The magnetic field is dipole-dominated in the stable polarity state and during the reversals it is multipolar. Quadrupole and octupole components of magnetic fields are stronger at the Prandtl number equal to 0.2 than at the Prandtl number equal to 1. Polarity reversals occur at higher values of the Rayleigh number, while at its lower values the magnetic field does not undergo reversals. The situation is the same with the magnetic Prandtl number: polarity reversals occur at higher values of the magnetic Prandtl number, while at its lower values the magnetic field does not undergo reversals (neither if the magnetic field becomes weak in the polar regions nor if it is strong). During the 1000 simulated time units two reversals occur in the case of uniform stratification and at both investigated values of the Prandtl number, while in the case of non-uniform stratification and at both investigated values of the Prandtl number only one reversal occurs.

Hydromagnetic dynamos in rotating spherical fluid shells in dependence on the Prandtl number, density stratification and electromagnetic boundary conditions

Abstract We present an investigation of dynamo in a simultaneous dependence on the non-uniform stratification, electrical conductivity of the inner core and the Prandtl number. Computations are performed using the MAG dynamo code. In all the investigated cases, the generated magnetic fields are dipolar. Our results show that the dynamos, especially magnetic field structures, are independent in our investigated cases on the electrical conductivity of the inner core. This is in agreement with results obtained in previous analyses. The influence of non-uniform stratification is for our parameters weak, which is understandable because most of the shell is unstably stratified, and the stably stratified region is only a thin layer near the CMB. The teleconvection is not observed in our study. However, the influence of the Prandtl number is strong. The generated magnetic fields do not become weak in the polar regions because the magnetic field inside the tangent cylinder is always regenerated due to the weak magnetic diffusion.

Magnetic and velocity fields in a dynamo operating at extremely small Ekman and magnetic Prandtl numbers

Abstract Numerical simulations of the geodynamo are becoming more realistic because of advances in computer technology. Here, the geodynamo model is investigated numerically at the extremely low Ekman and magnetic Prandtl numbers using the PARODY dynamo code. These parameters are more realistic than those used in previous numerical studies of the geodynamo. Our model is based on the Boussinesq approximation and the temperature gradient between upper and lower boundaries is a source of convection. This study attempts to answer the question how realistic the geodynamo models are. Numerical results show that our dynamo belongs to the strong-field dynamos. The generated magnetic field is dipolar and large-scale while convection is small-scale and sheet-like flows (plumes) are preferred to a columnar convection. Scales of magnetic and velocity fields are separated, which enables hydromagnetic dynamos to maintain the magnetic field at the low magnetic Prandtl numbers. The inner core rotation rate is lower than that in previous geodynamo models. On the other hand, dimensional magnitudes of velocity and magnetic fields and those of the magnetic and viscous dissipation are larger than those expected in the Earth’s core due to our parameter range chosen.