Control Volume Method for the Thermal Convection Problem in a Rotating Spherical Shell: Test on the Benchmark Solution

The development of the control volume method for the thermal convection problem in a rotating spherical shell is presented. In contrast to the spectral methods, commonly used in geodynamo simulations, the control volume method belongs to the class of grid methods (the solution is approximated by a set of discrete values in physical space). In the present paper we concentrate on some problems of convergence and stability of the method. Case 0 of the numerical dynamo benchmark (Christensen et al., 2001, Phys. Earth Planet. Inter., 128, 25-34) was used to check the correctness of our computer code. The results demonstrate good convergence to the suggested standard solution.     

Non-steady kinematic dynamo model with spiral convection

Summary The stability of steady states, the evolution of the magnetic field and possible changes of the magnetic field under small changes of velocity are studied on a non-stationary solution of a kinematic dynamo model.     

The Influence of a Homogeneous Magnetic Field on the Ekman and Stewartson Layers

This contribution is aimed at a comparison of two different methods of how to deal with the solid inner core in geodynamo models. The first method, based on a direct application of the non-slip boundary conditions, was frequently used in the past. The second one, developed by the authors of the present paper, is based on an advanced analytical solution within the boundary layers and consequent formulation of new boundary conditions on the flow in the volume of the outer core. As an example we have used the results obtained by Hollerbach (1997) in the study of the influence of an imposed axial magnetic field on the fluid flow in a differentially rotating spherical shell. In the case of a weak imposed magnetic field, our solutions are very similar to those of Hollerbach. This non-trivial correspondence confirms the correctness of both methods, which are different not only in the formulation of boundary conditions, but also in the numerical methods: whereas Hollerbach used spectral methods, our computer code is based on finite differences. The influence of the conductivity of the inner core on the fluid flow was also studied.     

Control Volume Method for the Dynamo Problem in the Sphere with the Free Rotating Inner Core

A model of thermally driven dynamo in the Boussinesq approximation in the spherical shell with the free rotating inner core is considered. To solve equations we use a new in dynamo modeling control volume technique (for details of this method for hydrodynamics see Patankar, 1980). The main advantage of this method over previous attempts to solve magnetohydrodynamics equations in the spherical grids is that no filtering of high harmonics in the pole regions is needed. We present the results of simulations for the self-consistent dynamo system evolution over the diffusion time and longer periods. Different ways of stabilizations of magnetohydrodynamics equations, when convective terms are of the same order (or larger) as conductive ones, are considered.     

Association Between Extraterrestrial Phenomena And Weather Changes In The Northern Hemisphere In Winter

This paper includes a discussion of the validity of theobjections which are usuallyraised against the physical plausibility of the correlationsbetween extraterrestrialphenomena and changes in circulation in the lower atmosphere.The behaviour of the winterlower troposphere in the Northern Hemisphere was analysed bothon a month-to-month timescale and on a day-to-day time scale. The mechanisms which cansatisfactorily explainthe behaviour of the winter lower troposphere on these timescales have been described.The basic features of the results presented were explained bymeans of a mechanism basedon the propagation of planetary waves. Attention was focussedon studying the connectionsamong the changes in the pressure and temperature fields, thechanges in solar/geomagnetic activity and QBO phases by the method of composites. It hasbeen found that the compositeswithout considering QBO phases are similar to the QBO-eastpatterns under the highestactivities. Pressure deviations during QBO-west high solaractivity or low geomagneticactivity and temperature deviations during QBO-east/west lowgeomagnetic activity provedto be of negligible statistical significance.     

The weak taylor state in an αω-dynamo

Abstract

A spherical αω-dynamo is studied for small values of the viscous coupling parameter ε ～ v^1/2, paying attention particularly to large dynamo numbers. The present study is a follow-up of the work by Hollerbach et al. (1992) with their choice of α-effect and Archimedean wind including also the constraint of magnetic field symmetry (or antisymmetry) due to equatorial plane. The magnetic field scaled by ε^1/2 is independent of ε in the solutions for dynamo numbers smaller than a certain value of D _b (the Ekman state) which are represented by dynamo waves running from pole to equator or vice-versa. However, for dynamo numbers larger than D _b the solution bifurcates and subsequently becomes dependent on ε. The bifurcation is a consequence of a crucial role of the meridional convection in the mechanism of magnetic field generation. Calculations suggest that the bifurcation appears near dynamo number about 33500 and the solutions for larger dynamo numbers and ε = 0 become unstable and fail, while the solutions for small but non-zero ε are characterized by cylindrical layers of local maximum of magnetic field and sharp changes of geostrophic velocity. Our theoretical analysis allows us to conclude that our solution does not take the form of the usual Taylor state, where the Taylor constraint should be satisfied due to the special structure of magnetic field. We rather obtained the solution in the form of a “weak” Taylor state, where the Taylor constraint is satisfied partly due to the amplitude of the magnetic field and partly due to its structure. Calculations suggest that the roles of amplitude and structure are roughly fifty-fifty in our “weak” Taylor state solution and thus they can be called a Semi-Taylor state. Simple estimates show that also Ekman state solutions can be applicable in the geodynamo context.     

Removal of nitrates from high-salinity wastewaters from desulphurization process with denitrifying bacteria encapsulated in Lentikats Biocatalyst

Successful elimination of high concentrations of N?CNO _x ^? (up to 250?mg/L) from high salinity wastewaters (up to 35?g/L Cl^??+?17?g/L SO₄ ^2?) originating from desulphurization process within coal power stations was achieved using pure cultures of denitrifying bacteria encapsulated in porous polyvinyl alcohol lenses (so called Lentikats Biocatalyst, LB). Laboratory batch tests revealed inhibitory influence of the raw wastewater on the denitrification activity, which was partially mitigated by the addition of P?CPO₄ ^3?. In following continuous tests, the denitrification activities reached the range 150?C450?mg?N/h/kg LB, i.e., values suitable for industrial scale applications. The higher activities were achieved under a lower salinity, higher N?CNO _x ^? influent concentrations and a prolonged retention time. The effluent N?CNO _x ^? concentrations were below the determination limit of 5?mg/L. After a period of 3?months, a significant decrease of denitrification activity of Lentikats Biocatalyst was observed. Addition of nutrients into the wastewater enabled fast regeneration of the initial activity. The overall results proved the applicability of Lentikats Biocatalysts for the removal of nitrates from high-salinity desulphurization water and other industrial wastewaters of similar character.