S. Ševčík

Problem of the Rotating Magnetoconvection in Variously Stratified Fluid Layer Revisited

The linear magnetoconvection in the rotating uniformly as well as non-uniformly stratified horizontal layer with azimuthal magnetic field is investigated for the various mechanical and electrical boundary conditions and especially, for various values of Roberts number. The developed diffusive perturbations (modes) are strongly influenced not only by the mentioned properties of boundaries but also by complicated coupling of viscous, thermal and magnetic diffusive processes. The mean electromotive force produced by developed hydromagnetic instabilities is also investigated to determine the hydromagnetic processes which are appropriate for α-effect. The presented paper is an unification of hitherto published results of the authors and gives a short survey of many developments of corresponding model by Soward (1979).

A significant decrease of the fundamental Schumann resonance frequency during the solar cycle minimum of 2008-9 as observed at Modra Observatory

A significant decrease of the fundamental Schumann resonance frequency during the solar cycle minimum of 2008-9 as observed at Modra Observatory The Schumann resonances (SR) are electromagnetic eigenmodes of the resonator bounded by the Earths surface and the lower ionosphere. The SR frequency variability has been studied for more than 4 decades. Using data from the period 1988 to 2002, Sátori et al. (2005) showed that the SR fundamental mode frequency decreased on the 11-year time scale by 0.07 - 0.2 Hz, depending on which component of the field was used for estimation and likely also on the location of the observer. A decrease by 0.30 Hz from the latest solar cycle maximum to the minimum of 2009 is found in data from Modra Observatory. This extraordinary fall of the fundamental mode frequency can be attributed to the unprecedented drop in the ionizing radiation in X-ray frequency band. Although the patterns of the daily and seasonal variations remain the same in the solar cycle minimum as in the solar cycle maximum, they are significantly shifted to lower frequencies during the minimum. Analysis of the daily frequency range suggests that the main thunderstorm regions during the north hemisphere summer are smaller in the solar cycle minimum than in the maximum.

MAC waves and related instabilities influenced by viscosity in dependence on boundary conditions

Abstract Marginal instabilities of MAC waves kind running in azimuthal directions are investigated in the rapidly rotating horizontal uniformly stratified fluid layer permeated by the azimuthal magnetic field linearly growing with the distance from vertical rotation axis. More combinations of horizontal perfectly thermally conducting boundaries are studied. They are either both rigid for viscous fluid or only impermeable for inviscid fluid, and either both perfectly electrically conducting or Earthlike ones of distinct finite electrical conductivities of upper and lower boundary. MAC waves and related instabilities in the model are possible only for Roberts number q R ≡κ/η=τ η /τ κ ≥ O (1) where τη, τκ are times of ohmic and thermal diffusion, respectively. The sensitivity of the investigated instabilities to viscosity is not typical only for smaller Elsasser numbers Λ O (1) . Greater frequencies of MAC waves induce their sensitivity to viscosity for greater Λ> O (1) , too. This sensitivity for Λ= O (1) , is apparent only for greater azimuthal wave numbers m≥ O (10) . However, the preferred modes are not influenced by viscosity and they are sensitive only to electromagnetic boundary conditions. In finite electrical conductivities cases MC waves develop for Λ≥ O (10 3 ) and non-zero viscosity in rigid boundaries cases causes complex competition of modes for Λ≥ O (1) .

Influence of a position of the critical level inside a plane layer on the rise of magnetically and thermally driven instabilities

The system under consideration is a horizontal stratified plane layer between z = ±d/2 filled by electrically conducting inviscid Boussinesq fluid rotating with a constant angular velocity under a vertical gravitational field and a non-uniform right-lined magnetic field B0 . An adverse temperature gradient β is applied to the layer. The imposed magnetic field in the form , where ℬ0 is a magnitude of the field, |z 0| < d/2, has a zero point inside the horizontal layer by which the condition of the existence of the critical level inside the layer is satisfied. The horizontal layer simulates the surroundings of the Earths core close to the rotation axis where the vectors Ω, g and β are considered to be parallel. Boundaries of the system are taken to be either perfectly conducting, perfectly insulating or mixed (perfectly conducting on the bottom and insulating on the top of the layer). An influence of shifting the critical level with respect to the central plane of the layer on the onset of an instability is studied by the linear stability analysis. Instabilities are obtained in the form of stationary convection determined by horizontal wavenumbers k c and l c in dependence of dimensionless parameters measuring heating of the system (Rayleigh number R) and magnetic field strength (Elsasser number Λ) and in dependence of boundary conditions. Also, magnetic instabilities are investigated for the layer without density stratification. The most unstable modes in a marginal stability state are characterised by a relatively simple structure along the z-axis.

Rotating Magnetoconvection in Dependence on Stratification, Diffusive Processes and Boundary Conditions

Instabilities of MAC-waves type influenced by three diffusive processes in planar rapidly rotating stratified fluid layer permeated by the azimuthal magnetic field (1b) were investigated in dependence on Elsasser, Ekman, Roberts numbers and stratification parameter (7) for various mechanical and electrically conductive boundaries (8, 9). Among corresponding MC-waves the westward ones significantly determined by viscosity were revealed.

The determination of Schumann resonance mode frequencies using iterative procedure of complex demodulation

Abstract The more precise determination of instantaneous peak frequency of Schumann resonance (SR) modes, especially based on relatively short signal sequences, seems to be important for detailed analysis of SR modal frequencies variations. Contrary to commonly used method of obtaining modal frequencies by Lorentzian fitting of DFT spectra, the attempt was made to employ the complex demodulation method in iterated form. The results for SR signals contaminated with low-frequency noise and hum in various degree as well as the comparison with standard method are presented. Real signals of vertical electric field component picked up at the Astronomical and Geophysical Observatory of Comenius University at Modra, Slovakia, were the primary sources.

On the relation between the red sprites and the transients in the ELF band

On the relation between the red sprites and the transients in the ELF band Under favourable conditions sprites appear above large storms. Long continuing current in tens of ms in the parent +CG stroke radiates electromagnetic energy also in the Schumann resonance (SR) band. Optical and Extremely Low Frequency (ELF) observations at the Astronomical and Geophysical Observatory (AGO) near Modra are analyzed to find these two effects associated with +CG discharges. Since April 2007 dozens of sprites have been captured by automated all-sky TV system at AGO. A majority (77%) of the optical transient events are accompanied with the transients in the SR band. No ELF counterparts are found for 23% of the captured sprites. Our observations are compared with similar observations in Sopron and Nagycenk (NCK). Example of the optical frames, the associated ELF time plot and the Fourier as well as dynamic spectrum are presented for one of the events simultaneously observed at AGO and NCK.

Viscously controlled nonlinear magnetoconvection in a non-uniformly stratified horizontal fluid layer

Abstract Weakly nonlinear analysis is adopted in order to study a model of magnetoconvection in a rotating horizontal fluid layer. The layer is supposed to be non-uniformly stratified and is permeated by an azimuthal magnetic field. The only nonlinearity brought in this convecting system is due to presence of Ekman layers along the horizontal mechanical boundaries. The governing equations for this model together with the expression for geostrophic flow, i.e., modified Taylors constraint are analysed with help of perturbation methods. As a result, the bifurcation structure in the vicinity of the critical Rayleigh number is revealed.

Mean Electromotive Force Due to Magnetoconvection in Rotating Horizontal Layer in Dependence on Boundary Conditions

The instability due to a vertical uniform temperature gradient is studied in a rapidly rotating horizontal layer of an electrically conducting fluid permeated by an azimuthal magnetic field linearly growing with the distance from the vertical axis of rotation. In addition to the boundary conditions used in Soward’s study (1979), that is, force-free surface and perfect electrical and thermal conductivity outside, also other conditions more realistic for the Earth’s core are considered, that is, rigid surface and electrically insulating walls. Using the concept of mean-field mhd mean electromotive and ponderomotive forces (E.M.F. and P.M.F.) are calculated and compared for various boundary conditions. The dependence of the E.M.F. and P.M.F. on the electromagnetic boundary conditions is strong (slight) if the boundaries are free (rigid).

The iterative complex demodulation applied on short and long Schumann resonance measured sequences

Abstract The precise determination of instantaneous frequency of Schumann resonance (SR) modes, with the possibility of application to relatively short signal sequences, seems to be important for detailed analysis of SR modal frequency variations. Contrary to commonly used method of obtaining modal frequencies by the Lorentz function fitting of DFT spectra, we employ the complex demodulation (CD) method in iterated form. Results of iterated CD method applied on short and long measured sequences are compared. Results for SR signals as well as the comparison with Lorentz function fitting are presented. Decrease of frequencies of all first four SR modes from the solar cycle maximum to solar cycle minimum has been found using also the CD method.