Current  Results

1.  G. D. Aburjania, Kh. Z. Chargazia, G.V. Jandieri, A. G. Khantadze and O. A. Kharshiladze

 Laboratory of Investigation of the Extraordinary Phenomena, I. Vekua Institute of Applied   Mathematics, Tbilisi State University,  2 University str., 0143, Tbilisi, Georgia

    Dynamics of the new modes of the low-frequency planetary-scale electromagnetic wave structures in the ionosphere

    Recent Res. Devel. Geophysics, 5(2003), pp. 1-36

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    In the present review the results of theoretical investigation of the dynamics of generation and propagation of planetary (with wavelength 103 km and more) ultra-low frequency (ULF) electromagnetic wave structures in the dissipative ionosphere are given.  The physical mechanism of generation of the planetary electromagnetic waves is proposed.  It is established that the global factor acting permanently in the ionosphere  in homogeneity (latitude variation) of the geomagnetic field-generates the fast and slow planetary ULF electromagnetic waves. The linear waves propagate along the parallels to the east as well as to the west.

    In E-region the fast waves  have  phase velocities (2÷20) km.s-1  and frequencies (10-1÷10-4)s-1; the slow waves propagate with local wind velocities and have frequencies (10-4÷10-6)s-1. In F-region the fast ULF electromagnetic waves propagate with phase velocities tens-hundreds km.s-1 and their frequencies are in the range of (10÷10-3)s-1. The waves generate the geomagnetic field from several tens to several hundreds nT. The large-scale waves are weakly damped.

    The features and the parameters of the theoretically investigated electromagnetic wave structures agree with those of large-scale ULF midlatitude long-period oscillations (MLO) and magnetoionospheric wave perturbations (MIWP) observed experimentally in the ionosphere.

    It is established that because of relevance of Coriolis and electromagnetic forces generation of slow planetary electromagnetic waves at the fixed latitude in the ionosphere can give rise to the reverse of the local wind structures and to the direction change of a general ionospheric  circulation.

    The investigation were carried out for a quasi-plane model (β-effect) as well as for spherical model of the Earth.

The physical mechanism of generation of the large-scale vortex electric field in E and F regions of the ionosphere is proposed. It is shown,  that the large-scale (with wavelength > 103 km) the synoptically short-period (from a few minutes to a few hours) and the fast (with propagation velocity more than 1 km.s-1) processes generate vortex electric field in the ionosphere. It exceeds the dynamo field generated by wind motion in the ionosphere, few times by order.

    It is established that planetary ULF electromagnetic waves can self-localize in the form of the nonlinear solitary vortices moving along the latitude circles  westward as well as eastward with velocity different from phase  velocity of corresponding linear waves. Characteristic size of the vortices is of order of 104 km and more. The vortices are weakly damped and long-lived. They cause the geomagnetic pulsations stronger than the linear waves by one order. The vortex structures transfer the trapped particles of medium and also energy and heat. That is why such nonlinear vortex structures can be the structural elements of strong macroturbulence of the ionosphere. It is shown that at low and middle latitudes superrotation (SR) of the atmosphere-ionosphere can be caused by planetary electromagnetic solitary wave structures mentioned above.

 

2.   G. D. Aburjania1, Kh. Z. Chargazia1, G.V. Jandieri2, A. G. Khantadze3 and   O. A. Kharshiladze4

     1. I. Vekua Institute of  Applied Mathematics, Laboratory of Investigation of Extraordinary Phenomena, Tbilisi State University, 2 University Str., 0143 Tbilisi, Georgia

     2. Georgian Technical University, Department of Physics, 77 Kostava Str.,  0175 Tbilisi, Georgia

     3. Chair of Meteorology and Hydrology, Tbilisi State University, 1 Chavchavadze Ave., 0175 Tbilisi, Georgia

     4. Tbilisi State University, Faculty  of Physics, 3 Chavchavadze Ave.,  0128 Tbilisi, Georgia

On the new modes of planetary-scale electromagnetic waves in the ionosphere

Annales Geophysical (2004), pp.: 1-9      

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    Using an analogy method the frequencies of new modes of the electromagnetic planetary-scale waves (with a wavelength of 103 km or more), having a weather forming nature, are found at different ionospheric altitudes. This method gives the possibility to determine spectra of ionospheric electromagnetic perturbations directly from the dynamic equations without solving the general dispersion equation. It is shown that the permanently acting factor-latitude variation of the geomagnetic field generates fast and slow weakly damping planetary electromagnetic waves in both the E- and F-layers of the ionosphere. The waves propagate eastward and westward along the parallels. The fast waves have phase velocities (I-5)km s-1 and frequencies (10-1- 10-4), and the slow waves propagate with velocities of the local winds with frequencies (10-4- 10-6)s-1 and are generated in the E-region of the ionosphere. Fast waves having phase velocities (10-1500)km s-1 and frequencies (1-10-3)s-1  are generated in the F-region of the ionosphere. The waves generate the geomagnetic pulsations of the order of one hundred nanoTesla by magnitude. The properties and parameters of the theoretically studied electromagnetic waves agree with those of large-scale ultra-low frequency perturbations observed experimentally in the ionosphere.

 

3.  Giorgi Aburjania, Khatuna Chargazia, Tamaz Kaladze, Archil Khantadze*, Oleg Kharshiladze

    I. Vekua Institute of Applied Mathematics, Tbilisi State University, 2 University Str., 0143 Tbilisi, Georgia, E-mail: aburj@mymail.ge, aburj@viam.hepi.edu.ge

   * Iv. Javakhishvili Tbilisi State University, 1 Chavchavadze Ave. 0128 Tbilisi, Georgia

         New generation mechanism of the planetary-scale internal vortical electric field in the Earth's ionosphere

  Journal of the Georgian Geophysical Society, 

  Issue (B), Physics of Atmosphere, Ocean and Space Plasma, v. 8, 2003, pp.122-135

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    The physical mechanism of large-scale vortical electric field generation in the ionospheric E and F - layers is suggested. It is shown that, in the ionosphere the large-scale (with the wavelength 103 km and more), synoptic short period (from several second to several hours), fast (with propagation velocity higher than 1km/s) processes excite planetary scale vortical electric field, which by its value may several times surpass the dynamo-field generated in the same ionospheric layer by local wind motion. It is established, that in the ionosphere a source of the vortical electric field generation is spatial inhomogeneity of the geomagnetic field.

 

4.  G. D. Aburjania, Kh. Z. Chargazia, G.V. Jandieri, G. Z. Machabeli, A. G. Khantadze and O. A. Kharshiladze

 Laboratory of Investigation of  Extraordinary Phenomena, I. Vekua Institute of Applied   Mathematics, Tbilisi State University,  2 University str., 0143, Tbilisi, Georgia

    Theoretical model for conjugate fotoelectron energy transfer and related to them night sky airglow enhancement in the local midlatitude ionospheric F-region

Recent Res. Devel. Geophysics., 5(2003), pp. 61-73

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    Physical and mathematical model of photoelectron energy transfer from magnetoconjugate region to the local ionosphere is suggested. The model is based on the strong wave turbulence. It is determined, that a direct transport of superthermal photoelectrons between conjugate ionospheres is difficult because of inevitable loss of energy by electron beam on excitation of different modes of wave perturbation. It is shown, that conjugate photoelectron flux effectively excites long wavelength Langmuir wave in the ionospheric sunlit region. Propagating in narrow cone along the Earth magnetic field lines and reaching the local ionosphere, modulation unstable Langmuir wave pumps its energy over the short-wave region via collapse. Strong damping of short-wave modes on the fast super-thermal electrons generates observed descending flux of superthermal electrons and transports it into the local midlattitude ionosphere. On the basis of this model observed pretwilight enhancement of red line airglow intensity in the ionospheric F-region is explained.

 

5.  T. Kaladze, J. Rogava, L. Tsamalashvili, M. Tsiklauri

 I. Vekua Institute of Applied   Mathematics, Tbilisi State University,  2 University str., 0143, Tbilisi, Georgia

Implicit Difference Schemes for the Charney-Obukhov Equation

Applied Mathematics, Informatics and Mechanics, Tbilisi University Press, Tbilisi, v.8,No.2, 2003,pp. 20-39.

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    In the present work, first- and second-order accuracy implicit difference schemes for the numerical solution of the nonlinear Charney-Obukhov equation are constructed. For each scheme the approximation error is estimated and the convergence of the iterative process is investigated. On the basis of numerical calculations accomplished by means of these schemes, the propagation of a two-dimensional nonlinear solitary Rossby vortex structure is studied. A comparative analysis of the obtained numerical results is carried out. In addition, for the considered equation there is proved the theorem of uniqueness of the solution in case of periodic boundary conditions and is obtained the sufficiently general law of integral conservation.

 

6. T. D. Kaladze, G. D. Aburjania, O. A. Kharshiladze, W. Horton*, Y. - H. Kim*

 I. Vekua Institute of Applied   Mathematics, Tbilisi State University,  Tbilisi, Georgia

* Department of Physics and Institute for Fusion Studies, University of Texas at Austin, Austin, Texas, USA

Theory of Magnetized Rossby Waves in the Ionospheric E Layer

Journal of Geophysical Research, v. 109, A05302, doi:10.1029/2003JA010049, 2004

Abstract

    For the weakly ionized E layer plasma, a generalized Charney-Obukhov equation for magnetized Rossby waves in derived. This magnetized Rossby wave is produced by the dynamo electric field and represents the ionospheric generalization of tropospheric Rossby waves in a rotating atmosphere  by the spatially inhomogeneous geomagnetic field. The basic characteristics of the wave are given. The modified Rossby velocity and Rossby-Obukhov radius are introduced. The mechanism of self-organization into solitary vortical nonlinear structures is examined. The mechanism of a self-organization of solitary structures is the result of the mutual compensation of wave dispersion and interaction through the scalar and Poisson bracket convective nonlinearities in the nonlinear wave equation. As a result, the solitary structures are anisotropic, containing a circular vortex superimposed on a dipole perturbation. The degree of anisotropy sharply increases when the vortex saze approaches the so-called intermediate geostrophic size.

 

  7. T. Kaladze, J.Rogava, L. Tsamalashvili, M. Tsiklauri

 I. Vekua Institute of Applied Mathematics, Tbilisi State University,  2 University str., 0143, Tbilisi, Georgia

 First and Second-order Accurate Implicit Difference  Schemes

for the Charney-Obukhov Equation 

 Physics Letters A,  v. 328, No. 1, 2004, pp. 51-64.       

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    In the present work, first- and second-order accurate implicit difference schemes for the numerical solution of the nonlinear Charney-Obukhov equation are constructed. For each constructed scheme, the approximation error is estimated and the convergence of the iterative process is investigated. On the basis of numerical calculations accomplished by means of these schemes, The propagation of a two-dimensional nonlinear solitary Rossby vortex structure is studied. A comparative analysis of the obtained numerical results is carried out.

 

8. Kaladze T., Rogava J., Tsamalashvili L., Tsiklauri M.

 

I. Vekua Institute of Applied Mathematics, Tbilisi State University,  2 University str., 0143, Tbilisi, Georgia



 ON NUMERICAL RESOLUTION AND UNIQUENESS OF SOLUTION OF

INITIAL-BOUNDARY VALUE PROBLEM FOR THE GENERALIZED

CHARNEY-OBUKHOV EQUATION

 

Enlarged Sessions of the Seminar of I. Vekua Institute of Applied Mathematics Tbilisi State University; Reports, v.19, No.1, pp. 34-42,  2004 .

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       In the present work, first order accuracy implicit difference schemes for the numerical solution of the nonlinear generalized Charney-Obukhov equation with scalar nonlinearity is constructed. On the basis of numerical calculations accomplished by means of these schemes, the dynamics of a two-dimensional nonlinear solitary Rossby vortex structure is studied. In addition, for the considered equation the theorem of uniqueness of the solution in case of periodic boundary conditions is proved.