CRDF-GRDF GEORGIAN-U.S. BILATERAL
GRANTS PROGRAM
FINAL PROJECT REPORT
Award
Number: 3317
1) Brief
statement of project’s major accomplishment : Physical and mathematical models describing the
propagation dynamics of planetary electromagnetic waves and associated
nonlinear solitary vortical structures in the ionospheric D, E and F-layers are
constructed which are in good accordance with experimental observations. In
addition such permanently acting global factors as the spatial inhomogeneity
and curvature of the geomagnetic field are taking into account.
2) Public Summary (English) : Fundamental theoretical investigation of the propagation of large-scale planetary waves (with wavelengths 1000 km or longer) and associated nonlinear solitary vortical structures in the Earth’s ionosphere taking into account the interaction of the induction electric current and the spatially inhomogeneous geomagnetic field is the major goal of the presented project. Based on the developed fluid dynamics and MHD equations, the research is accomplished by means of both analytical and numerical methods. It is shown that permanently acting global factors - the spatial inhomogeneity and curvature of the geomagnetic field are the generation sources of the planetary ultra-low frequency (ULF) electromagnetic waves.
The shallow water theory is developed for perturbations propagating in the ionospheric E-layer. For such weakly-ionized plasma, a nonlinear generalized Charney-Obukhov (GChO) equation for magnetized Rossby waves is derived. These waves are 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. It is shown that the mechanism of a self-organization of solitary vortical structures is the result of the mutual compensation of wave dispersion and interaction through the scalar and Poisson bracket convective nonlinearities in the wave equation. As a result, the solitary structures are anisotropic, containing a circular vortex superimposed on a dipole perturbation. Stationary nonlinear solutions in case of synoptic-scale perturbations are analyzed analytically. The instability of the magnetized Rossby waves in the limit of ageostrophic velocities is revealed. The new implicit difference schemes of the first and second accuracy used to obtain numerical solutions of the GChO equation are constructed. The new physical model of generation of experimentally observed large-scale vortical electric fields in the ionospheric E and F-layers is elaborated. It is established that in the ionospheric E and F-layers so called fast and slow ULF electromagnetic planetary waves may be excited.
Obtained results are original and in good accordance with the existing ionospheric observations. They stimulate new experimental investigations. On the basis of the obtained results, a new method of definition of both ionospheric particles number densities and local winds velocities is suggested.
3) Technical
Report:
In the present report the results of theoretical investigation of the dynamics of generation and propagation of large-scale planetary (with wavelengths 10 km and more) ultra-low frequency (ULF) electromagnetic wave structures (linear waves and nonlinear solitary vortices) in the different layers of the Earth’s ionosphere are given. In addition, such permanent features of the global ionosphere as the spatial inhomogeneity and curvature of the geomagnetic field are taken into account. Namely the main goals of the research project were as follows: 1) to develop a linear theory of low frequency electromagnetic waves (Rossby, MHD, and acoustic-gravity) propagating in D, E and F-layers of the ionosphere; 2) to derive and analyze a self-consistent model system of MHD nonlinear equations describing the dynamics of two- and three-dimensional large-scale solitary vortical structures related to different types of waves in the upper atmosphere and the ionosphere; 3) to construct stationary analytical solutions for spatially strongly localized solitary vortices; 4) to carry out numerical simulation (i.e., composition of numerical schemes, study of their convergence, computer realization) of the relevant partial differential equations; 5) to define the main characteristics of perturbations being under consideration and to carry out a comparison of the obtained results with the existing satellite data and ground based experimental observations in the upper atmosphere and ionosphere. Based on the developed fluid dynamics and MHD equations, the research was accomplished by means of both analytical and numerical methods.
First, the dynamic possibilities of generation of planetary electromagnetic wave structures (both linear and nonlinear) in the ionosphere are investigated. It is shown that not all kinematicly possible movements (even if they are the exact solutions of the corresponding kinematic equations) can be realized in the ionosphere. Ionospheric movements should satisfy additional conditions which are called the dynamic possibility conditions of movement. These conditions express the necessary and sufficient conditions to define the dynamic characteristics of movement (velocities, pressure, magnetic field, etc.). In case of large-scale, planetary motions the dynamic possibility conditions for the motion velocity of medium and perturbations of magnetic induction in the form of the closed nonlinear partial differential equations are obtained. These conditions restrict the medium velocity and wave vector for the planetary electromagnetic waves. It is shown that these conditions give a possibility of wave modes to be correctly filtered and correspondingly to obtain such a dispersion equation which doesn’t contain complex roots (they usually appear when the spatial inhomogeneity of the Earth’s angular rotation velocity and geomagnetic field are taken into account).
The shallow water theory is developed for
perturbations propagating in the ionospheric E-layer. It is shown that in the
weakly ionized E-layer plasma, the new magnetized Rossby waves occur that give
rise to a mixture of waves and vortex structures. These waves don’t
significantly perturb the geomagnetic field. They are induced by the
latitudinal inhomogeneity both of the Earth’s angular velocity and of the
geomagnetic field measured by β and α , respectively. They are
excited by the ionospheric dynamo electric field when the Hall effect due to
the interaction with the ionized ionospheric component in the E-layer is
included. The basic characteristics of the freely decaying waves and waves
driven by the magnetospheric corotation in the presence of the day/night
electron density variation are described. The dynamics of propagation
essentially depends on the alternating generalized Rossby parameter (α +
β) and the modified Rossby-Obukhov radius r
. Immersed in the spatially inhomogeneous geomagnetic field,
magnetized Rossby waves acquire an additional degree of freedom and, unlike
usual Rossby waves, can propagate either westward or eastward at a fixed
latitude. The Lorentz force opposes the Coriolis force vorticity and therefore
partial or full compensation of the Coriolis deviation by the magnetic
deviation is possible. Correspondingly, the propagation phase velocity of the
linear waves also decreases. The period of these waves is of order of tenths of
hours. The frequency of magnetized Rossby waves varies within the range (10
-10
)s
, whereas its wavelength is of the order 10
km and longer, and the
phase velocity is of the order the velocity of the local winds, i.e., ~ (10 -
100) m/s. These waves correspond to longitudinal mode numbers less than 8 – 10.
As the magnetized Rossby waves may have
wavelengths greater than the Rossby - Obukhov radius (r~ 1000 – 3000 km) the generalized magnetized Rossby waves
(GMRW) equation is derived which describes the dynamics of propagation of
nonlinear magnetized Rossby solitary vortical structures of arbitrary size.
This equation is the generalized Charney-Obukhov (GChO) equation modified by
the inhomogeneous geomagnetic field. The GMRW equation corresponds to the
intermediate geostrophic approximation in geophysical hydrodynamics, for which
the perturbation of the free surface of the atmosphere is taken into account.
The GMRW equation contains both “scalar” (KdV) and “vectorial” (Poisson
bracket) nonlinearities. The mechanism of a self-organization into solitary
vortical nonlinear 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, generally a
solitary structure is intrinsically anisotropic and contains a circular vortex
superimposed on a dipole perturbation. The degree of anisotropy sharply
increases as the size approaches the vortex scale of the so-called intermediate
geostrophic size. As we determined, numerical calculations show a large-scale
dipole vortex splits into two monopoles (a cyclone and anticyclone), with a
vortex of one polarity being long-lived whereas the vortex of opposite polarity
disperses. In case of magnetized Rossby waves, only those anticyclones survive
that propagate faster than the maximum velocity of corresponding linear waves.
We derived the trapping condition necessary for the long-time existence of
solitary structure. This condition requires that the structure rotate faster
than it propagates. In this case, in the system moving with the vortex, the
stream lines form a separatrix, inside of which particles of the medium are
trapped. The most important driving mechanism is thought to be the ionospheric
electric field and the day-night variation of the electron density.
Small-scale (synoptic) magnetized Rossby
waves in the ionospheric E-layer having the wavelength less than r are described by the
ordinary magnetized Rossby waves (OMRW) equation with only the Poisson bracket
convective nonlinearity. Such equation has solutions in the form of
synoptic-scale nonlinear solitary dipole vortical structures of 1000 km
diameters. The nonlinear steepening should be balanced by waves dispersive
spreading. Hence the OMRW equation corresponds to the quasi-geostrophic
approximation in geophysical hydrodynamics for which structures are considered
as purely two-dimensional, perturbations of the free surface of the liquid
motion being considered either absent or negligibly small (two-dimensional
velocity divergence is close to zero). In order to be long-lived and not
radiate linear magnetized Rossby waves, the solitary vortex structure
propagates at a velocity lying outside the range of velocities for linear
magnetized Rossby waves. The direction of propagation depends on the sign of
the generalized Rossby parameter (α + β) with westward propagation
when the Coriolis gradient parameter β dominates. The corresponding
permitted regions of linear and nonlinear waves are established. Note that
long-lived solitary monopole vortices (cyclone or anticyclone) are absent
within the framework of the OMRW equation. Particular solutions of the
corresponding nonlinear differential equation for the magnetized Rossby waves
have been obtained which are describing the stationary propagation of solitary
vortical structures. By means of them the main parameters are established which
determine the propagation dynamics of such nonlinear structures in the
ionospheric E-layer. Stationary nonlinear vortical solutions of the synoptic
scale are analyzed analytically. Basic characteristics of such stationary
vortical structures of magnetized Rossby waves are investigated. To establish
the nature of obtained solitary vortical structures, we have used the
equivalence conditions with geophysic modons. In case of dipole vortical structures
(so called “modons”), they are satisfied and consequently they describe moving
in the opposite directions two vortical structures and each of them consists of
only two vortices which are rotating in opposite directions. The vortical
structures have continuous vortex field. Mixed vortical structures consisting
of dipole (“carrier”) and an axially symmetric (“kernel”) are also formulated
and investigated. The kernel cannot exist without the carrier. In this case of
mixed structures, vortex field is not continuous. The usual solitary dipole
vortical structures propagate just faster than the generalized Rossby speed.
But there exist a resting (U = 0) solitary dipole vortical structures as well.
In this case, the equivalence condition is not satisfied, and instead of
“modons”, a close packed vortex array, called a “modon-sea” appears. In this
case each “modon” is composed of a coupled cyclone-anticyclone system which is
separated by a vorticity discontinuity (free streamline) from the surrounding
fluid.
The refined generalized equation for magnetized Rossby waves in the ageostrophic velocities approximation is obtained. The instability of such waves is revealed. In view of the key role of the Rossby vortices in the troposphere and oceans, we argue that the magnetized Rossby waves and vortices in the E-layer are likely to be important in ionospheric weather.
Experimental observations fix propagation
of planetary electromagnetic waves in the ionosphere. The physical mechanism of
generation of the planetary electromagnetic waves is proposed. It is
established that inhomogeneity (latitude variation) and curvature of the
geomagnetic field and inhomogeneity of the angular velocity of the Earth’s
rotation create additional quasi-elastic force and generate the new fast and
slow planetary ULF electromagnetic waves. The general dispersion equation for
fast and slow planetary waves is obtained. The expressions describing their
dispersion are obtained. The main features of such waves are defined. The
linear waves propagate along the parallels at fixed latitude to the east and to
the west as well but particles oscillate along meridians in the south-north
direction. It should be noted that influence of the curvature of the
geomagnetic field on planetary waves dynamics is investigated for the first
time. It is shown that the geomagnetic field curvature confers an anisotropic
elasticity of electromagnetic nature to the ionospheric plasma. In consequence,
planetary waves in E and F-layers undergo additional dispersion and there
appears anisotropy in the propagation direction: waves propagate faster in the
west-east direction than backwards. In
the E-region, the fast waves have the phase velocities (2 – 20) km/s and
frequencies (10- 10) s; the slow waves propagate with the local winds velocities
(10 – 200 m/s) and have frequencies (10 - 10
) s. In the F-region the fast ULF electromagnetic waves
propagate with phase velocities tens-hundreds km/s and their frequencies are in
the range of (10 - 10
) s. Actually the slow mode represents itself the magnetized
Rossby wave in the E-layer. The fast disturbances are also the new modes of the
eigen oscillations of the ionosphere, which are associated with oscillations of
the ionospheric electrons frozen in the geomagnetic field and are connected
with the large-scale internal vortical electric field generation in the
ionosphere. 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 magnetospheric 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 local wind
structures and to the direction change of general ionospheric circulation.
Numerical experiments indicate an instability of such waves owing to the
inhomogeneity of the geomagnetic field. Such planetary waves may be registered
by worldwide ionospheric and magnetic observatories network. Properties of
studied waves are in conformity with features of already observed wave
perturbations.
Dynamics of the slow planetary
electromagnetic waves in the ionosphere is studied experimentally more or less.
Experimental investigation of features of the new fast large-scale
electromagnetic waves should be realized. Our investigations show that the fast
electromagnetic large-scale ionospheric waves have general-planetary character and
occupy latitudes from the pole to the equator both in E and F-regions of the
ionosphere. The fast electromagnetic waves at the ionospheric altitudes can be
experimentally revealed and registered using their following specific features:
1) wide range of phase velocity dependence on a latitude (phase velocities of
these waves are increased from the pole to the equator; they are doubled at the
equator); 2) the planetary electromagnetic fast modes in the F-region and slow
modes in the E-region propagate in the eastward direction faster than in the
westward direction but the fast planetary electromagnetic mode in the E-region
propagates along parallels in the westward direction faster than in the
eastward direction; 3) high magnitude variation of electron concentration
substantially increases phase velocity of fast waves in the E-region at nightly
conditions (from a few hundreds m/s in daytime to a few tens km/s at night); 4)
application of the well-known profiles of electron concentration allows us to
calculate the unique height distribution of the phase velocity of the fast
waves in the E-region of the ionosphere and, conversely, from a height
distribution of the phase velocity of fast waves we can plot the dependence of
electron concentration on an altitude; 5) altitude variation of the neutral
component concentration leads to strong increase of the phase velocity of fast
waves (phase velocity of fast waves at heights of 200 – 500 km is increased
from a few km/s up to 1000 km/s) in F-region of the ionosphere; 6) response of
fast waves in the E and F-regions on the earthquake, magnetic storms,
artificial explosions and magnetic activity of the sun; 7) registration of
electromagnetic large-scale (10 - 10
) km character of fast waves in the E and F-regions by
world-wide network of ionospheric and magnetospheric observatories.
It is considered also one more class of
the waves, called as the slow magnetohydrodynamic (MHD) waves, which
inhomogeneity of the Coriolis and Ampere forces does not influence. These waves
appear as an admixture of the slow Alfven and whistler type perturbations. In
the long wavelength limit they propagate along the meridian with a decreased
Alfven speed loaded by the dense neutral component. The reason for that loading
is that the ions in the E-layer are completely dragged by the neutral
particles. Owing to that fact, any perturbation in the ionized components is
immediately transferred to the neutral component. In the short wavelength limit
these waves smoothly convert to helicons or gyrotropic waves. The slow Alfven
waves have typical periods of 0.5 – 2 h and wavelengths of the order of 10km. The typical phase velocities of these waves are of order
of 1 – 2 km/s. The waves generate the geomagnetic field from several tens to
several hundreds nT and more.
The new physical mechanism of generation of
large-scale (planetary) internal vortical electric fields in the ionospheric E
and F-layers is suggested. It is shown that in the ionosphere the large-scale
(with wavelengths 10 km and more),
synoptically short period (from several second to several hours) fast (with a
propagation velocity higher than 1 km/s) processes excite a planetary-scale
vortex electric field that may be much higher than the dynamo field generated
in this region by local ionospheric winds. The generated electric fields are of
order 10- 10
V/m. It is established
that in the ionosphere the spatial inhomogeneity of the geomagnetic field is
the source of the internal vortical electric field generation.
A vortical model which is being described by the two-dimensional oscillator having ω fundamental frequency in a noninertial system rotating with a Ω frequency is developed to investigate stability of the planetary both ordinary and magnetized Rossby waves. The possibility of such simulation is stipulated with adequacy of exact vortical solution of hydrodynamic equations of incompressible liquid by the presentation of rotating solid body when the equations of the two-dimensional oscillator are used. In contrast to existing models it is shown that in frequency band ω << Ω the movement of the oscillator becomes unstable without taking into account dissipative processes. When describing such waves by the β-plane approximation nonlinear effects are generating summarized, difference and doubled frequency discrete spectra.
Taking into account the nonhomogeneity of the curvilinear geomagnetic field excitation and typical peculiarity of an ionospheric cyclone (anticyclone) in the E and F-layers are investigated. The theoretical model of ionospheric cyclones (anticyclones) is constructed on the basis of conditions of dynamic possibility of large-scale ionospheric motion. To this end we have used the original approach: a concrete kinematic motion form was coordinated with the perturbations really observed in the ionosphere. In this connection a vertical velocity of displacement is not equal zero. Such method simplifies strongly the initial nonlinear equations of the ionospheric dynamics and in many cases it makes possible to integrate these equations analytically. In such a way, we have constructed the theoretical models of ionospheric vortical motions which are consistent with the observations. It is shown that for the real vortices the vertical velocity provides transfer mechanism of a momentum toward the vertical direction in a non-dissipative ionosphere. It is established that in the E-layer the three-dimensional non-stationary vortical motions of cyclone (anticyclone) type may be excited which are stipulated by the baroclinicity of the ionosphere and are of the hydrodynamic nature. The induced magnetic field doesn’t influence the structure practically and the properties of vortex are defined from the induction equation at fixed field of velocities of medium. It is shown that in the F-layer large-scale cyclonic (anticyclonic) vortices are of the magnetohydrodynamic nature. They are three-dimensional and may be both stationary and nonstationary. Owing to the isothermality of upper atmosphere in the F-layer the baroclinicity as a source of vortex generation is absent. It is revealed that magnetic energy of the geomagnetic field is the main source of vortical generation. Vortices are existing in a form of magneto-vortical rings which intensity and stationary state (non-stationary state) depend on orientation of hydrodynamic velocity and magnetic displacement vectors.
Discovered by us long-scale (planetary) nonlinear solitary vortices are weakly damped and long-lived. They cause the geomagnetic pulsations by one order stronger than the linear waves. 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. Parameters and characteristic features of revealed and theoretically investigated in the project of planetary ULF electromagnetic wave structures are in good accordance with the ground based and satellite ionospheric observations.
The results obtained in this project can have the following components of commercial value in the scientific marketplace:
The investigated ULF planetary electromagnetic waves are registered by the worldwide network of the magnetic observatories. The frequencies and phase velocities of these waves in E-region depend on charged particle concentration (electrons, ions), but in F-region they depend on the neutral particle density. Thus, measuring frequency and phase velocity of these waves gives a method to determine the charged particle concentration in E-region and neutral particle density in F-region. Electron concentration measurements require strong receiving-transmitting devices (ionospheric station). Neutral density measurements would require launching of special devices, by braking of which neutral component density will be determined at the given latitude.
The group velocity of the fast ULF electromagnetic waves in F-region is approximately equal to the mean wind velocity at the given layer. Therefore, measurements of the group velocity can provide important information about wind velocity in the F-region. No other technique is currently available for determination of this important parameter (the wind velocity) of the upper atmosphere.
The proposed methods of particle concentration, density and mean wind velocity measurements in the upper atmosphere can have big economic and commercial effects. It is essential that existing and new magnetic dataset in the network of magnetic observatories are sufficient to implement these methods. No new facilities are required.
First- and second-order accurate implicit difference schemes for the numerical solution of the spatially two-dimensional Charney-Obukhov (ChO) partial differential equation containing only vectorial nonlinearity and describing dynamics of the synoptic scale solitary vortical structures on planetary Rossby waves is developed. In contrast to known explicit schemes they are characterized by the high stability factor. Numerical calculations show that the evolution of stream function is stable in the characteristic time interval and it increases with the decrease of step with respect to time and spatial variables. For the ChO nonlinear partial differential equation uniqueness of the solution of the periodic boundary value problem is studied. It is shown that this problem has unique solution in the class of sufficiently smooth functions. The sufficiently general integral conservation law is established. For each constructed scheme, the approximation error is estimated and the convergence of the iterative process is investigated. The results of numerical experiments are analyzed.
Implicit difference schemes of the first- and second-order accuracy are used to obtain solutions of the generalized Charney-Obukhov (GChO) and generalized Hasegawa-Mima (GHM) partial differential equations. In these solutions, both the vector nonlinearity and the scalar nonlinearity, often called the Korteweg – de Vries (KdV) nonlinearity, are taken into account. For the considered equations the initial-boundary value problem is set. Using an energy analysis method it is shown that the periodic boundary value problem with regard to scalar nonlinearity has unique solution in class of sufficiently smooth functions. The sufficient convergence conditions of iterative method is established. The error of approximate solution is estimated. By means of the proposed schemes numerical experiments are carried out and the dynamics of nonlinear solitary vortical structures are studied. It becomes obvious that the scalar nonlinearity changes caused by the vectorial nonlinearity bipolar vortical structure by the unipolar one. In addition an intensity of the left structure (cyclone or anticyclone) is increasing at the expense of energy of other damping structure. The dynamic relation between solutions of the GChO and GHM equations is established. It is shown that in spite of the prevalent opinion, the scalar nonlinearity in the case of the GHM equation develops monopolar anticyclone structures while in the case of the GChO equation monopolar cyclone structures are developed. On the basis of such scheme, we have studied the propagation of both monopole and dipole impulses. As a result, due to the influence of the scalar nonlinearity, the initial impulse splits into several small vortices in the midst of one monopole solitary vortex which is the main structure containing most of the flow energy. For large time intervals the superiority of the second order accurate scheme is obvious.
We have substantially enriched the class of possible low-frequency waves in the ionosphere, resolved uncertainties, filled in gaps in the present understanding, and improved the existing physical and mathematical models. Experimental data from ground and satellite measurements were used in order to elaborate the relevant physical models.
The Web-site www.viam.hepi.edu.ge/IMPP/grant.htm
describing the grant scientific activities is created at the server of I. Vekua
Institute of Applied Mathematics of
Bibliography
of Project-Related Publications
1. Aburjania, G.D., Kh.Z. Chargazia, A.G. Khantadze, and O.A.
Kharshiladze. “Dynamics
of the low-frequency planetary-scale electromagnetic wave structures in the
ionosphere”. Recent Research Developments in Geophysics 5 (2003):
157-192. (
2. Aburjania, G.D., Kh.Z. Chargazia,
G.V. Jandieri, G.Z. Machabeli, A.G. Khantadze, and O.A. Kharshiladze.
“Theoretical model for conjugate fotoelectron energy transfer and related to
them night sky airglow enhancement in the local midlatitude ionospheric
F-region”. Recent Research Developments in Geophysics 5 (2003): 193-205. (
3. Aburjania, G.D., Kh.Z. Chargazia,
T.D. Kaladze, A.G. Khantadze, and O.A. Kharshiladze. “New generation mechanism
of the planetary-scale internal vertical electric field in the Earth’s
ionosphere”. Journal of the Georgian Geophysical Society, Issue B. Physics
of Atmosphere, Ocean and Space Plasma 8B (2003): 122-135. (
4. Aburjania, G.D., Kh.Z. Chargazia,
G.V. Jandieri, A.G. Khantadze, and O.A. Kharshiladze. “On the new modes of
planetary-scale electromagnetic waves in the ionosphere”. Annales
Geophysicae 22 (2004): 525-534. (
5. Aburjania, G.D., and A.G. Khantadze.
“Propagation peculiarities of planetary electromagnetic ULF waves in the
Earth’s ionosphere stipulated by curvature of the geomagnetic field”. Geomagnetizm
and Aeronomia 45 (2005): will be published. (
6. Aburjania, G.D., and A.G. Khantadze.
“Dynamical possibility conditions of movement for large-scale electromagnetic
waves in the ionosphere”. Izvestia RAN. Fizika Atmosferi I Okeana 41
(2005): will be published. (
7. Aburjania, G.D., Kh.Z. Chargazia,
J.G. Lominadze, A.G. Khantadze, and O.A. Kharshiladze. “Generation and
propagation of the ULF planetary-scale electromagnetic wavy structures in the
ionosphere”. Planetary and Space Science 53 (2005): will be published. (
8. Aburjania, G.D., J.G. Lominadze,
A.G. Khantadze, and O.A. Kharshiladze. “Generation mechanism and propagation
peculiarities of ULF planetary electromagnetic wave structures in the
ionosphere”. Kosmicheskaya Nauka I Tekhnologia (2005): will be published (
9. Kaladze, T., J. Rogava, L.
Tsamalashvili, and M. Tsiklauri. “Implicit difference schemes for the Charney –
Obukhov equation”. Applied Mathematics, Informatics and Mechanics 8
(2003): 20-39. (
10. Kaladze, T.D., G.D. Aburjania, O.A.
Kharshiladze, W. Horton, and Y. –H. Kim. “Theory of magnetized Rossby waves in
the ionospheric E layer”. Journal of Geophysical Research 109 (2004):
A05302, 1-14. (
11. Kaladze, T., J. Rogava, L.
Tsamalashvili, and M. Tsiklauri. “First and second-order accurate implicit
difference schemes for the Charney – Obukhov equation”. Physics Letters A
328 (2004): 51-64. (the
12. Kaladze, T., J. Rogava, L.
Tsamalashvili, and M. Tsiklauri. “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
13. Kaladze, T., J. Rogava, L. Tsamalashvili,
and M. Tsiklauri. “Investigation and numerical resolution of initial-boundary
value problem for the generalized Charney-Obukhov and Hasegawa-Mima equations”.
Physics Letters A (2005): submitted for publication (the
14. Kaladze, T.D., and W. Horton.
“Synoptic-scale nonlinear stationary magnetized Rossby waves in the ionospheric
E-layer”. Annales Geophysicae (2005): submitted for publication. (
15.
Kaladze, T. D. “ Planetary electromagnetic waves in the ionospheric E-layer”. Proceedings
of the First
16.
Horton, W. “Laboratory simulation of magnetospheric plasma shocks”. Advances
in Space Research (2005): accepted for publication. (
17.
Horton, W., M. J. Mithaiwala, E. A. Spencer and I. Doxas, “WINDMI: A
family of physics network models for storms and substorms,” a chapter in the
book, “Multiscale Coupling of Sun-Earth Processes, edit. A. T. Y. Lui, Y.
Kamide and G. Consolini, Published by Elsevier for release in May 2005.
Conference
Presentation List
1. Aburjania G.D., KH.Z. Chargazia, and O.A. Kharshiladze. “ULF
Electromagnetic Wavy Structures in F-region of the Spherical Ionosphere Caused
from Inhomogeneity of the Geomagnetic Field”. Proceedings of ISAP04.,
2. Aburjania
G.D., J.G. Lominadze, A.G. Khantadze, and O.A. Kharshiladze. “Generation
Mechanism and Propagation Peculiarities of ULF planetary electromagnetic wavy
structures in the ionosphere”, (Oral Presentation) The 4th Ukraine
Conference on Cosmic Investigations, September 19-26,
3. Aburjania
G.D., A.G. Khantadze, and L.S. Alperovich. “Planetary and Local ULF
Electromagnetic Waves in the E- and F-layers”. (Poster Presentation),
International Workshop on Seismo Electromagnetics (IWSE 2005), March, 15-17,
4. Kaladze, T.D., G.D. Aburjania, O.A.
Kharshiladze, and W. Horton. “On the Nonlinear Theory of Magnetized Rossby
Waves in the Ionospheric E layer”, (Poster Presentation), International Topical
Conference on Plasma Physics “Complex Plasmas in the New Millennium”, September
8-12, 2003, Santorini, Greece. ITCPP03 Programme and Abstract Book, p. PII-10,
2003.
5. Kaladze
T.D. “Planetary Electromagnetic Waves in the Ionospheric E-layer”, (Invited
Lecture), First Cairo Conference on Plasma Physics & Applications,
6. Kaladze
T.D., and W. Horton. “Propagation of Solitary Magnetized Rossby Waves in the
Ionospheric E-layer”, (Oral Presentation), Second International Conference on
the Frontiers of Plasma Physics and Technology,
7. Horton, W., J. Kim, T. Kaladze, and G.
Aburjania, “Magnetized Rossby Vortices in the E-Layer Ionosphere, (Oral
presentation), 35th COSPAR Scientific Assembly 2004, Paris, France, July 18-25,
2