This proposal have been selected for an award( # 12206) under the first Georgian-U.S. Bilateral Grants Program by the U.S. Civilian Research & Development Foundation (CRDF) and the Georgian Research & Development Foundation (GRDF) in 2002. Duration: 24 months.
Project Narrative
I. BACKGROUND & JUSTIFICATION FOR UNDERTAKING THE PROJECT
II. OBJECTIVES AND POTENTIAL RESULTS
III. SCIENTIFIC DESCRIPTION OF THE PROGRAM AND RESOURCES
IV. DESCRIPTION OF RESEARCH TEAMS AND THEIR COOPERATION
VI. DELIVERABLES, EXPLOITATION AND DISSEMINATION OF RESULTS
Carrying out of the 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 is proposed. Fluid dynamics and MHD equations will be developed to study how perturbations on different types of waves (Rossby, MHD and acoustic-gravity) propagate. The interaction of the induction electric current and spatially inhomogeneous Earth’s magnetic field will be taken into account. Doing so will substantially enrich the class of possible low-frequency waves in the ionosphere, resolve uncertainties, fill in gaps in the present understanding, and improve the existing physical and mathematical models. The research will be accomplished by means of both analytical and numerical methods. Experimental data from ground and satellite measurements will be used in order to elaborate the relevant physical models. By including the spatial inhomogeneity of the geomagnetic field and the angular velocity of the Earth’s rotation, obtaining the following scientific results is expected:
1. Development of the linear theory of the low-frequency electromagnetic waves propagating in the D, E and F-layers of the ionosphere;
2. Derivation and analysis of the self-consistent model system of nonlinear MHD 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. Construction of the stationary analytical solutions for spatially strongly localized solitary vortices;
4. Carrying out of the numerical simulation of the relevant partial differential equations;
5. Definition of the main characteristics of the perturbations under consideration and compare the results with existing satellite data and ground-based experimental observations in the upper atmosphere and ionosphere.
I. BACKGROUND & JUSTIFICATION FOR UNDERTAKING THE PROJECT
Large-scale planetary waves are of interest because of their significant influence on global atmospheric circulation // Pedlosky, J., Geophysical Fluid Dynamics, Springer-Verlag, Berlin, 1982; Petviashvili, V.I., and O.A. Pokhotelov, Solitary waves in plasmas and in the atmosphere, Gordon and Breach, Reading, 1992 //. It is known that similar perturbations can exist in the ionospheric conductive layers.
Most of the ionospheric phenomena such as super-rotation of the Earth’s atmosphere //Rishbeth, H., Super rotation of the upper atmosphere, Rev. Geophys. Space Phys., 25, 799, 1972 //, ionospheric precursors to certain extraordinary phenomena //Haykowicz, L.A., Global onset and propagation of large-scale traveling ionospheric disturbance as a result of the great storm of 13 March 1989, Planet. Space Sci., 39, 583, 1991; Liperovski V.A., O.A. Pokhotelov, and S.L. Shalimov, Ionospheric earthquake precursors, Nauka, Moscow, 1992 //, and ionospheric response to anthropogenic activity // Pokhotelov, O.A., Parrot, M., Fedorov, E.N., Pilipenko, V.A., Surkov, V.V., and Gladychev, V.A. Response of the ionosphere to natural and man-made acoustic sources, Annales Geophysicae, 13, 1197, 1995; Shaefer, L.D., D.R. Rock, J.P. Lewis et al., Detection of explosive events by monitoring acoustically-induced geomagnetic perturbations, Lawrence Livermore Laboratory, Livermore, CA 94550, 63, 1999 // are in the frequency range of planetary waves. In reality, these perturbations display themselves as background oscillations. Recent observations show that forced oscillations of that kind appear in impulsive impacts on the ionosphere or during magnetospheric storms //see above Haykowicz, 1991; W.Horton, H.Vernon Wong, R.Weigel, and I.Doxas, Interchange trigger for substorms in a nonlinear dynamics model, Phys.Space Plasmas, 15, 169, 1998//. They may also arise from earthquakes, volcano eruptions, or man-made activities //see above, Liperovsky et al., 1992; Cheng, K.Y., and N. Huang, Ionospheric disturbances observed during the period of Mount Pinatubo eruptions in June 1991, J. Geophys. Res. 97, 16995, 1992 //. In the last case, the corresponding perturbations appear in the form of solitary wave structures, due to nonlinearity.
The solitary form of such structures is the result of competition between the dispersive spreading and nonlinear self-focusing. Among these, the solitary vortical structures deserve special attention. As opposed to one-dimensional solitons, vortices represent stable multi-dimensional rotational structures, which can effectively trap particles and transport them over long distances // see above, Petviashvili and Pokhotelov, 1992 //. This is accompanied by strong particle diffusion and convective mixing of the medium. Nonlinear solitary vortex structures are universal phenomena. They are found in various natural phenomena. In particular, they are important in climate formation and its variation. Recently, their study as the precursors to earthquakes has been begun // Aburdzaniya G.D., Self-Organization of Acoustic-Gravity vortices in the ionosphere before earthquakes, Plasma Phys. Reports, 22, 864, 1996 //.
Since the ionosphere is a partially ionized plasma consisting of electrons, ions and neutrals, its behaviour as a whole is determined by its neutral component because the charged particle number density is much smaller than that for the neutrals. However, the existence of charged particles in a system brings into play the influence of both the conductivity of the Earth’s ionosphere and the external magnetic field. Thus, the upper atmosphere and the ionosphere are significantly affected not only by spatially inhomogeneous mechanical forces, but also by spatially inhomogeneous electromagnetic forces.
The study of the generation and dynamics of planetary Rossby waves that are induced by the spatial inhomogeneity of the Earth’s angular velocity in the ionospheric plasma has accordingly been a subject of a great deal of theoretical and experimental investigation in recent years. The presence of charged particles in the ionosphere may substantially enrich the class of possible low-frequency wave modes in the ionosphere.
Dokuchaev //Dokuchaev, V.P., Influence of the Earth’s magnetic field on the ionospheric winds, Izvestia AN SSSR, Seria Geophysica, 5, 783, 1959 // first pointed out the importance of the interaction of the induction electric current with the Earth’s magnetic field. He demonstrated that the effect of the spatially homogeneous Ampere force results in a deviation of the zonal flows from their geostrophic values. Tolstoy // Tolstoy I., Hydromagnetic gradient waves in the ionosphere, J. Geophys. Res., 72, 1435, 1967 // included this effect by taking into account the spatial inhomogeneity of the forces and examined linear Rossby type waves, which were called hydromagnetic gradient (HMG) waves. He suggested that HMG waves may be observed as traveling-wave perturbations of the Sq current system and that they can produce strong variations of the geomagnetic field. In more recent publications devoted to nonlinear vortex structures in the ionosphere // Kaladze, T.D., and L.V. Tsamalashvili, Solitary dipole vortices in the Earth’s ionosphere, Physics Letters A, 232, 269, 1997; Kaladze, T.D., Magnetized Rossby waves in the Earth’s ionosphere, Plasma Phys. Reports, 25, 284, 1999 //, Kaladze has also taken into account the effect of spatially inhomogeneous forces. These planetary perturbations, which do not perturb the geomagnetic field, have the same dispersion relation as that for the HMG waves and are produced solely by the ionospheric dynamo electric field. In order to distinguish them from the HMG waves, they were termed magnetized Rossby waves // see above, Kaladze and Tsamalashvili, 1997; Kaladze, 1999//.
Up to now, a large amount of magnetometer and ionospheric observations have been collected that confirm the existence of slow, long-period planetary waves with phase velocities of the order of the velocity of the local ionospheric winds (20 - 300 m/s). At middle-latitudes their wavelengths are of the order of 1000 km or longer, and the wave periods constitute a few days at any season // Gossard, E., and Y. Heoke, Waves in the atmosphere, Elsevier, Amsterdam, 1975; Sorokin, V.M., and G.V. Fedorovich, Physics of slow MHD waves in the ionospheric plasma, Nauka, Moscow, 1982 //. Contrary to ordinary Rossby waves, these slow waves are associated with a strong perturbation of the geomagnetic field (from a few to several tenths of nT). This fact shows their electromagnetic (EM) origin. Apart from the slow waves, there is evidence for the existence of fast large-scale EM perturbations in the middle-latitude ionosphere. Such waves propagate along the Earth’s surface with the velocity 2 - 20 km/s. Their periods vary from a few minutes to a few tenths of minutes, the wavelength is of the order of 1000 km or longer, and the wave amplitude is between ten to a hundred nT. The phase velocity of the fast perturbations differs for the day- and night-time ionospheric conditions. The relatively low phase velocities and strong diurnal variations exclude the possibility of their identification with the ordinary MHD waves.
In this respect the study of possible mechanisms for the generation and evolution of such EM planetary perturbations in the ionosphere is of great importance for the interpretation of ground-based and ionospheric observations. For that purpose it is necessary to elucidate the relevant physical factors that govern the generation and existence of such perturbations. We note that previous reports, devoted to the analysis of EM planetary waves in the ionosphere, suffered from the lack of an analysis of the effects caused by the latitudinal gradient of the magnetic field, which is inevitably inherent in the Earth’s magnetic field. Moreover, no nonlinear theory has been developed to describe the propagation of EM solitary vortical structures in the spatially inhomogeneous geomagnetic field.
II. OBJECTIVES AND POTENTIAL RESULTS
The main objective of the proposed scientific research is to develop a comprehensive theoretical model 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, with the spatially inhomogeneous forces described in Section I. The model will allow a description of the main characteristics of the perturbations under consideration. The results of the study may then be applied to the analysis and interpretation of existing satellite data and ground-based experimental observations in the upper atmosphere and ionosphere. The research will be accomplished by theoretical analysis and numerical simulations. Our plan is as follows:
The results to be obtained may yield the following possibilities:
1. An explanation of numerous satellite data and ground-based experimental observations of the atmosphere and ionosphere.
III. SCIENTIFIC DESCRIPTION OF THE PROGRAM AND RESOURCES
In the framework of the prposed project, we plan to develop physical and mathematical models that describe the propagation of large-scale planetary waves and associated nonlinear solitary vortical structures in the Earth’s ionosphere on the basis of fluid dynamics and MHD equations. Based on complex analysis of satellite and ground-based observations, relevant theoretical models will be developed to resolve uncertainties, fill the gaps in our present understanding, and improve the current point of view. The research will be accomplished by means of both analytical and numerical methods.
The proposed work will be realized by bringing together Georgia and US research teams that have unique and relevant expertise of a complementary nature. The specific objectives of this proposal are a consequence of existing, ongoing joint research among the team members and emerge directly from the actual state of the art, combining theory and experimental data in an almost ideal configuration.
The scientists involved in the project have extensive experience in the investigation of wave propagation problems in various media, the construction and application of corresponding physical and mathematical models, the creation of methods of solution for the derived nonlinear equations, and the construction of algorithms and the implementation of corresponding numerical simulations.
By including the spatial inhomogeneity of the geomagnetic field and the angular velocity of the Earth’s rotation, we expect to obtain the following types of scientific results:
1. Develop a linear theory of the low-frequency electromagnetic waves propagating in the D, E, and F-layers of the ionosphere;
2. Derive and analyze a self-consistent model system of nonlinear MHD 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. Construct stationary analytical solutions for spatially strongly localized solitary vortices;
4. Carry out numerical simulation of the relevant partial differential equations; and
5. Define the main characteristics of the perturbations under consideration and compare the results with existing satellite data and ground-based experimental observations in the upper atmosphere and ionosphere.
IV. DESCRIPTION OF RESEARCH TEAMS AND THEIR COOPERATION
The consortium consists of a team from the I. Vekua Institute of Applied Mathematics (IAM) of Tbilisi State University (Georgia) and a team from the Institute for Fusion Studies of The University of Texas at Austin (USA). From the Georgian side former defence scientists are included. Along with experienced scientists, the consortium has one young promising researcher. Thus an important educational element in the project is to train students and young scientists as participants.
The IAM team from Georgia consists of seven researchers: Dr. T.D. Kaladze (Principal Investigator, physicist), Dr. G.D. Aburjania (physicist), Dr. J.L. Rogava (mathematician), Dr. L.V. Tsamalashvili (mathematician-programmer, researcher), Dr. O. A. Kharshiladze (physicist), M. A. Tsiklauri (mathematician), and K.K. Purtseladze (engineer-programmer).
The IAM team consists of physicists and mathematicians who have extensive experience in physical and mathematical modeling of different problems arising in the linear and nonlinear theory of wave propagation in different media, including the processes that occur in a thermonuclear tokamak reactor.
Dr. T.D. Kaladze and Dr. G.D. Aburjania are well-known specialists in the theory of linear and nonlinear waves. They have broad experience in modeling the nonlinear behavior of turbulence on the basis of solitary vortex dynamics. In collaboration with Dr. L.V. Tsamalashvili and Dr. O.A. Kharshiladze, they have published in refereed scientific journals many papers related to the problems being proposed for consideration.
In the proposed project, the research team will make substantial contributions, as follows:
1. The development of linear theory for low-frequency electromagnetic waves propagating in the D, E, and F layers of the ionosphere [T.D. Kaladze, G.D. Aburjania ,and O.A. Kharshiladze, with W. Horton from the US team].
2. The construction of a self-consistent model system of MHD nonlinear equations that describe the dynamics of two- and three-dimensional large-scale solitary vortical structures [T.D. Kaladze, G.D. Aburjania, and O.A. Kharshiladze, with W. Horton from the US team].
3. The performance of numerical simulations [J.L. Rogava, L.V. Tsamalashvili, M.A. Tsiklauri, O.A. Kharshiladze and K.K. Purtseladze]. The extensive numerical experience of the US team will also be used.
The US team will consist of one researcher, Prof. Wendell Horton. Dr. Horton has worked on theory and applications of magnetosphere-ionosphere coupling processes. He has extensive experience in modeling the role of the self-consistent interaction between the ionosphere and magnetosphere in controlling the amount of electrical power that is coupled into auroral ionosphere and energetic particles into the inner magnetosphere. He has also investigated triggering mechanisms for the episodic energy release events known as substorms.
The Georgian team will carry out its part of the proposed project at the I. Vekua Institute of Applied Mathematics of Tbilisi State University. The US co-PI will conduct his corresponding research at the Institute for Fusion Studies of The University of Texas at Austin. The Principal Investigators of the two teams will be responsible for the overall management of the project. They will conduct thorough supervision and monthly discussion of the results at seminars. The other participants in the project will provide substantial help to them. All exchange of current information on ongoing studies, co-ordination, and cross talk will primarily be conducted by telecommunication (e-mail, fax, and telephone). Mutual visits in collaborating countries will greatly contribute to exchanging scientific expertise and results, carrying out the necessary calculation, coordination of work and acquainting the teams with new publications. Visit to USA of PI Dr. T. Kaladze is planned. In the second year the Georgia and US participants will hold a meeting in the form of a workshop.
The main scientific benefit to the Georgian team will be the possibility—in the midst of the current severe economic situation—of obtaining of new scientific information and observational experimental data, gaining skills to undertake complex numerical simulations, and exchanging techniques to solve significant scientific problems via mutual cooperation with the scientifically experienced and technically well-equipped US team. Undoubtedly it will also raise the scientific and technological capability of the Georgian team and will assist in the solution of difficult social problems.
VI. DELIVERABLES, EXPLOITATION AND DISSEMINATION OF RESULTS
The results of the proposed project will be disseminated through publication in scientific journals and by participation at major international topical conferences. A special webpage for the project, with necessary URL links to enable a user-friendly interface, will be set up on the IAM server. The more public part of the project will be made transparent by use of the internet. The final performance report in proper form will be delivered to CRDF and GRDF at the end of the project duration.