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内容記述 |
The magnetic fields of planetary and astrophysical bodies, such as the Sun and the Earth, are believed to be generated by a dynamo action in a moving electrically conducting fluid. The mathematical problem describing the generation of magnetic fields by self-inductive action in an electrically conducting fluid is called the dynamo problem. The dynamo process converts the mechanical energy of electrically conducting fluid into the magnetic <br />energy and dissipates it in the form of ohmic heat.<br /><br /> On the surface of the Earth and above, the dipole component of the Earth's magnetic field is dominant, and its dipole axis is ever changing. The Earth's magnetic field has existed on average at roughly its present strength in its history and is constantly changing. Its polarity has reversed many hundreds of times at irregular intervals during the Earth's <br />history.<br /><br /> Recent accelerated development in supercomputer technology makes it possible to achieve three-dimensional MHD dynamo simulations which self-consistently solve for fluid flow and magnetic field in three dimensions. Significant progress in recent years is the development of numerical simulation of convection-driven dynamo in rotating spherical shells that achieve self-sustaining dynamo actions. Some models have realized dominant dipole fields outside the shells. Several numerical models of convective dynamos even suc- cessfully have thus far reproduced some of the basic properties of the Earth's magnetic field.<br /><br /> Reversal of the magnetic field is one interesting and challenging problem in MHD theory. Some authors have already succeeded in demonstration of magnetic field reversal by three dimensional dynamo simulations. In particular, Glatzmaier and Roberts presented the first numerical simulation of a complete field reversal. The first numerical simulation of dynamical flip-flop type transition of the magnetic energy level and its association with the reversals of the dipole and octupole field polarity were obtained by Kageyama and Sato. Later, Glatzmaier et al. showed that more frequent reversals occur in their simulation by changing the core-mantle boundary condition. Coe et al. described the evolution of the morphology and/or spectral energy of simulated magnetic fields duringreversals. <br />However, physical understanding of the mechanism of magnetic polarity reversals is yet veiled.<br /><br /> The mechanism of the magnetic field reversal still remains one of the challenging phenomena in MHD dynamo theory. To understand the mechanism by which the polarity of the magnetic field is reversed in MHD dynamo, a very long time numerical simulation is carried out by using Kageyama-Sato MHD dynamo model in this thesis. The simulation results show that the generated magnetic field is dipole dominated in most simulation time and reverses its polarity. The reversals of magnetic field occur repeatedly and irregularly. The magnetic field reversal appears to occur without any regular rule. It does reverse suddenly and the reversal does continue endlessly. As a whole, it is unlikely that the existence of one polarity predominates over the other.<br /><br /> The thermal convection in the rapidly rotating spherical shell is caused by gravity and the temperature difference between inner and outer cores, which takes the form of columnar cells which are parallel to the rotation axis. The magnetic field is generated and amplified through the fluid convection motion which stretches and twists the magnetic field lines. The magnetic field structure inside the spherical shell is very complicated. Generally, the magnetic field lines spiral around the convection columns. Interestingly, in the whole evolution, the total magnetic and kinetic energies exhibit a flip-flop alternation between a high energy state and a low energy state. The different energy states correspond to different magnetic field configurations and convection patterns. In low energy states, the convection columns drift westwards and keep almost unchanged structures. The convection motion in high energy states exhibits the basic columnar structure, but nevertheless it is time-dependent.<br /><br /> The magnetic field reversal is studied in details. From the analysis of the time evolution of magnetic field, we obtain the necessary conditions for the occurrence of a dipole reversal: (1) the system is in a high energy state, (2) the high energy state lasts for a certain period, (3) the quadrupole mode is on the average in a growing phase, and (4) the magnitude of the quadrupole mode exceeds that of the dipole mode on the outer boundary.<br /><br /> The magnetic field is generated by the convection motion of the electrically conducting fluid in the sphere shell. So the magnetic field pattern is strongly correlated with the fluid flow. In low energy states, the axial component of fluid velocity in the equatorial plane (i.e., trans-equatorial flow) is very weak. The convection motion is symmetric around the equatorial plane. While in high energy states, the trans-equatorial component of fluid velocity in the equatorial plane is very strong. The north-south symmetry around the equatorial plane is broken. The existence of the trans-equatorial flows in high energy states suggest that there is a strong interaction of fluid motion between the northern hemisphere and the southern hemispheres. This strong interaction of fluid flow is likely to initiate a reversal of magnetic field.<br /><br /> The most important and crucial discovery of this thesis is the generation of trans-equatorial flows in a spherical system that make the convection pattern vulnerable and the whole system marginally stable, the reversal of the dipole magnetic field thereby being triggered occasionally and unexpectedly.<br /><br /> The effects of electrical resistivity and the temperature difference between the inner and outer boundaries to the magnetic field reversals are also analyzed. We find that the electrical resistivity is one of important physical parameters to the generation and reversal of the magnetic field.<br /><br /> To sum up, in our numerical simulations of MHD dynamo, we have observed repeated and sudden magnetic field reversals, and obtained the conditions for magnetic field rever- sal. Furthermore, we have studied the physical mechanism of the magnetic field reversals and come to the conclusion that the break of the north-south symmetry around the equa-torial plane of convection motion must be the primary cause of the magnetic field reversal. |
要旨・審査要旨 / Abstract, Screening Result (395.1 kB)
