Shear Alfven waves and shear flow instabilities in the Earth's magnetosphere

The objective of this thesis is the theoretical and computational study of nonlinear shear Alfven waves and shear flow instabilities in the Earth's magnetosphere. We have developed a computer code to solve the nonlinear set of magnetohydrodynamic (MHD) equations in curvilinear coordinates. This code has been used to simulate the excitation, growth, coupling of shear Alfven waves and magneto-acoustic modes, and nonlinear saturation of standing shear Alfven waves in the dipolar magnetosphere. The computational results were verified by comparing them with a nonlinear analytical model which was derived as part of this study.;Using computer simulations, we have shown that shear Alfven waves in the field line resonance region develop into an azimuthally stretched and radially confined region of a large amplitude shear flow in the equatorial magnetosphere. This shear flow may become unstable with respect to a shear flow instability with characteristic e-folding time smaller than a half-period of the shear Alfven wave. Therefore, we have used the computer model to study shear flow and shear flow ballooning instabilities which can arise in the association with field line resonance regions.;Initially, we used the MHD code to model the shear flow and ballooning instabilities in the equatorial plane of the Earth's magnetosphere. We have shown that a shear flow vortex couples effectively with a ballooning mode and grows with a characteristic time scale of tens of seconds extracting the potential energy from the ambient magnetic configuration. Therefore, the instability results in the generation and propagation of a large scale vortex structure which appears to be in agreement with observed scales of the vortices seen in auroral arcs.;Finally, the study of shear flow and ballooning instabilities was accomplished using a three-dimensional computer model. We discuss the structure of vortices, magnetic field, and field-aligned currents obtained from the three-dimensional computer simulations and conclude that these instabilities may lead to vortices associated with discrete auroral arcs.