Magnetohydrodynamic Studies of Ideal and Resistive Tearing Modes with Equilibrium Shear Flow
Abstract
In this dissertation, two magnetohydrodynamic (MHD) instabilities are studied. A simple sufficient condition is given for the linear ideal instability of plane parallel equilibria with antisymmetric shear flow and symmetric or antisymmetric magnetic field. Application of this condition demonstrates the destabilizing effect of the magnetic field on shear flow driven KelvinHelmholz instabilities. For the resistive tearing instability the effect of equilibrium shear flow is systematically studied, using the boundary layer approach. Both the constantpsi tearing mode and the nonconstantpsi tearing mode are analyzed in the presence of flow. It is found that the shear flow has a significant influence on both the external ideal region and the internal resistive region. In the external ideal region, the shear flow can dramatically change the value of the matching quantity Delta^'. In the internal resistive region, the tearing mode scalings are sensitive to the flow shear at the magnetic null plane. When the flow shear is larger than the magnetic field shear at the magnetic null plane, both tearing modes are stabilized. Also, the transition to ideal instability has been traced. Furthermore, the influence of small viscosity on the constant psi tearing mode in the presence of shear flow is considered. It is found that the influence of viscosity depends upon the parameter{V _sp{0}{'}(0)over B_sp{0}{'}(0)}, where V_sp{0}{ '}(0) and B_sp{0 }{'}(0) denote the flow shear and magnetic field shear at the magnetic null plane, respectively. Viscosity basically tends to suppress the tearing mode. Finally, the nonlinear interaction of two near marginal tearing modes in the presence of shear flow is studied. To find the time asymptotic states, the resistive MHD equations are reduced to four amplitude equations, using center manifold reduction. These amplitude equations are subject to the constraint of translational symmetry of the physical problem. Bifurcation analysis is employed to find various possible time asymptotic states.
 Publication:

Ph.D. Thesis
 Pub Date:
 1991
 Bibcode:
 1991PhDT........24C
 Keywords:

 RESISTIVE TEARING;
 Physics: Fluid and Plasma;
 KelvinHelmholtz Instability;
 Magnetic Fields;
 Magnetohydrodynamic Flow;
 Magnetohydrodynamic Stability;
 Plasma Equilibrium;
 Shear Flow;
 Tearing Modes (Plasmas);
 Antisymmetry;
 Manifolds (Mathematics);
 Trees (Mathematics);
 Viscosity;
 Plasma Physics