Doctor of Philosophy (Ph.D.)
The stability and transition properties of a bounded, current carrying magnetofluid are explored, using the hydrodynamic theory developed for plane shear flows as a guide. A driven magnetohydrodynamic sheet pinch equilibrium is employed. A sixth order, complex eigenvalue equation which governs the normal modes of small oscillations is derived, and solved numerically by the Chebyshev tau method. Eigenfunctions are shown, as well as the curve of neutral stability. The locus of critical Lundquist numbers has the form of a hyperbola. The nonlinear stability of a primary disturbance of the system is considered. For regions in parameter space close to criticality, a nonlinear stability equation of the Landau type is derived. These regions are characterized by low values of the Lundquist numbers, in contrast with the inviscid, highly conducting limit considered by Rutherford (1973). Amplitude phase planes for these disturbances are exhibited. The full set of two dimensional magnetohydrodynamic equations is solved numerically by a semi-implicit, mixed Fourier pseudospectral-finite difference algorithm. Both linear and random perturbations of the system are followed numerically into the nonlinear regime. Current sheets and deflection currents are nonlinear structures found to be significant to the evolution of the system. A secondary instability mechanism, the dynamic rupturing of the current density sheet, is also observed.
© The Author
Dahlburg, Russell B., "Stability and transition of the driven magnetohydrodynamic sheet pinch" (1985). Dissertations, Theses, and Masters Projects. Paper 1539623755.