Magnetohydrodynamic studies of ideal and resistive tearing modes with equilibrium shear flow
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 Kelvin-Helmholz instabilities. For the resistive tearing instability, the effect of equilibrium shear flow is systematically studied, using the boundary layer approach. Both the constant-psi tearing mode and the nonconstant-psi 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 was 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 sub 0'(O)B sub 0'(O), where V sub 0'(O) and B sub 0'(O) 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.
- Research Organization:
- Texas Univ., Austin, TX (United States)
- OSTI ID:
- 5394146
- Resource Relation:
- Other Information: Thesis (Ph.D.)
- Country of Publication:
- United States
- Language:
- English
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Related Subjects
SUPERCONDUCTIVITY AND SUPERFLUIDITY
MAGNETOHYDRODYNAMICS
INSTABILITY
HELMHOLTZ INSTABILITY
MAGNETIC FIELDS
MHD EQUILIBRIUM
SHEAR
SYMMETRY
TEARING INSTABILITY
VISCOSITY
EQUILIBRIUM
FLUID MECHANICS
HYDRODYNAMICS
MECHANICS
PLASMA INSTABILITY
PLASMA MACROINSTABILITIES
665510* - Magnetohydrodynamics- (1992-)