Resistive tearing mode instability with shear flow and viscosity

Journal Article · Sat Jun 01 04:00:00 EDT 1991 · Physics of Fluids B; (USA)

DOI:https://doi.org/10.1063/1.859701· OSTI ID:5460153

Ofman, L; Chen, X L; Morrison, P J ^[1]; Steinolfson, R S ^[2]

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1. Department of Physics and Institute for Fusion Studies, The University of Texas at Austin, Austin, Texas 78712 (USA)
2. Department of Space Sciences, Southwest Research Institute, San Antonio, Texas 78228 (USA)

The linear theory of the resistive tearing mode instability in slab geometry, has been recently extended by introducing the effect of equilibrium shear flow and viscosity (Phys. Fluids {bold 29}, 2563 (1986); Phys. Fluids B {bold 1}, 2224 (1989); {ital ibid}. {bold 2}, 495 (1990); {ital ibid}. {bold 2}, 2575 (1990)). In the present analysis, numerical solutions of the time-dependent resistive equations are generalized to this problem and growth rate scaling is obtained. The results of the computations are compared to previous work, and the computed growth rate scalings agree with analytical predictions. Namely, the constant-{psi}'' growth rate scales as {ital S}{sup {minus}1/2} and the nonconstant-{psi}'' growth rate scales as {ital S}{sup {minus}1/3}, where {ital S} is the magnetic Reynolds number. The Furth--Killeen--Rosenbluth (FKR) scaling of {ital S}{sup {minus}3/5} is reproduced for small values of shear flow. The presence of flow introduces a new peak in the eigenfunction, which is outside of the peak that occurs in the case without flow. The introduction of viscosity and small shear alters the growth rate scaling to {ital S}{sup {minus}2/3}({ital S}{sub {ital v}}/{ital S}){sup 1/6} where {ital S}{sub {ital v}} is the ratio of the viscous time to the Alfven time. When the shear flow is large, the growth rate behaves in a more complex way, and Kelvin--Helmholtz instability effects are present.

• DOE Contract Number: FG05-80ET53088
• OSTI ID: 5460153
• Journal Information: Physics of Fluids B; (USA), Journal Name: Physics of Fluids B; (USA) Vol. 3:6; ISSN PFBPE; ISSN 0899-8221
• Country of Publication: United States
• Language: English

Related Subjects

70 PLASMA PHYSICS AND FUSION TECHNOLOGY
700107* -- Fusion Energy-- Plasma Research-- Instabilities
BOUNDARY LAYERS
DOCUMENT TYPES
EIGENFUNCTIONS
EQUILIBRIUM
FINITE DIFFERENCE METHOD
FUNCTIONS
HELMHOLTZ INSTABILITY
INSTABILITY
INSTABILITY GROWTH RATES
ITERATIVE METHODS
LAYERS
MAGNETIC RECONNECTION
MAGNETIC REYNOLDS NUMBER
NUMERICAL SOLUTION
PLASMA
PLASMA DRIFT
PLASMA INSTABILITY
PLASMA MACROINSTABILITIES
REVIEWS
REYNOLDS NUMBER
SCALING LAWS
SHEAR
SLABS
TEARING INSTABILITY
TIME DEPENDENCE
VISCOSITY