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 29, 2563 (1986); Phys. Fluids B 1, 2224 (1989); ibid. 2, 495 (1990); ibid. 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‐ψ’’ growth rate scales as S−1/2 and the ‘‘nonconstant‐ψ’’ growth rate scales as S−1/3, where S is the magnetic Reynolds number. The Furth–Killeen–Rosenbluth (FKR) scaling of S−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 S−2/3(Sv/S)1/6 where Sv is the ratio of the viscous time to the Alfvén time. When the shear flow is large, the growth rate behaves in a more complex way, and Kelvin–Helmholtz instability effects are present.
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June 1991
Research Article|
June 01 1991
Resistive tearing mode instability with shear flow and viscosity
L. Ofman;
L. Ofman
Department of Physics and Institute for Fusion Studies, The University of Texas at Austin, Austin, Texas 78712
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X. L. Chen;
X. L. Chen
Department of Physics and Institute for Fusion Studies, The University of Texas at Austin, Austin, Texas 78712
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P. J. Morrison;
P. J. Morrison
Department of Physics and Institute for Fusion Studies, The University of Texas at Austin, Austin, Texas 78712
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R. S. Steinolfson
R. S. Steinolfson
Department of Space Sciences, Southwest Research Institute, San Antonio, Texas 78228
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Phys. Fluids B 3, 1364–1373 (1991)
Article history
Received:
August 27 1990
Accepted:
February 18 1991
Citation
L. Ofman, X. L. Chen, P. J. Morrison, R. S. Steinolfson; Resistive tearing mode instability with shear flow and viscosity. Phys. Fluids B 1 June 1991; 3 (6): 1364–1373. https://doi.org/10.1063/1.859701
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