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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. 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-$" growth rate scales as S -i'2 and the "nonconstant+" growth rate scales as S -"3, where S is the magnetic Reynolds number. The Furth-KilleenRosenbluth (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 -"3(S,/S) IF6 where S is the ratio of the viscous time to the Alfvitn time. When the shear flow is large, the grow& rate behaves in a more complex way, and KelvinHelmholtz instability effects are present.

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The first nonlinear study of the instability of the resonant absorption is presented in this paper. The nonlinear evolution of the resonant absorption of Alfvén waves in an inhomogeneous plasma is studied via solution of the time‐dependent 3‐D, low‐β, resistive MHD equations. Highly sheared velocities that are subject to the Kelvin‐Helmholtz like instability are found at the narrow dissipation layers. Three dimensional Kelvin‐Helmholtz like vortices appear at and near the dissipation layers and propagate along the slab of plasma. The narrow resonant heating layers are deformed by the self‐consistent shear flow. In the solar active regions where the resonant absorption of Alfvén waves is believed to occur the instability may lead to turbulent enhancement of the dissipation parameters and account for the observed turbulent velocities inferred from the non‐thermal broadening of x‐ray and EUV emission lines.