CORONAL HEATING BY THE RESONANT ABSORPTION OF ALFVEN WAVES - THE EFFECT OF VISCOUS STRESS TENSOR

The time-dependent linearized MHD equations for a fully compressible, low-beta, viscoresistive plasma are solved numerically using an implic it integration scheme. The full viscosity stress tenser (Braginskii 19 65) is included with the five parameters eta(i), i = 0-4. In agreement with previous studies, the numerical simulations demonstrate that the dissipation on inhomogeneities in the background Alfven speed occurs in a narrow resonant layer. For an active region in the solar corona t he values of eta(i) are eta(0) = 0.65 g cm(-1) s(-1), eta(1) = 3.7 x 1 0(-12) g cm(-1) s(-1), eta(2) = 4 eta(1), eta(3) = 1.4 x 10(-6) g cm(- 1) s(-1), eta(4) = 2 eta(3), with n = 10(10) cm(-3), T = 2 x 10(6) K, and B = 100 G. When the Lundquist number S = 10(4) and R(1) much great er than S(where R(1) is the dimensionless shear viscous number) the wi dth of the resistive dissipation layer d(r) is 0.22a (where a is the d ensity gradient length scale) and d(r) similar to S--1/3. When S much greater than R(1) the shear viscous dissipation layer width d(v) scale s as R(1)(-1/3) The shear viscous and the resistive dissipation occurs in an overlapping narrow region, and the total heating rate is indepe ndent of the value of the dissipation parameters in agreement with pre vious studies. Consequently, the maximum values of the perpendicular v elocity and perpendicular magnetic field scale as R(1)(1/3) It is evid ent from the simulations that for solar parameters the heating due to the compressive viscosity (R(0) = 560) is negligible compared to the r esistive and the shear viscous (R(1)) dissipation and it occurs in a b road layer of order a in width. In the solar corona with S approximate to 10(14) and R(1) x 10(14) (as calculated from the Braginskii expres sions), the shear viscous resonant heating is of comparable magnitude to the resistive resonant heating.