Nonlinear Evolution of Coronal Heating by the Resonant Absorption of Alfv\'{e}n Waves
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**Session 59 -- Solar Surface and Corona**
*Oral presentation, Thursday, January 13, 10:15-11:45, Salon VI Room (Crystal Gateway)*

## [59.04] Nonlinear Evolution of Coronal Heating by the Resonant Absorption of Alfv\'{e}n Waves

*L. Ofman$^*$ (NASA/GSFC), J.M. Davila (NASA/GSFC), R.S. Steinolfson (SwRI)*

The nonlinear 3-D MHD equations for a fully compressible, low-beta, visco-resistive plasma are solved numerically using the Lax-Wendroff
integration scheme (the explicit integration scheme was found to converge
considerably faster in terms of physical time per CPU time than the Alternating
Direction Implicit method). The calculations are initiated with the solutions of the linearized version of the MHD equations (Ofman, Davila, and Steinolfson
1994, Ap.J., in press), with inhomogeneous background density, and a constant
magnetic field. The numerical simulations demonstrate that the narrow
dissipation layer is affected by the self-consistent velocity shear: i.e., the
regions of high ohmic heating are carried around by the flow. Consequently, the
topology of the perpendicular magnetic field and the ohmic heating regions
differs significantly from the linear case. Additional harmonics of the
driver frequency appear in the temporal oscillations with the dominant
frequency of double the driver frequency. When the Lundquist number is
$S=10^3$ the average width of the resistive dissipation layer is $0.4a$
(where $a$ is the density gradient length scale) and consistent with the
linear results. When the driver amplitude is small compared to the
average Alfv\'{e}n speed the dissipation layer appears to be stable and the
ohmic heating rate is enhanced by about 15\% over the linear heating rate.
When the driver amplitude is comparable to the average Alfv\'{e}n speed the
nonlinear effects dominate the evolution and the resonant heating layer
may become unstable. A parametric study of the instability is presented. The effect of the self-consistent velocity on the instability is considered by generalizing the linear theory (Davila 1987) to include shear flow and solving the linearized dispersion relation of the resonant absorption with the background shear flow.

$^*$NRC-NAS Resident Research Associate.

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