Date of Award

Spring 1992

Project Type


Program or Major


Degree Name

Doctor of Philosophy

First Advisor

Joseph V Hollweg


This thesis studies the physics of resonance absorption of MHD surface waves and examines the effects of velocity shear on the rate of resonance absorption. Theoretical analyses and numerical calculations demonstrate that resonance absorption of MHD surface waves is a viable mechanism for heating of the solar corona.

It is shown that resonance absorption has a very simple physical interpretation in terms of driven harmonic oscillators. This insight greatly simplifies the mathematics and allows a thorough discussion of the solar coronal heating. It is found that resonance absorption of MHD surface waves can occur rapidly enough to heat the solar coronal active region loops, which have the largest heating requirements, consistent with the observation that the surface brightness of the loops is roughly independent of loop size. It is suggested that the large velocity shears near the resonant field line could drive a Kelvin-Helmholz instability which would in turn lead to an effective eddy viscosity and ultimately to dissipation into heat. The effects of three different forms of viscosity on the Alfven resonance are considered. Only classical shear viscosity is able to absorb the energy which is pumped into the thin resonant layer. In the steady state, the net heating rate is independent of the viscosity coefficient, if the heating occurs in a thin layer.

The effects of velocity shear on the rate of resonance absorption are investigated for both incompressible and compressible MHD surface waves. Velocity shear can either increase or decrease the rate of resonance absorption. It is very interesting to discover that resonance can lead to an instability at values of velocity shear below the threshold for the Kelvin-Helmholz instability. The numerical results reveal these effects are not dramatic for very sub-Alfvenic field-aligned flow in the solar corona, but may play an important role in the super-Alfvenic solar wind streams.