International Journal of Mathematics and Mathematical Sciences
Volume 22 (1999), Issue 1, Pages 161-169

Reflection and dissipation of oblique Alfvén waves in an isothermal atmosphere

Hadi Yahya Alkahby1 and M. A. Mahrous2

1Department of Mathematics and Computer Science, Dillard University, New Orleans 70122, LA, USA
2Department of Mathematics, University of New Orleans, New Orleans 70148, LA, USA

Received 25 April 1996

Copyright © 1999 Hadi Yahya Alkahby and M. A. Mahrous. This is an open access article distributed under the Creative Commons Attribution License, which permits unrestricted use, distribution, and reproduction in any medium, provided the original work is properly cited.


In this article, we investigate the combined effects of viscosity and Ohmic electrical conductivity on upward and downward propagation oblique Alfvén waves in an isothermal atmosphere. It is shown that the presence and direction of the magnetic field play an important role in the structure and the heating mechanism of solar atmosphere. In addition, the atmosphere can be divided into two distinct regions connected by a transition region. In the lower region, the solution can be written as a linear combination of an upward and a downward propagation wave with unequal wavelengths. In the upper region, the solution decays exponentially with the altitude. Moreover, the magnetic field creates a reflecting and a non-absorbing transition region. On the contrary, the viscosity and Ohmic electrical conductivity produce a reflecting and an absorbing transition region. The nature of the transition region depends on the relative strength of the viscous diffusivity with respect to the resistive diffusivity and on the direction of the magnetic field. A unique solution is determined. The reflection coefficient and damping factors are derived and the conclusions are discussed in connection with the nature of the heating mechanism of the solar atmosphere.