International Journal of Mathematics and Mathematical Sciences
Volume 20 (1997), Issue 3, Pages 605-610
doi:10.1155/S0161171297000823

On viscous and resistive dissipation of Alfvén waves in an isothermal atmosphere

Hadi Yahya Alkahby

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

Received 30 June 1995; Revised 10 November 1995

Copyright © 1997 Hadi Yahya Alkahby. 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.

Abstract

In this article we will investigate reflection and dissipation of Alfvén waves, resulting from a uniform vertical magnetic field, in a viscous, resistive and isothermal atmosphere. It is shown that the atmosphere may be divided into two distinct regions connected by an absorbing and reflecting transition layer. In the transition layer the reflection, dissipation and absorption of the magnetic energy of the waves take place and in it the kinematic viscosity changes from small to large values. In the lower region the effect of the resistive diffusivity and kinematic viscosity changes from small to large values. In the lower region the effect of the resistive diffusivity and kinematic viscosity is negligible and in it the solution can be represented as a linear combination of two, incident and reflected, propagating waves with different wavelengths and different dissipative factors. In the upper region the effect of the resistive diffusivity and kinematic viscosity is large and the solution, which satisfies the prescribed boundary conditions, will behave as a constant. The reflection coefficient, the dissipative factors are determined and the conclusions are discussed in connection with solar heating.