The effect of newtonian cooling on the reflection and dissipation of hydromagnetic waves in a viscous and thermally conducting isothermal atmosphere

摘要

In this paper, we investigate the problem of the effect of Newtonian cooling on vertically propagating magneto-acoustic waves resulting from a uniform horizontal magnetic field in a viscous and thermally conducting isothermal atmosphere. We consider the case in which the combined effect of the viscosity and the magnetic field is large compared to that of the thermal conduction. It will be shown that the atmosphere may be divided into two distinct regions connected by a transition layer in which the reflection and the modification of the waves take place. In the lower region the effect of the thermal diffusivity, kinematic viscosity and Alfv#xE9;n speed is negligible, whereas in the upper region the effect of these quantities is more pronounced. Moreover, if the Newtonian cooling coefficient is large compared to the adiabatic cut off frequency, it will act directly to eliminate the temperature perturbation associated with the wave in a short time compared to the period of oscillation. This eliminates the attenuation in the amplitude of the wave since the isothermal regime is dissipationless. Also, the magnitude of the reflection coefficient depends on the relative strength of the viscosity with respect to the magnetic field. The reflection coefficient and the attenuation factor are derived for arbitrary values of the Newtonian cooling coefficient. This problem leads to a singular perturbation problem which may be solved by matching inner and outer approximations in an overlapping domain.