International Journal of Mathematics and Mathematical Sciences
Volume 18 (1995), Issue 2, Pages 371-382
Acoustic-gravity waves in a viscous and thermally conducting isothermal atmosphere
Department of Mathematics and Computer Science, Adelphi University, Garden City 11530, NY, USA
Received 14 April 1993; Revised 24 May 1993
Copyright © 1995 H. Y. 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.
In this paper we will investigate the effect of Newtonian cooling on the propagation
of acoustic-gravity waves in a viscous and thermally conducting isothermal atmosphere for large
Prandtl number and for an arbitrary values of Newtonian cooling coefficient. This problem leads
to a singular perturbation problem which is solved by matching inner and outer approximations.
It is shown that the viscosity creates an absorbing and reflecting layer. Below it the oscillatory
process is adiabatic, for small Newtonian cooling coefficient, and above it the solution will decay
to constant before it is influenced by the effect of the thermal conductivity. Newtonian cooling is
a volume effect and influences mainly the lower adiabatic region, in which it causes attenuation in
the amplitude of the wave. Finally it is shown that when Newtonian cooling coefficient goes to
infinity it acts directly to eliminate the temperature perturbation associated with the wave and the
attenuation factor in the amplitude of the wave. Accordingly the wavelength changes to the one
consistent with the Newtonian sound speed. The reflection coefficient and the attenuation factor of
the amplitude of the wave are derived for all values of Newtonian cooling coefficient.