期刊名称：International Journal of Mathematics and Mathematical Sciences
印刷版ISSN：0161-1712
电子版ISSN：1687-0425
出版年度：1997
卷号：20
DOI：10.1155/S0161171297000471
出版社：Hindawi Publishing Corporation
摘要：In this paper we will investigate the combined effect of Newtonian cooling, viscosity and
thermal condition on upward propagating acoustic waves in an isothermal atmosphere. In part one of this
series we considered the case of large Prandtl number, while in part two we investigated the case of small
Prandtl number. In those parts we examined only the limiting cases, i.e. the cases of small and large
Prandtl number, and it is more interesting to consider the case of arbitrary Prandtl number, which is the
subject of this paper, because it is a better representative model. It is shown that if the Newtonian
cooling coefficient is small compared to the frequency of the wave, the effect of the thermal conduction is
dominated by that of the viscosity. Moreover, the solution can be written as a linear combination of an
upward and a downward propagating wave with equal wavelengths and equal damping factors. On the
other hand if Newtonian cooling is large compared to the frequency of the wave the effect of thermal
conduction will be eliminated completely and the atmosphere will be transformed from the adiabatic form
to an isothermal. In addition, all the linear relations among the perturbations quantities will be modified.
It follows from the above conclusions and those of the first two parts, that when the effect of Newtonian
cooling is negligible thermal conduction influences the propagation of the wave only in the case of small
Prandtl number.
