Acoustic-gravity waves in a viscous and thermally conducting isothermal atmosphere (part III: for arbitrary Prandtl number)
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...
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| Main Author: | |
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| Format: | Article |
| Language: | English |
| Published: |
Wiley
1997-01-01
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| Series: | International Journal of Mathematics and Mathematical Sciences |
| Subjects: | |
| Online Access: | http://dx.doi.org/10.1155/S0161171297000471 |
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| Summary: | 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. |
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| ISSN: | 0161-1712 1687-0425 |