Acoustic-gravity waves in a viscous and thermally conducting isothermal atmosphere
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 perturbat...
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| Format: | Article |
| Language: | English |
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Wiley
1995-01-01
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| Series: | International Journal of Mathematics and Mathematical Sciences |
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| Online Access: | http://dx.doi.org/10.1155/S0161171295000469 |
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| author | H. Y. Alkahby |
| author_facet | H. Y. Alkahby |
| author_sort | H. Y. Alkahby |
| collection | DOAJ |
| description | 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. |
| format | Article |
| id | doaj-art-daaa17f0f6ed4131a1cf8f03de07bd56 |
| institution | Kabale University |
| issn | 0161-1712 1687-0425 |
| language | English |
| publishDate | 1995-01-01 |
| publisher | Wiley |
| record_format | Article |
| series | International Journal of Mathematics and Mathematical Sciences |
| spelling | doaj-art-daaa17f0f6ed4131a1cf8f03de07bd562025-02-03T06:08:27ZengWileyInternational Journal of Mathematics and Mathematical Sciences0161-17121687-04251995-01-0118237138210.1155/S0161171295000469Acoustic-gravity waves in a viscous and thermally conducting isothermal atmosphereH. Y. Alkahby0Department of Mathematics and Computer Science, Adelphi University, Garden City 11530, NY, USAIn 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.http://dx.doi.org/10.1155/S0161171295000469acoustic-gravity wavesatmospheric waveswave propagation. |
| spellingShingle | H. Y. Alkahby Acoustic-gravity waves in a viscous and thermally conducting isothermal atmosphere International Journal of Mathematics and Mathematical Sciences acoustic-gravity waves atmospheric waves wave propagation. |
| title | Acoustic-gravity waves in a viscous and thermally conducting isothermal atmosphere |
| title_full | Acoustic-gravity waves in a viscous and thermally conducting isothermal atmosphere |
| title_fullStr | Acoustic-gravity waves in a viscous and thermally conducting isothermal atmosphere |
| title_full_unstemmed | Acoustic-gravity waves in a viscous and thermally conducting isothermal atmosphere |
| title_short | Acoustic-gravity waves in a viscous and thermally conducting isothermal atmosphere |
| title_sort | acoustic gravity waves in a viscous and thermally conducting isothermal atmosphere |
| topic | acoustic-gravity waves atmospheric waves wave propagation. |
| url | http://dx.doi.org/10.1155/S0161171295000469 |
| work_keys_str_mv | AT hyalkahby acousticgravitywavesinaviscousandthermallyconductingisothermalatmosphere |