On the Frequency of Internal Gravity Waves in the Atmosphere: Comparing Theory with Observations
This paper is devoted to the dynamics of the propagation of non-planetary scale internal gravity waves (IGWs) in the stratified atmosphere. We consider the system of equations describing internal gravity waves in three approximations: (1) the incompressible fluid approximation, (2) the anelastic gas...
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2025-01-01
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| author | Robert G. Zakinyan Alaa H. Kamil Vladislav A. Svetlichny Arthur R. Zakinyan |
| author_facet | Robert G. Zakinyan Alaa H. Kamil Vladislav A. Svetlichny Arthur R. Zakinyan |
| author_sort | Robert G. Zakinyan |
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| description | This paper is devoted to the dynamics of the propagation of non-planetary scale internal gravity waves (IGWs) in the stratified atmosphere. We consider the system of equations describing internal gravity waves in three approximations: (1) the incompressible fluid approximation, (2) the anelastic gas (compressible fluid) approximation, and (3) a new approximation called the non-Boussinesq gas approximation. For each approximation, a different dispersion relation is given, from which it follows that the oscillation frequency of internal gravity waves depends on the direction of propagation, the horizontal and vertical components of the wave vector, the vertical gradient of the background temperature, and the background wind shear. In each of the three cases, the maximum frequency of internal gravity waves is different. Moreover, in the anelastic gas approximation, the maximum frequency is equal to the Brunt–Väisälä buoyancy frequency, and in the incompressible fluid approximation, it is larger than the Brunt–Väisälä frequency by a factor of <inline-formula><math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><semantics><mrow><msqrt><mn>7</mn></msqrt><mo>≅</mo><mn>2.6</mn></mrow></semantics></math></inline-formula>. In the model proposed in this paper, the value of the maximum frequency of internal gravity waves occupies an intermediate position between the above limits. The question arises: which of the above fluid representations adequately describe the dynamics of internal gravity waves? This paper compares the above theories with observational data and experiments. |
| format | Article |
| id | doaj-art-4b46066d623b4cdfa168a0a2cd2b56a1 |
| institution | Kabale University |
| issn | 2073-4433 |
| language | English |
| publishDate | 2025-01-01 |
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| series | Atmosphere |
| spelling | doaj-art-4b46066d623b4cdfa168a0a2cd2b56a12025-01-24T13:21:55ZengMDPI AGAtmosphere2073-44332025-01-011617310.3390/atmos16010073On the Frequency of Internal Gravity Waves in the Atmosphere: Comparing Theory with ObservationsRobert G. Zakinyan0Alaa H. Kamil1Vladislav A. Svetlichny2Arthur R. Zakinyan3Department of Theoretical and Mathematical Physics, North-Caucasus Federal University, 355017 Stavropol, RussiaDepartment of Physics, University of Misan, Amarah 62001, IraqDepartment of Theoretical and Mathematical Physics, North-Caucasus Federal University, 355017 Stavropol, RussiaDepartment of Theoretical and Mathematical Physics, North-Caucasus Federal University, 355017 Stavropol, RussiaThis paper is devoted to the dynamics of the propagation of non-planetary scale internal gravity waves (IGWs) in the stratified atmosphere. We consider the system of equations describing internal gravity waves in three approximations: (1) the incompressible fluid approximation, (2) the anelastic gas (compressible fluid) approximation, and (3) a new approximation called the non-Boussinesq gas approximation. For each approximation, a different dispersion relation is given, from which it follows that the oscillation frequency of internal gravity waves depends on the direction of propagation, the horizontal and vertical components of the wave vector, the vertical gradient of the background temperature, and the background wind shear. In each of the three cases, the maximum frequency of internal gravity waves is different. Moreover, in the anelastic gas approximation, the maximum frequency is equal to the Brunt–Väisälä buoyancy frequency, and in the incompressible fluid approximation, it is larger than the Brunt–Väisälä frequency by a factor of <inline-formula><math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><semantics><mrow><msqrt><mn>7</mn></msqrt><mo>≅</mo><mn>2.6</mn></mrow></semantics></math></inline-formula>. In the model proposed in this paper, the value of the maximum frequency of internal gravity waves occupies an intermediate position between the above limits. The question arises: which of the above fluid representations adequately describe the dynamics of internal gravity waves? This paper compares the above theories with observational data and experiments.https://www.mdpi.com/2073-4433/16/1/73internal gravity wavesdispersion relationBrunt–Väisälä frequencyTaylor–Goldstein equationphase velocitygravity wave breaking |
| spellingShingle | Robert G. Zakinyan Alaa H. Kamil Vladislav A. Svetlichny Arthur R. Zakinyan On the Frequency of Internal Gravity Waves in the Atmosphere: Comparing Theory with Observations Atmosphere internal gravity waves dispersion relation Brunt–Väisälä frequency Taylor–Goldstein equation phase velocity gravity wave breaking |
| title | On the Frequency of Internal Gravity Waves in the Atmosphere: Comparing Theory with Observations |
| title_full | On the Frequency of Internal Gravity Waves in the Atmosphere: Comparing Theory with Observations |
| title_fullStr | On the Frequency of Internal Gravity Waves in the Atmosphere: Comparing Theory with Observations |
| title_full_unstemmed | On the Frequency of Internal Gravity Waves in the Atmosphere: Comparing Theory with Observations |
| title_short | On the Frequency of Internal Gravity Waves in the Atmosphere: Comparing Theory with Observations |
| title_sort | on the frequency of internal gravity waves in the atmosphere comparing theory with observations |
| topic | internal gravity waves dispersion relation Brunt–Väisälä frequency Taylor–Goldstein equation phase velocity gravity wave breaking |
| url | https://www.mdpi.com/2073-4433/16/1/73 |
| work_keys_str_mv | AT robertgzakinyan onthefrequencyofinternalgravitywavesintheatmospherecomparingtheorywithobservations AT alaahkamil onthefrequencyofinternalgravitywavesintheatmospherecomparingtheorywithobservations AT vladislavasvetlichny onthefrequencyofinternalgravitywavesintheatmospherecomparingtheorywithobservations AT arthurrzakinyan onthefrequencyofinternalgravitywavesintheatmospherecomparingtheorywithobservations |