Spectra of Acoustic-Gravity Waves in the Atmosphere with a Quasi-Isothermal Upper Layer

In this paper, we study, in theoretical terms, the structure of the spectrum of acoustic-gravity waves (AGWs) in the nonisothermal atmosphere having asymptotically constant temperature at high altitudes. A mathematical problem of wave propagation from arbitrary initial perturbations in the half-infi...

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Vydáno v:Atmosphere Ročník 12; číslo 7; s. 818
Hlavní autoři: Kshevetskii, Sergey P., Kurdyaeva, Yuliya A., Gavrilov, Nikolai M.
Médium: Journal Article
Jazyk:angličtina
Vydáno: Basel MDPI AG 01.07.2021
Témata:
Acoustic gravity waves
Acoustic properties
Acoustic waves
Acoustics
Altitude
Atmosphere
Atmospheric temperature
Boundary conditions
Brunt-Vaisala frequency
Eigenfunctions
Eigenvalues
Eigenvectors
Energy
Energy conservation
Evolution
Gravity waves
Heat conductivity
High altitude
Hydrodynamic equations
Hydrodynamics
Internal gravity waves
Internal waves
Ionosphere
Mathematical models
Modes
Numerical models
Operators (mathematics)
Perturbation
Propagation
Properties
Sound waves
Spectra
Stratification
Temperature
upper atmosphere
Wave energy
wave frequency spectrum
Wave power
Wave propagation
ISSN:2073-4433, 2073-4433
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Popis
Shrnutí:In this paper, we study, in theoretical terms, the structure of the spectrum of acoustic-gravity waves (AGWs) in the nonisothermal atmosphere having asymptotically constant temperature at high altitudes. A mathematical problem of wave propagation from arbitrary initial perturbations in the half-infinite nonisothermal atmosphere is formulated and analyzed for a system of linearized hydrodynamic equations for small-amplitude waves. Besides initial and lower boundary conditions at the ground, wave energy conservation requirements are applied. In this paper, we show that this mathematical problem belongs to the class of wave problems having self-adjoint evolution operators, which ensures the correctness and existence of solutions for a wide range of atmospheric temperature stratifications. A general solution of the problem can be built in the form of basic eigenfunction expansions of the evolution operator. The paper shows that wave frequencies considered as eigenvalues of the self-adjoint evolution operator are real and form two global branches corresponding to high- and low-frequency AGW modes. These two branches are separated since the Brunt–Vaisala frequency is smaller than the acoustic cutoff frequency at the upper boundary of the model. Wave modes belonging to the low-frequency global spectral branch have properties of internal gravity waves (IGWs) at all altitudes. Wave modes of the high-frequency spectral branch at different altitudes may have properties of IGWs or acoustic waves depending on local stratification. The results of simulations using a high-resolution nonlinear numerical model confirm possible changes of AGW properties at different altitudes in the nonisothermal atmosphere.
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ISSN:2073-4433
2073-4433
DOI:10.3390/atmos12070818