TY - JOUR

T1 - Spectra of acoustic-gravity waves in the atmosphere with a quasi-isothermal upper layer

AU - Kshevetskii, Sergey P.

AU - Kurdyaeva, Yuliya A.

AU - Gavrilov, Nikolai M.

N1 - Publisher Copyright: © 2021 by the authors. Licensee MDPI, Basel, Switzerland.

PY - 2021/6/25

Y1 - 2021/6/25

N2 - 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 eigenval-ues 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.

AB - 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 eigenval-ues 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.

KW - Acoustic waves

KW - Acoustic-gravity waves

KW - Internal gravity waves

KW - Upper atmosphere

KW - Wave frequency spectrum

KW - acoustic-gravity waves

KW - BREAKING

KW - acoustic waves

KW - wave frequency spectrum

KW - upper atmosphere

KW - JETS

KW - PROPAGATION

KW - internal gravity waves

UR - http://www.scopus.com/inward/record.url?scp=85109165818&partnerID=8YFLogxK

UR - https://www.mendeley.com/catalogue/a3026506-7bd7-3026-bfb8-b605f9480e1b/

U2 - 10.3390/atmos12070818

DO - 10.3390/atmos12070818

M3 - Article

AN - SCOPUS:85109165818

VL - 12

JO - ATMOSPHERE

JF - ATMOSPHERE

SN - 1598-3560

IS - 7

M1 - 818

ER -