Archives of Acoustics, 43, 3, pp. 497–503, 2018
10.24425/123921

Decomposition of Acoustic and Entropy Modes in a Non-Isothermal Gas Affected by a Mass Force

Sergey LEBLE
Immanuel Kant Baltic Federal University
Russian Federation

Anna PERELOMOVA
Gdansk University of Technology
Poland

Diagnostics and decomposition of atmospheric disturbances in a planar flow are considered in this work. The study examines a situation in which the stationary equilibrium temperature of a gas may depend on the vertical coordinate due to external forces. The relations connecting perturbations are analytically established. These perturbations specify acoustic and entropy modes in an arbitrary stratified gas affected by a constant mass force. The diagnostic relations link acoustic and entropy modes, and are independent of time. Hence, they provide an ability to decompose the total vector of perturbations into acoustic and non-acoustic (entropy) parts, and to establish the distribution of energy between the sound and entropy modes, uniquely at any instant. The total energy of a flow is hence determined in its parts which are connected with acoustic and entropy modes. The examples presented in this work consider the equilibrium temperature of a gas, which linearly depends on the vertical coordinate. Individual profiles of acoustic and entropy parts for some impulses are illustrated with plots.
Keywords: acoustics of non-uniform media; initialization of hydrodynamic field
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References

Borovikov V.A., Kelbert M.Y. (1985), Adaptation of initial conditions for internal waves in weakly compressible liquid [in Russian], Nauka, Tbilisi.

Brekhovskikh L.M., Godin A.O. (1990), Acoustics of layered media, Springer-Verlag, Berlin.

Brezhnev Y., Kshevetsky S., Leble S. (1994), Linear initialization of hydrodynamical fields, Atmospheric and Oceanic Physics, 30, 10, 84–88.

Gordin A.V. (1987), Mathematical problems of hydrodynamical weather prediction. Analytical aspects [in Russian], Gydrometeoizdat, Leningrad.

Karpov I.V., Kshevetsky S.P., Borchevkina O.P. et al. (2016), Disturbances of the upper atmosphere and ionosphere caused by acoustic-gravity wave sources in the lower atmosphere, Russian Journal of Physical Chemistry B, 10, 1, 127–132.

Leble S.B. (1990), Nonlinear waves in waveguides with stratification, Springer-Verlag, Berlin.

Leble S., Perelomova A. (2013), Problem of proper decomposition and initialization of acoustic and entropy modes in a gas affected by the mass force, Applied Mathematical Modelling, 37, 629–635.

Leble S., Vereschagina I. (2016), Problem of disturbance identification by measurement in the vicinity of a point, Task Quarterly, 20, 2, 131–141.

Pedloski J. (1987), Geophysical fluid dynamics, Springer-Verlag, New York.

Perelomova A.A. (1998), Nonlinear dynamics of vertically propagating acoustic waves in a stratified atmosphere, Acta Acustica, 84, 1002–1006.

Perelomova A.A. (2000), Nonlinear dynamics of directed acoustic waves in stratified and homogeneous liquids and gases with arbitrary equation of state, Archives of Acoustics, 25, 4, 451–463.

Perelomova A. (2009), Weakly nonlinear dynamics of short acoustic waves in exponentially stratified gas, Archives of Acoustics, 34, 2, 127–143.

Sun L., Robinson W.A., Chen G. (2012), The predictability of stratospheric warming events: more from the troposphere or the stratosphere?, Journal of the Atmospheric Sciences, 69, 2, 768–783.

U.S. Standard Atmosphere, U.S. Government Printing Office, Washington, D.C., 1976.




DOI: 10.24425/123921

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