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Astron. Astrophys. 332, 314-324 (1998)


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Waves in a convective atmosphere: 1D periodical model

Y.D. Zhugzhda 1, 2

1 Kiepenheuer-Institut für Sonnenphysik, Schöneckstr. 6, D-79104 Freiburg, Germany
2 Institute of Terrestrial Magnetism, Ionosphere and Radio Wave Propagation of the Russian Academy of Sciences, Troitsk City, Moscow Region, 142092 Russia

Received 4 April 1997 / Accepted 27 November 1997

Abstract

This paper treats a one-dimensional model of stationary convection. In this model I derive the equation governing acoustic waves in an atmosphere that is structured by hot and cold flows. An exact solution is obtained in terms of an infinite Hill determinant. The physics of acoustic waves in a convective atmosphere and in a crystal lattice are similar, and some of the concepts of solid state physics are generalized to the current problem. It is shown that there are three basic wave modes, namely, acoustic waves, vibrational waves and turbulent sound, which are all different from acoustic waves in a uniform atmosphere. The vibrational waves could appear due to local oscillations of the convective elements. The turbulent sound is driven only by the dynamical pressure. The temperature and velocity fluctuations in a convective atmosphere are responsible for the appearance of Brillouin zones. Waves with frequencies within the band gap of the convective atmosphere undergo reflection at the edge of the Brillouin zones, where they meet a potential barrier. The application of the model to a turbulent atmosphere is discussed. Some effects relevant to helioseismology are outlined.

Key words: convection – hydrodynamics – turbulence – waves – Sun: oscillations – stars: oscillations

© European Southern Observatory (ESO) 1998

Online publication: March 10, 1998
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