Abstract
The investigation of the convective stability of mechanical equilibrium of two horizontal layers of immiscible fluids has revealed the characteristics of such systems [1–3]. In particular, it has been found that, as distinct from a homogeneous horizontal layer, under certain conditions two-layer systems experience convective instability when uniformly heated from above and, moreover, oscillatory instability when heated from below. In [1–3] the problem was solved for a system with isothermal outer boundaries. In this paper the stability of equilibrium of two-layer systems is investigated for thermally insulated outer boundaries. Special attention is given to the study of the long wave instability mode.
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G. Z. Gershuni and E. M. Zhukhovitskii, “Instability of the equilibrium of a system of horizontal layers of immiscible fluids heated from above,” Izv. Akad. Nauk SSSR, Mekh. Zhidk. Gaza, No. 6, 28 (1980).
G. Z. Gershuni and E. M. Zhukhovitskii, “Monotonic and oscillatory instability of a two-layer system of immiscible fluids heated from below,” Dokl. Akad. Nauk SSSR,265, 302 (1982).
G. Z. Gershuni, E. M. Zhukhovitskii, and E. A. Pershina, “Occurrence of convection in certain two-layer systems,” in: Convective Flows [in Russian], Permsk. Ped. Inst., Perm' (1983), pp. 3–24.
L. G. Poddubnaya, Yu. P. Rudakov, and G. F. Shaidurov, “Thermal instability of a two-layer fluid in a spherical cavity,” Uch. Zap. Permsk. Gos. Univ., No. 184, 23 (1968).
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Translated from Izvestiya Akademii Nauk SSSR, Mekhanika Zhidkosti i Gaza, No. 2, pp. 22–28, March–April, 1986.
The authors wish to thank O. V. Kustova for assisting with the computations.
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Gershuni, G.Z., Zhukhovitskii, E.M. Connective instability of a two-layer system with thermally insulated boundaries. Fluid Dyn 21, 185–190 (1986). https://doi.org/10.1007/BF01050167
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DOI: https://doi.org/10.1007/BF01050167