Abstract
The model system of ordinary differential equations [1, 2] governing the behavior of a non-uniformly heated fluid in a tilted cavity is used for studying the stability of steady regimes of thermal convection at arbitrary (not small) tilting of the rectangular cavity. The bifurcation curve is constructed, which separates the region of parameters (the Rayleigh number — the cavity tilting angle) into two regions — the internal and external ones. In the external region, the system has one stable steady solution, and in the internal region, it has three steady solutions. One of them is always unstable in a monotone way, and two others may be both stable and unstable. The neutral curves are constructed, which determine the boundaries of the incipience of the oscillatory and monotone instabilities.
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A.I. Nikitin and A.N. Sharifulin, Concerning the bifurcations of steady-state thermal convection regimes in a closed cavity due to the Whitney folding-type singularity, Heat Transfer — Sov. Res., 1989, Vol. 21, No. 2, P. 213
A.I. Nikitin and A.N. Sharifulin, On bifurcations of steady regimes of thermal convection in a closed cavity engendered by the Whitney folding-type singularity, in: Processes of Heat and Mass Transfer of Viscous Fluid, the Urals Sci. Center of the USSR Acad. Sci., Sverdlovsk, 1986, P. 32–39.
E. Lorenz, Deterministic nonperiodic flow, J. Atmospheric Sci., 1963, No. 20. P.130–141.
V.I. Tshernatynsky and M.I. Shliomis, Convection near critical Rayleigh numbers at a nearly vertical temperature gradient, Fluid Dyn., 1973, Vol. 8, No. 1, P. 64–70.
J. Mizushima and Y. Hara, Routes to unicellular convection in a tilted rectangular cavity, J. Phys. Soc. Japan, 2000, Vol. 69, No. 8, P. 2371–2374.
G.Z. Gershuni and E.M. Zhukhovitsky, Convective Stability of Incompressible Fluid, Nauka, Moscow, 1972.
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The work was financially supported by the Russian Foundation for Basic Research (Grant No. 07-01-96070).
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Sagitov, R.V., Sharifulin, A.N. Stability of steady thermal convection in a tilted rectangular cavity in low-mode approximation. Thermophys. Aeromech. 15, 233–241 (2008). https://doi.org/10.1134/S0869864308020078
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DOI: https://doi.org/10.1134/S0869864308020078