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Two-dimensional oscillatory convection in a gravitationally modulated fluid layer. (English) Zbl 0798.76023

This paper studies the problem of thermal convection between two horizontal plates at different temperatures when the gravitational field varies sinusoidally with time. The method employed studies the two space dimensional problem and expands the variable representing the velocity field and the temperature as a Galerkin representation in sines and cosines for the time variable, cosines for the horizontal variable, while the vertical functions are to be determined numerically. The stability of finite amplitude solutions is investigated in much careful detail. Many numerical results are presented for Prandtl numbers varying between 0.71 and 50.

MSC:

76E15 Absolute and convective instability and stability in hydrodynamic stability
76E30 Nonlinear effects in hydrodynamic stability
80A20 Heat and mass transfer, heat flow (MSC2010)
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