Abstract
The instability of a fluid layer induced by modulated irradiation is studied numerically. Based on the Eddington approximation for the equation of transfer, the time-periodic temperature profile of the basic state is solved analytically. A system of linear equations with periodic coefficients describing the behavior of disturbances is obtained by linear stability theory. Using Floquet's theory, the disturbances are expanded by a double series of mixed Fourier and Chebyshev form. An algorithm combining Galerkin and collocation methods is developed and successfully traces the stability boundary between stable and transiently stable states. For the case of a fluid layer heated from below by a modulated temperature, the results show that modulation has a destabilizing effect at low frequencies and a stabilizing effect at high frequencies, which is in agreement with the available theoretical analyses and experimental data. The effects of Biot number and radiative parameters, such as Planck number and optical thickness, on the critical Rayleigh number are analyzed and compared with the unmodulated cases.
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