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Rayleigh-B\'enard convection is studied under the influence of an external driving force due to a time-dependent Rayleigh number and sidewall heating. Using the Melnikov method we show that if the ratio of dissipation to forcing is sufficiently small, chaotic behavior occurs. The chaotic threshold is studied as a function of the frequency of the driving terms. It is shown that the limits, 0 reduce the size of the chaotic region in parameter space. ₌₀ₗ, the most chaotic frequency, is computed and discussed.
Paul K. Newton (Mon,) studied this question.