Time-modulated convection with zero mean temperature gradient

We study numerically the onset of temporally modulated Rayleigh-B\'enard convection with zero mean gradient for cases of antisymmetric and asymmetric boundary temperatures over a continuous range of nondimensional frequencies {ω}, from ω~O(10^-1) to ω~O(10³). For {ω} below 1, the neutral curves for Pr=7 in both cases alternate between synchronous and subharmonic responses, with increasingly shorter intervals as {ω} becomes small. At large {ω}, the critical wave number kc asymptotes to ω1/2 and the critical Rayleigh number Rc asymptotes to ω3/2, via a subharmonic response in both cases. A comparison with the experimental results of Niemela and Donnelly [Phys. Rev. Lett. 57, 583 (1986)] shows fairly reasonable agreement.