Time-modulated convection with zero mean temperature gradient

We study numerically the onset of temporally modulated Rayleigh-Bénard convection with zero mean gradient for cases of antisymmetric and asymmetric boundary temperatures over a continuous range of nondimensional frequencies omega, from omega approximately O(10(-1)) to omega approximately O(10(3)). For omega below 1, the neutral curves for Pr=7 in both cases alternate between synchronous and subharmonic responses, with increasingly shorter intervals as omega becomes small. At large omega, the critical wave number k(c) asymptotes to omega(1/2) and the critical Rayleigh number R(c) asymptotes to omega(3/2), 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.