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A possible explanation for the apparent phase stability of the 11.07-year Schwabe cycle of the solar dynamo was the subject of a series of recent papers [1-3]. The synchronization of the helicity of an instability with the azimuthal wavenumber m = 1 by a tidal m = 2 perturbation played a key role here. To analyze this type of interaction in a paradigmatic setup, we study a thermally driven Rayleigh-Bénard convection of a liquid metal under the influence of a tide-like electromagnetic forcing. As shown previously, the time-modulation of this forcing emerges as a peak frequency in the m = 2 mode of the radial flow velocity component. In this paper, we present new numerical results on the interplay between the large-scale circulation of a Rayleigh-Bénard convection flow and the time modulated electromagnetic forcing. [ABSTRACT FROM AUTHOR]