Dynamics of the large-scale circulation in turbulent Rayleigh-B\'enard convection with modulated rotation*

We present measurements of the azimuthal rotation velocity $\dot{\theta}$ and thermal amplitude $\delta$ of the large-scale circulation (LSC) in turbulent Rayleigh-B\'enard convection with modulated rotation. Both $\dot{\theta}$ and $\delta$ exhibit clear oscillations at the modulation frequency $\omega$. Fluid acceleration driven by oscillating Coriolis force plays a role in determining the LSC rotations and causes an increasing phase lag in $\dot{\theta}$ when $\omega$ increases. The applied modulation also produces oscillatory boundary layers and the resulting time-varying viscous drag modifies $\delta$ periodically. Oscillation of $\dot{\theta}$ with the maximum amplitude occurs at an intermediate ${\omega}^{\star}$. Such a resonance-like phenomena is interpreted as a result of the optimal coupling of $\delta$ to the sample rotation velocity. We show that an extended LSC model with a relaxation time for $\delta$ to response to modulated rotations provides predictions in close agreement with the experimental results.