Memory-Induced Low Frequency Oscillations in Closed Convection Boxes

The origin of the low frequency oscillation of the large-scale, recirculating flow specific to the high Rayleigh number regime in closed convection cells is investigated. It is shown how the oscillations result from the delayed coupling of the boundary layer instabilities by the slow convective motion of the recirculation. The model developed explains (i) the form of the dependence of the oscillation frequency with the Rayleigh number $f\sim {\mathrm{Ra}}^{\gamma }$, including the prefactor, the "anomalous" value of the exponent $\gamma \approx 0.49$, and (ii) the opposition of phase of the oscillations between the top and bottom boundary layers.