Optimizing thermal convection by phase-locking circulation to wall oscillations

Abstract

This study numerically investigates two-dimensional Rayleigh-Benard convection subjected to horizontal oscillation of the bottom plate, with Prandtl number Pr=4.3, Rayleigh numbers Ra ranging from 5e6 to 1e8, and oscillation frequencies f between 0.0001 and 0.5. The imposed oscillation breaks the up-down symmetry of the classical system, inducing a strong frequency-dependent response in global heat transport, with the maximum Nusselt number enhancement exceeding 60% compared to the uncontrolled case. Central to this control efficiency is a phase-locking mechanism: at the optimal frequency, the intrinsic response time of the large-scale circulation (LSC), quantified by the sign-recovery of volume-averaged angular momentum, locks precisely to the wall oscillation period, enabling perfectly synchronized LSC reversals. Deviations from this optimal condition lead to a marked mismatch; the LSC response time becomes substantially longer when frequency exceeds the optimum and significantly shorter when frequency falls below it. In contrast, boundary layer velocities simply follow the wall oscillations and fail to distinguish control efficiency. Fourier mode analysis reveals that at the optimal frequency, a single-roll mode remains dominant throughout the cycle, facilitating efficient plume transport, whereas higher frequencies yield incomplete reversals and lower frequencies produce a double-roll structure that diminishes heat-transfer efficiency. This frequency-locking mechanism is shown to persist for optimal controls across the entire investigated Rayleigh number range, thus offering robust insight for active control strategies in thermally driven turbulent flows.