Thermal reversing and non-reversing flows in zero-mean time-modulated Rayleigh–Bénard convection

Abstract Inspired by the occurrence of reversing and non-reversing flows in time-modulated Taylor–Couette flow, the presence of these flows in time-modulated Rayleigh–Bénard (RB) convection systems remains intriguing, especially in light of similarities between these flow configurations considered at steady boundary conditions as hydrodynamical twins by several authors in the literature. In this paper and using Floquet analysis, we report the existence of reversals of convective rolls in three-dimensional RB systems with infinite horizontal extent subjected to zero-mean time-periodic temperatures. It is revealed that the convective cells reverse their direction of rotation during an oscillation period T in the cases of single-plate and out-of-phase sinusoidal forcing. These flow reversals set in particularly at the system transition from the cooling to the heating phases via either subharmonic or harmonic instability modes. Reversing flows attributed to quasi-periodic instability modes are also observed in the in-phase modulation case despite the absence of a well-defined alternation between heating and cooling phases. These reversing flows occur when the forcing frequency exceeds a high critical frequency, below which only non-reversing flows are detected. In addition, it turns out that a reversing flow alternates the sense of the convective heat transport between the fluid and the bottom plate in contrast to the non-reversing flow where the heat transport is permanently maintained from either the fluid to the lower plate or vice versa depending on the nature of the thermal forcing at the boundaries. Finally, similarities and discrepancies between the R–B and the Taylor–Couette systems under time-periodic boundary conditions are also addressed. Movies are also available in the supplementary material.