We carry out direct numerical simulations of horizontally or vertically vibrated Rayleigh–Bénard (RB) convection over a wide range of Rayleigh number $\left(Ra\right)$ and dimensionless vibration frequency $\left(\omega \right)$ at fixed Prandtl number $Pr=4.38$ and dimensionless vibration amplitude $a=1.52\times {10}^{-3}$. It is shown that the global heat transport (measured by the Nusselt number $Nu$) is close to the value of standard RB convection in buoyancy-dominant regime at small $\omega$, whereas it is significantly enhanced by horizontal vibration or suppressed by vertical vibration in the vibration-dominant regime at large $\omega$. The division between the two regimes yields a critical vibration frequency ${\omega }^{*}$, which indicates the onset of vibration-induced $Nu$ enhancement or $Nu$ reduction. The values of ${\omega }^{*}$ are obtained based on the fitting between the numerical data and our proposed crossover functions. The dependence of ${\omega }^{*}$ on $Ra$ is then studied. It is found that the fitted critical frequency exhibits two close scaling relations: ${\omega }^{*}\sim R{a}^{-0.164}$ in horizontally vibrated RB convection and ${\omega }^{*}\sim R{a}^{-0.172}$ in vertically vibrated cases. Moreover, based on the competition of the kinetic energy production between buoyancy-dominant and vibration-dominant regimes, a physical model is proposed to predict the scaling behavior between ${\omega }^{*}$ and $Ra$, i.e., ${\omega }^{*}\sim R{a}^{-1/6}$, which agrees well with the measured scaling exponents of our numerical data.

• Received 27 April 2023
• Accepted 3 October 2023

DOI:https://doi.org/10.1103/PhysRevFluids.8.113501