Turbulent vertical convection under vertical vibration

Abstract

Vertical convection (VC) under the action of vertical vibration in a square cavity has been investigated using direct numerical simulation. The simulations are conducted with Prandtl number Pr fixed at 4.38 and Rayleigh number Ra ranging from [Formula: see text] to [Formula: see text]. To examine the influence of vertical vibration, the dimensionless vibration frequency is varied in the range of [Formula: see text] and a small dimensionless amplitude is fixed at [Formula: see text]. First, for low vibration frequency, trivial results are obtained where flow structures and the scalings of Nu and Re resemble that of the standard VC cases. In contrast, when the vibration frequency ω increases beyond a critical value [Formula: see text], a strong shearing effect from vibration leads to abundant eruptions of thermal plumes from sidewalls, and thus a laminar-turbulent transition of the bulk flow. As a result, heat-transport is greatly enhanced and the scaling exponent β of [Formula: see text] substantially increases in such the vibration-dominated regime. In specific, the scaling relations obtained transit from [Formula: see text] and [Formula: see text] at ω = 0 in the laminar regime to [Formula: see text] and [Formula: see text] at [Formula: see text] in the turbulent regime. Analysis of the mean flow field shows that the vibration thins the thermal boundary layer and enhances the thermal dissipation rate in the bulk region. Furthermore, we found that the trend of Nu and Re can be well described by the vibrational Rayleigh number [Formula: see text]. In particular, Nu is insensitive to [Formula: see text] for [Formula: see text], whereas [Formula: see text] for [Formula: see text], where the critical vibrational Rayleigh number exhibits a scaling relation [Formula: see text] obtained from numerical results.