Resonant Thermal Convections in a Square Cavity Induced by Heat-Flux Vibration on the Bottom Wall

Abstract

In this study, two-dimensional thermal convections vibrated by the sinusoidal heat-flux vibration on the bottom wall in a square cavity are numerically examined. The Prandtl number Pr and the Rayleigh number Ra are held fixed at 0.71 and 10⁶, respectively, and the amplitude a and the angular frequency ω of the vibration are changed. As a result, four types of (multiple) resonant mode are observed as a increases. They are attributed to the resonance with either the internal gravity wave or the circulatory flow, which is observed when a is sufficiently large.

Notes

The indices are computed on both 100 × 100 and 200 × 200 grids, and the error is defined by the ratio of their absolute difference to the value computed on the 200 × 200 grid.