Internal Gravity Wave Resonance of Thermal Convection Fields in a Square Cavity with Heat-Flux Vibration

Abstract

In this paper, the thermal convection field and its resonance phenomena in a square cavity with sinusoidal heat-flux vibration were numerically examined. As angular velocity ω is changed, the thermal convection field at Pγ=0.71, Rα=10⁶ is found to be classified into 5 regions and, particularly, the field has the local maximum of relative amplitude of midplane Nusselt's number at ω_c=350, which corresponds to the angular velocity of internal gravity wave ω_γ estimated by a theoretical equation proposed by Thorpe. This shows the local enhancement is induced by an internal gravity wave resonance. Such correspondence is observed for Rα≥10⁵, Rα≥10⁶ for Pγ=0.71, 7.1, respectively. For the range of Rα we proposed a correlation equation, a function of Pγ and Gγ only, to estimate the resonant angular velocity.