旋转穿透对流在地球科学和工程领域受到广泛关注，由于水在4℃附近具有密度倒置特性，因此以冷水作为工质研究竖直圆筒内的旋转穿透Rayleigh-Bénard对流(RBC)。对不同参数条件(密度倒置参数θm=0.0,0.5，罗斯比数的倒数0≤1/Ro≤10，瑞利数104≤Ra≤108)下的冷水对流传热开展直接数值模拟研究。结果表明，当1/Ro=0时，θm=0.5的穿透对流呈现上下非对称性，上热边界层厚度δtopθ大于下热边界层厚度δbottomθ，努塞尔数Nu和δθ与Ra的标度指数约为±0.3；在中等1/Ro条件下，θm=0.0的冷、热羽流均能够形成涡柱结构；而θm=0.5的流动因受冷水密度倒置特性影响，仅热羽流能够形成涡柱，冷流体仍保持羽流形态，因此，涡柱的形成对于θm=0.5的对流传热增强效果并不显著。旋转穿透RBC的热边界层厚度在中高1/Ro时满足1/Ro1/2标度律，而此时的速度边界层厚度仍遵循1/Ro-1/2标度律。
The rotating penetrative convection in the fields of Earth science and engineering has attracted extensive attention. Due to the density inversion property of water near 4℃, cold water is used as the working fluid in the present paper to study the rotating penetrative Rayleigh-Bénard convection in a vertical annulus. Direct numerical simulation is performed to analyze the convective heat transfer of cold water under various parameter conditions, with the density inversion parameter θm=0.0,0.5, the inverse Rossby number 1/Ro and the Rayleigh number Ra changing in the ranges 0≤1/Ro≤10 and 104≤Ra≤108. The present results show that in the non-rotating cases (i.e. 1/Ro=0), the penetrative convection of cold water with θm=0.5 exhibits significant up-down asymmetry, with the top thermal boundary layer thickness δtopθ greater than the bottom one δbottomθ. The scaling exponents of the Nusselt number Nu and δθ versus Ra are approximately ±0.3. In the rotating cases (i.e. 1/Ro>0), the flow changes with increasing the rotation rate (i.e. 1/Ro), leading to the transition of flow regime from thermal plumes to vortex columns at moderate 1/Ro. Particularly noteworthy is that for θm=0.0 both the cold and hot plumes are strong enough to form vortex columns in a certain range of 1/Ro, while the density inversion property at θm=0.5 renders the cold plumes weak so that only hot plumes can be converted into vortex columns. As a result, the augmentation of heat transfer, induced by the formation of vortex columns, for θm=0.5 is not as significant as that for θm=0.0. For the rotating penetrative convection of cold water with θm=0.5, at moderate to high 1/Ro, the thermal boundary layer thickness δθ exhibits a scaling law δθ~1/Ro1/2, while the velocity boundary layer thickness δu still follows δu~1/Ro-1/2.
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