Mixing in internally heated natural convection flow and scaling for a quasi-steady boundary layer
Mixing in internally heated natural convection flow and scaling for a quasi-steady boundary layer
复制标题
混合内部加热的自然对流并缩放以获得准稳态边界层
作者：
T. Hattori;J. Patterson;C. Lei
摘要本文研究了受太阳辐射加热的水体中的自然对流。对这种类型的自然对流流动的调查是出于这样一个事实，即它是已知的白天在天然水库和湖泊的浅水区的热量和质量传递中起着至关重要的作用，从而对生物活动产生影响。这种内部加热系统的温度解析解表明，温度层化由上部稳定层化和下部不稳定层化组成。这种非线性温度分层的重要后果之一是由上升的热羽流驱动的混合的限制，羽流的穿透长度尺度决定了较低的混合层厚度。理论分析表明，在相对较深的沃茨中，低混合层厚度等于辐射的衰减长度，这对水质，包括水体中污染物和营养盐的传输具有重要意义。还获得了准定常边界层的标度。理论分析与数值模拟进行了验证。
Abstract This study considers the natural convection flow in a water body subjected to heating by solar radiation. The investigation into this type of natural convection flow has been motivated by the fact that it is known to play a crucial role in the daytime heat and mass transfer in shallow regions of natural water reservoirs and lakes, with a resultant impact on biological activity. An analytical solution for temperature in such an internally heated system shows that the temperature stratification consists of an upper stable stratification and a lower unstable stratification. One of the important consequences of such a nonlinear temperature stratification is the limitation of the mixing driven by rising thermal plumes with the penetration length scale of the plumes determining the lower mixed layer thickness. A theoretical analysis conducted in the present study suggests that in relatively deep waters, the lower mixed layer thickness is equal to the attenuation length of the radiation, which has important implications for water quality, including the transport of pollutants and nutrients in the water body. Scalings are also obtained for the quasi-steady boundary layer. The theoretical analysis is validated against numerical simulations.