Mixing in internally heated natural convection flow and scaling for a quasi-steady boundary layer

被引:12
作者
Hattori, Tae [1 ]
Patterson, John C. [1 ]
Lei, Chengwang [1 ]
机构
[1] Univ Sydney, Sch Civil Engn, Sydney, NSW 2006, Australia
基金
澳大利亚研究理事会;
关键词
boundary layers; buoyancy-driven instability; convection; NAVIER-STOKES EQUATIONS; ITERATIVE SOLUTION; RESERVOIR SIDEARM; SOLAR-RADIATION; FLUID LAYER; ABSORPTION; STABILITY; ACCURACY; SUBJECT; SURFACE;
D O I
10.1017/jfm.2014.680
中图分类号
O3 [力学];
学科分类号
08 ; 0801 ;
摘要
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.
引用
收藏
页码:352 / 368
页数:17
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