稳定分层流密度界面处湍流混合与分形结构

采用室内混合箱研究稳定分层流(上层淡水、下层盐水) 无剪切密度界面处的湍流混合与分形结构. 湍流通过浸没在盐水层中的振动格栅产生, 密度界面结构通过在盐水层中添加荧光剂或染料可视化, 共进行12 组实验. 实验观测并记录了:(1) 淡、盐水密度界面距混合箱底部的平均高程(h);(2) 淡、盐水层的密度(ρ₀,ρ), (3) 淡、盐水密度界面. 其中, 淡、盐水密度界面通过照片、录像进行记录. 观测结果用于计算:(1) 盐水层密度;(2) 卷挟速度, (3) 整体理查孙数(Ri_o), (4) 二维、三维密度界面, (5) 二维、三维密度界面的分形维度. 结果分析发现:(1) 湍流卷挟率随Rio 增大而减小, 并且满足Ri_o的-3=2 或-7=4 幂律;表明随着湍流强度的减弱, 混合的速度也越来越缓慢;(2) 二维密度界面分形维度大于1, 三维密度界面分形维度大于2;表明二维、三维密度界面存在分形结构;(3) 分形维度随Ri_o的增大而减小;表明随着湍流强度的减弱, 密度界面也越来越趋于光滑. 

TURBULENT MIXING AND FRACTAL STRUCTURE AT A DENSITY INTERFACE IN A STABLY STRATIFIED FLUID

Laboratory mixing box experiments were undertaken to examine turbulent mixing and fractal structure at a density interface in a stably stratified two-component fluid (fresh on salt), subjected to shear-free turbulence induced by an oscillating grid within the salt water layer. The density interface was visualized by adding fluorescein and dye into the salt water layer. A total of 12 runs were made. Measurements were made of (a) the height of the mean density interface above the bottom of the mixing box; (b) the densities of the fresh water and salt water layers. Photographs and videos were made of the two-dimensional and three-dimensional density interfaces. Calculations were made for (1) the entrainment velocity; (2) the overall Richardson number (Ri₀); and (3) the fractal dimension of the two-dimensional and three-dimensional density interfaces. The entrainment rate decreases with an increasing overall Richardson number. It can be expressed as Ri_o to the -3/2 or -7/4 power. This indicates that the rate of mixing deceases with decreasing turbulence intensity. Fractal dimension of the two-dimensional density interface is larger than 1, while that of the three-dimensional density interface is larger than 2. Fractal structures are present on the two-dimensional and three-dimensional density interfaces. Fractal dimension decreases with an increasing overall Richardson number. This suggests that the density interfaces become smoother with decreasing turbulence intensity.