稳定分层流密度界面处湍流混合与分形结构

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

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(Rio),(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Rio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Rio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.

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 Rioto 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.