A mixing-length model for shallow turbulent wakes
A mixing-length model for shallow turbulent wakes
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DOI：
10.1017/s0022112003006384
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发表时间：
2003-11
影响因子：
3.7
通讯作者：
P. Stansby
中科院分区：
文献类型：
--
作者：
P. Stansby
本文将浅水流动的三维边界层模型推广到湍流流动，该模型假定静水压力，数值扩散和波浪阻尼可以忽略不计。一个标准的两层混合长度模型确定垂直长度尺度。水平混合长度是垂直值的倍数$\beta$，$\beta$是通过与实验比较确定的。涡动粘度是一种一般的三维形式，其中，例如，水平混合长度和相关的应变率确定涡动粘度的大小，因此垂直混合（反之亦然）。直接比较与以前的实验为亚临界流周围的一个锥形岛的小边坡表现出从一个有力的旋涡脱落尾流稳定的再循环尾流的稳定性参数，$St$，增加的过渡。$\beta$的值影响尾流结构，特别是对于接近临界值（尾流变得稳定或稳定的值）的稳定性参数。在实验中的临界值是0.4，这是重现在模型与$\beta \，{=}\，6 $。定性地再现了$\hbox{\it St} \，{=}\，0.26$和0.36的旋涡脱落模式。流量是亚临界的开始弗劳德数约为0.2，与接近0.6-0.7的深度平均涡量也是最大的，在一个小的距离湿/干交叉的地区。在这个交叉点处，深度平均涡度接近零，而位涡度（深度平均涡度/深度）处于最大值，表明交叉点作为涡度原点的重要性。
A three-dimensional boundary-layer model of shallow-water flows assuming hydrostatic pressure with negligible numerical diffusion and wave damping has been extended to turbulent flow. A standard two-layer mixing-length model determines vertical length scales. The horizontal mixing length is made a multiple $\beta$ of the vertical value and $\beta$ is determined from comparison with experiment. Eddy viscosity is of a general three-dimensional form where, for example, the horizontal mixing length and associated strain rates determine the magnitude of eddy viscosity and hence vertical mixing (and vice versa). Direct comparison is made with previous experiments for subcritical flow around a conical island of small side slope which exhibits the transition from a vigorous vortex-shedding wake to a steady recirculating wake as the stability parameter, $St$, is increased. The value of $\beta$ influences wake structure, particularly for stability parameters close to the critical (the value at which the wake becomes steady or stable). The critical value in the experiments was 0.4 and this was reproduced in the model with $\beta \,{=}\,6$. Vortex shedding patterns with $\hbox{\it St} \,{=}\, 0.26$ and 0.36 were qualitatively reproduced. The flows were subcritical with an onset Froude number of about 0.2, with values approaching 0.6–0.7 in areas where depth-averaged vorticity magnitude was also greatest, at a small distance from the wet/dry intersection. At this intersection, depth-averaged vorticity approached zero while potential vorticity (depth-averaged vorticity/depth) was at a maximum, indicating the importance of the intersection as an origin for vorticity.