Turbulence in the wake of a roughness patch

Little research was done in the past concerning the propagation of three dimensional effect in shallow wake flow caused by a roughness patch. To get a better understanding of the consequences of the three dimensionality of the flow structures, experiments are performed in a wide shallow flume to examine these structures. The main objective is to examine whether the wake structure of a roughness patch can be treated as (quasi)-two-dimensional. The objective has been answered by a combination of a literature study and an experiment performed at the faculty’s laboratory. The results show four dominant mechanisms in the wake of a roughness patch: transverse mass flux, bottom friction, mixing layer and the secondary circulation. Based on a momentum balance the transverse mass flux and the bottom friction are the largest contributions to this balance. Although the contribution of the mixing layer and the secondary circulation to the recovery of the wake are of the order of 10%, their influence on the flow structure is more pronounced. The mixing layer is shifted towards the wake centerline due to the presence of a transverse mass flux forming a misalignment between the maximum spanwise Reynolds stress and the position of the wake half width. Since this shift is of limited influence on the position of the secondary circulation, a misalignment if formed between the maximum momentum transport by the secondary circulation and the mixing layer causing a lower streamwise velocity at the edge of wake with respect to the wake of an emerging obstruction. The secondary circulation is responsible for the transport of low momentum fluid towards the edge of the wake near the bottom, and high momentum fluid towards the wake centerline near the surface. This behavior is responsible for the cross gradient in the streamwise velocity profiles as shown by the data obtained. For modeling purposes of well mixed quantities, a (quasi)-two-dimensional approach only holds if the weaker streamwise velocity near the edge of the wake is taken into account. In the case a prediction of depth varying quantities is desired, the cross gradient caused by the secondary circulation needs to be implemented as well which results in the need of a three-dimensional modeling approach.

以往针对粗糙斑块引发的浅滩尾流中三维效应传播的研究较为匮乏。为深入明晰流动结构三维特性带来的影响，本研究于大型浅水槽中开展实验以观测此类流动结构。本研究的核心目标为验证：粗糙斑块的尾流结构是否可按（准）二维方式进行近似处理。通过结合文献调研与该学院实验室开展的相关实验，本研究完成了上述目标的验证。研究结果表明，粗糙斑块尾流存在四种主导作用机制：横向质量通量、床面摩擦、混合层与二次环流。基于动量平衡分析，横向质量通量与床面摩擦为该平衡中的主要贡献项。尽管混合层与二次环流对尾流恢复的贡献仅约为10%，但其对流动结构的影响更为显著。由于横向质量通量的存在，混合层会向尾流中心线偏移，导致最大展向雷诺应力（spanwise Reynolds stress）与尾流半宽度位置出现错位。由于该偏移对二次环流的位置影响有限，二次环流的最大动量输运与混合层之间会形成错位，进而使得尾流边缘的顺流向速度相较于露头障碍物的尾流更低。二次环流负责将近床面区域的低动量流体输运至尾流边缘，并将近表层的高动量流体输运至尾流中心线。这一特性使得顺流向速度剖面出现横向梯度，与实验获取的观测数据一致。若针对充分混合量开展建模，仅当考虑尾流边缘处较低的顺流向速度时，（准）二维建模方法才具备适用性。若需预测沿水深变化的物理量，则需纳入二次环流引发的横向梯度，此时必须采用三维建模方案。