Flow topology around a surface-mounted square cylinder at high Reynolds numbers


Surface-mounted square cylinders with finite lengths are common in engineering applications. Unlike cylinders with infinite heights, their aerodynamic properties are characterized by salient 3D effects in the vertical direction because of ground surface and free end. Generally, the time-averaged wake structures comprise dipole and quadrupole types characterized by two and four patches of alternating senses of rotation, respectively.

The extensive studies on the dynamic flow structures in the wake have provided many insights into the vortex-shedding wake, which is influenced by several factors, such as Reynolds number (Re), aspect ratio and boundary layer thickness. Although a range of vortex-shedding models have been proposed, most of them have several drawbacks, such as their inability to illustrate the formation of the base and streamwise tip vortices and associated interactions with flow structures. In addition, the development of base vortex and the effects of different Re values are still poorly understood.

There are limited studies on the near-wall flow patterns despite their practical implications, attributed to the technical difficulties regarding the dynamic and time-averaged patterns. While numerical simulations are effective for investigating near-wall flow patterns, most studies focus on the low Re values, which is inadequate to provide the true nature of the near-wall flow in the engineering applications (usually with high Re). Considering the potential applications at higher Re values number, near-wall flow patterns at high Re values and their associated variations caused by increasing the Re is worth studying.

To address these research gaps, a team of researchers at Shanghai Jiao Tong University: Dr. Yong Cao, Professor Dai Zhou, Dr. Yan Bao and Dr. Zhaolong Han in collaboration with Professor Tetsuro Tamura from Tokyo Institute of Technology studied the near-wall flow structures of a surface-mounted square cylinder at high Re of and thick turbulent boundary layer. A combination of critical-point theory and high-resolution simulations was adopted to rationally construct the flow topology. The work is currently published in the Journal of Fluid Mechanics.

The authors observed a large-scale near-wake vortex consisting of two connected segments that were rolled up from the free end and sides of the cylinder. This vortex was rooted on two foci on the ground plane behind the cylinder. A second large-scale side vortex was observed next to the side walls at a high Re value. This vortex was characterized by variations in the vertical direction and was rooted on two notable foci on the two walls, which made it grow continuously through the cylinder height. The side vortex in the junction region moved upwards in a curved trajectory to form nodes on the ground surface. However, it was compressed in the free-end region to form a smaller trailing-edge vortex that moved downstream.

Only tip vortices occurred in the far wake. The vorticity of the tip vortex and near-wake vortex emanated from the outer and inner regions of the shear-dominated flow, respectively. Besides the influences of the boundary layer thickness on the strength of the upwash flow, an increase in Re from 500 to o(104) played a vital role in generating upwash flow in both moderate and near wakes. The separation-reattachment process was noted at high Re at the training-edge vortices and in the junction region. The former affected the side vortex strength while the latter reduced the pressure near the trailing edge.

In summary, the authors are the first to topologically describe the near-wall flow patterns around a surface-mounted square cylinder at high Re values. The study further compared the flow topologies at low and high Reynolds numbers to clarify the effects of Re values. In a statement to Advances in Engineering, Dr. Yong Cao, first author explained that their findings would contribute to the construction of robust flow topologies and understanding of flow organization for validating the available databases with the similar configurations.

Flow topology around a surface-mounted square cylinder at high Reynolds numbers - Advances in Engineering
(a) Isosurface of the second invariant of the velocity gradient tensor (QD^2)⁄(U_∞^2 ), which is coloured by the streamwise vorticity.
(b) Flow visualization of 3-D separation in the junction region
(c) Flow topology projected in the cross-section by using critical-point concepts.

About the author

Yong Cao received his Ph.D. from Tokyo Institute of Technology in 2016 under the supervision of Professor Tetsuro Tamura. In 2020, he joined Shanghai Jiao Tong University as Associate Professor in Department of Civil Engineering. His research interests include computational fluid dynamics, bluff-body aerodynamics and wind-resistance design of structures.


About the author

Tetsuro Tamura is currently emeritus professor of Tokyo Institute of Technology, Japan. His research interests are in the broad field of wind engineering and environmental turbulence, and include large-eddy simulation prediction of strong wind disaster under extreme meteorological events, environmental complex turbulence (thermal and rotational effects), aerodynamic and aero-elastic behavior for cylindrical structures, atmospheric dispersion and risk estimation for hazardous gasses.

Since 1993, Professor Tamura has been involved in Architectural Institute of Japan (AIJ) and took a leadership on CFD technique for buildings. His scientific results have been implemented to the AIJ book: Practical Guide of CFD for Wind Resistant Design. He was a member of the editorial board of transaction of AIJ. He was a president of Japan Society of Fluid Mechanics in 2017. Professor Tamura was awarded Japan Association for Wind Engineering Award on CFD estimation for wind-structure interaction problems in 2000, also awarded the prize of AIJ 2012 at Research Theses Division for a sequence of studies on development and application of CFD technology for wind disaster reduction at buildings in a city.


Cao, Y., Tamura, T., Zhou, D., Bao, Y., & Han, Z. (2022). Topological description of near-wall flows around a surface-mounted square cylinder at high Reynolds numbers. Journal of Fluid Mechanics, 933, A39. doi:10.1017/jfm.2021.1043

Cao, Y., Tamura, T., & Kawai, H. (2019). Investigation of wall pressures and surface flow patterns on a wall-mounted square cylinder using very high-resolution Cartesian mesh. Journal of Wind Engineering and Industrial Aerodynamics, 188, 1-18. doi:10.1016/j.jweia.2019.02.013

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