Analyzing the threshold angles for vortex formation in shallow water open channels

Vortices are widely present in nature and hydraulic engineering, particularly in rivers, lakes, and open channels. Most vortices in water bodies are shallow, meaning the horizontal scale of the vortex is significantly larger than the water depth. While vortex studies exist in hydraulic engineering, they primarily focus on practical projects. The thresholds for vortex formation under varying sudden expansion angles in open channels, as well as the extent of vortex fluctuations, remain unclear. We employed the Shear Stress Transport k-ω turbulence model to analyze the flow field structure by testing 24 different sudden expansion angles, based on the characteristics of shallow water vortices in the sudden expansion section of an open channel. The results indicate that when the vortex area is defined as 0.1% of the total area of the sudden expansion section, the vortex generation threshold is 10.61° under the Q criterion, and 10.71° under the Ω criterion. Contrary to the common assumption that a larger sudden expansion angle results in a larger vortex, the optimal angle for controlling vortex formation is 19.33°. This angle significantly reduces vortex fluctuations, especially when the sudden expansion angle is 18°, with a reduction rate of 79.11% in the vortex area under the Q criterion. Thus, studying the different expansion angles of shallow water vortices in open channels offers critical design references for hydraulic engineering and has broader implications for shallow water flow regimes.