Structural and dynamic characteristics of horseshoe vortex systems in front of rigid vegetation inclined upstream under conditions of overland flow

Inclined angle significantly impacts horseshoe vortex (HV) system and subsequent flow events upstream of vegetation stems, which are crucial for understanding of erosion mechanisms and geodynamics. Flume experiments were conducted to investigate dynamic characteristics of horseshoe vortex (HV) system upstream of inclined rigid vegetation stems under shallow overland flow conditions. Five inclination angles (10°, 20°, 30°, 40°, 50°) were tested alongside a vertical column (0°) across four low Reynolds number conditions (Re_D = 2995–4639). Using high-precision particle image velocimetry (PIV) system, we measured the flow field in upstream symmetry plane of the cylinder. Then time-averaged primary HV features were analyzed in terms of the location, radius, vorticity, swirling strength, flow direction and vertical velocity. The increasing inclination angle weakens the formation of the HV system. This is evident in the decrease of vorticity and swirling strength, as well as the gradual diffusion and eventual rupture of the HV system. In the horizontal direction, the primary HV gradually moves away from the cylinder, with minimal vertical impact. The radius of the main HV is positively correlated with the tilt angle, while vorticity and rotation intensity are negatively correlated. We also examined the time-resolved characteristics of the velocity components. The probability density functions (PDFs) of streamwise and vertical velocity components show asymmetric double peaks, indicating two high-frequency events: backflow and downwelling. Linear random estimation revealed that the backflow event is driven by a high-momentum counter current passing through the primary HV, which is mainly dominated by a backflow mode, while the downwelling event arises from low-momentum fluid that cannot penetrate the HV, dominated by a zero-flow mode. These two modes exhibited minimum and maximum time percentages within the current time range, highlighting erosion dynamics from the perspectives of flow event frequency and momentum theory.