Multi-stage dynamics of horseshoe vortex around a bed-mounted cylinder: From laminar to fully turbulent flow

The horseshoe vortex (HV) generated around a bed-mounted cylinder is the dominant flow structure responsible for initiating local scour at pile foundations of bridges, offshore platforms, port terminals, and other coastal and hydraulic engineering structures. Despite existing knowledge on HV characteristics and their influencing factors, several key knowledge gaps remain. First, the Reynolds number can vary over a wide range from laminar to fully turbulent conditions, yet systematic investigations covering the entire spectrum are lacking. Second, existing studies have primarily focused on velocity and vortex strength, while other critical dynamic parameters—such as bed shear stress and pressure gradient—remain underexplored. Third, a universal mesh size criterion for high-fidelity simulations of the HV is lacking. To address these issues, this study employs the detached-eddy simulation method to perform high-resolution three-dimensional numerical simulations over Reynolds numbers (ReD) ranging from 100 to 106. The results reveal the multi-stage dynamics of the HV, characterized by four distinct regimes: laminar, transitional, weakly turbulent, and fully turbulent. The mechanical characteristics of the HV in each regime—including morphology, velocity and pressure fields, vortex strength, and bed shear stress—are identified, and engineering-oriented dimensionless empirical correlations are proposed to describe the variations of key HV parameters within the investigated Reynolds-number range. In addition, a mesh criterion is proposed based on grid independence tests.