Hydrodynamic Moment and Entrainment of Partially Submerged Boulders in Transcritical Flow

Abstract The stability and incipient motion of isolated boulders in shallow, high-energy open-channel flows are governed by the balance of hydrodynamic forces and overturning moments, yet direct measurements of these moments remain scarce. This study provides, to the best of our knowledge, the first direct laboratory measurements of the hydrodynamic overturning moment acting on a partially submerged boulder under transitional (near-critical) flow conditions, where the water depth is smaller than or equal to the boulder height. The dimensionless overturning moment coefficient C M is evaluated as a function of flow regime and relative submergence. The results show that C M attains its maximum under near-critical conditions, while fully supercritical flow produces lower overturning moments despite higher velocities. The consistency of a previously proposed entrainment framework is assessed by comparing velocity-based and force-based mobility formulations using independently measured drag and lift forces. The findings highlight the importance of near-critical hydraulic conditions in promoting overturning and boulder mobility and provide the first dataset of hydrodynamic moments spanning conditions from nonentrainment to incipient motion.