Unified Friction Factor Model for Dune Beds from High to Low Submergence

Accurate prediction of flow resistance in dune-bed streams is critical for river engineering and flood management. Traditional methods, which rely on empirically partitioning total shear stress into skin and form drag, often fail under low-submergence conditions where the flow is profoundly influenced by large roughness elements. This study presents a unified model that predicts the total Darcy-Weisbach friction factor without requiring such partitioning. The approach conceptualizes dunes as macro-roughness, adopting a gravel-bed resistance formula. The key finding is a physically based equivalent roughness height k s , derived from a momentum analysis of sudden-expansion head loss, which scales as k s ∼ δ 2 / λ , where δ and λ denote dune height and length, respectively. Calibration with fixed dune data yields k s = 13.0 δ 2 / λ . The model demonstrates strong performance for fixed dunes and predicts independent mobile dune data acceptably without recalibration, validating its general applicability across a wide range of submergence.