First-principles based modeling of equilibrium scour depth around a submarine pipeline in a sandy seabed under power-law shear flow

Existing formulas for predicting the equilibrium scour depth below pipelines are primarily derived from empirical fittings of laboratory data. Consequently, they suffer from significant scale effects and poor generalizability. To address this fundamental limitation, this study develops a physics-based theoretical model for predicting equilibrium scour depth below a pipeline under steady unidirectional currents and non-cohesive sandy seabed conditions. A generalized framework is first established via dimensional analysis and similarity principles. Subsequently, a theoretical formula is developed by integrating turbulence phenomenology within a first principles based scaling framework, applicable to both clear-water and live-bed scour conditions. The proposed model, grounded in first principles, integrates all key governing parameters, thereby effectively mitigating the inherent scale effects. High predictive accuracy was confirmed by validating the model against 310 experimental datasets. The model achieves excellent agreement in clear-water conditions, with its predictions for live-bed scour also remaining within acceptable error margins. A comprehensive parametric analysis for two representative pipeline diameters (D = 0.1 and 1.0 m) reveals the distinct influences of relative roughness, gap ratio, relative water depth, and Froude number on scour depth, demonstrating scale-dependent behaviors and providing process-based insights into the underlying physical mechanisms. This work provides a paradigm shift from purely empirical correlations to physics-based prediction, yielding valuable insights for pipeline scour predictions.