Mapping Mean Velocity Field over Bed Forms Using Simplified Empirical-Moment Concept Approach

The log-wake law was successful in mapping velocity fields for uniform flow over flat surfaces, even cases of wake effects (velocity dips, wall effects, and secondary currents). However, natural riverbeds with undulations bedforms challenge these models. This study introduces a moment-based empirical method rough estimation the stationary 2D bedforms. It proposes three polynomial profile templates (first, fifth, eighth orders) coefficients deduced analytically while taking into account an array conditions assumptions, including slip at bed, mass moment momentum conservations, imposing inviscid potential near water surface, incorporation near-bed shear stress utilizing Chezy formula. Remarkably, polynomials are primarily reliant on two crucial scales, depth-averaged (uo) moment-derived integral (u1), along dimensionless reattachment coefficient (Kr). Validation proposed approach comes from ten lab experiments, spanning Froude numbers 0.1 to 0.32, offering data validate obtained profiles establish relationship spatial variation normalized u1 reveals that assumption boundary condition bed generally enhances accuracy predicted profiles. eighth-order excels within eddy zone close points, fifth-order performs better downstream, approaching crest. Importantly, efficacy this extends beyond encompass airflow scenarios, such as negative step. research findings highlight linear velocity, employed Vertically Averaged Moment models (VAM), exhibits approximately 70% less mismatch compared constant (VA) Moreover, utilization results substantial improvements, reducing by 86% 90%, respectively, comparison VA insights gained hold significant implications advancing vertically averaged models, enabling generation approximate yet more realistic scenarios involving These directly impact applications related sediment transport mixing phenomena.