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Abstract Alongshore current‐supported turbidity currents (ACSTCs) are a subclass of wave‐ and current‐supported turbidity currents. They are one of the agents responsible for the dispersal of the river‐borne sediments on the continental shelf, which constitutes a major phenomenon controlling the geomorphic evolution of ocean‐basin margins over geological time. Therefore, parameterization of the sediment flux associated with ACSTCs will help its implementation in operational models and quantify the sediment flux budgets on the continental shelf. The velocity structure of ACSTCs and the amount of sediments suspended by them are crucial to determine the suspended sediment flux. This study investigates the velocity structure of a simplified miniature ACSTC over an erodible bed composed of fine sediments. Direct numerical simulations are conducted for various bed erosion parameters and sediment settling velocity. The role of sediment‐induced stable density stratification on the velocity structure of ACSTCs is analyzed. The simulation results indicate that density stratification and the drag coefficient are functions of the product of sediment settling velocity and sediment concentration. The velocity profile was found to deviate toward the alongshore direction with strengthening density stratification, which enhances the drag coefficient. By using the Monin‐Obukhov theory, the drag coefficient associated with the cross‐shelf propagation of ACSTCs is formulated as a function of the Reynolds number, sediment concentration, and sediment settling velocity.