A process-based formula for sheet flow transport induced by combined wave-current action

A process-based formula for sheet flow transport has garnered significant attention in ocean engineering due to the necessity of topographic predictions. The process-based formula, applicable to a mobile seabed, is derived through integrating concentration and velocity profiles under the condition of asymmetric wave and current. The concentration profile accounts for the effects of acceleration and phase lag, adhering to the classical exponential law based on mass conservation principles. Conversely, the velocity profile comprises two interacting components influenced by asymmetric oscillatory wave force and current force. The formula encompasses a fundamental component that yields the classical 3/2 power law in terms of the Shields parameter, similar to traditional formulas, along with parameters related to wave boundary layer thickness. Given the limited understanding of the significance of wave shape and current, the formula is segmented into a part pertaining to wave force and another part pertaining to current force, thereby highlighting their respective importance according to different wave shapes. The instantaneous sheet flow transport is examined as a power function of velocity, incorporating phase lag, current, and wave shape. Overall, the proposed formula demonstrates satisfactory performance in both instantaneous sediment flux and net transport rate, which are the combined effects of acceleration, phase lag, wave (boundary layer) asymmetry, and wave–current interaction.