A simple procedure for calculating the mean and maximum bed stress under wave and current conditions for rough turbulent flow based on Soulsby and Clarkeʹs (2005) method

In the marine environment, particularly on continental shelves, the processes of wave dissipation and sediment transport depend crucially on the bed shear stress. When waves and currents are superimposed the bed shear stress exhibits non-linear behaviour such that it is insufficient to simply sum vectorially the wave-alone and current-alone stress components. Soulsby and Clarke (2005) [Bed shear-stresses under combined waves and currents on smooth and rough beds. Report TR 137. HR Wallingford, Wallingford, UK, 22 pp.] developed a simple analytical, non-iterative method for calculating the mean and maximum bed shear stress in combined wave and current flows. For rough turbulent flow their method produces non-linearities in the mean and maximum bed stress that are consistent with those measured, while it under-predicts the non-linearities in the bed stresses in comparison with model predictions. Here their method is generalised such that it may be used to predict non-linearities in the bed stresses that are consistent with either the measurements or the models, for the case of rough turbulent flow. Also the Soulsby and Clarke method relies on the fact that the depth-averaged current is already known. However, in the field it is often the case that the current at a particular height above the bed is measured, so here their method is reposed in terms of a current measured at a particular height. A MATLAB script is provided for this modified Soulsby and Clarke method, such that either strong or weak non-linearity can be included in the wave–current interaction and the current can be input at a particular height or as a depth average.