Bed Shear Stresses Parameterization in Wave–Current Interaction by k − ω Turbulence Model

For a flow generated by the wave–current interaction (WCI), an accurate estimate of the maximum (τmax) and the mean (τm) bed shear stresses is important for the sediment transport calculation. These two parameters are usually estimated by numerical modeling which can prove to be difficult to implement and very costly in CPU time. This paper then proposes analytic parameterization of τmax and τm by simple relationship depending on the current and wave shear stresses (τc and τw). The proposed parameterization was performed in two steps: the first step is to build a numerical database of τmax and τm for different combinations of flow variables. This step was carried out by an one-dimensional vertical (1DV) model of turbulent bottom boundary layer using the k − ω turbulence model. The second step is to represent this database by predefined analytical relations. This step was performed by an optimization procedure adopting the GlobalSearch (GS) (function of Matlab software). The proposed parameterization based on the “k − ω/GS” combination provides very good estimations of τmax and τm. These estimations are similar to those proposed by other authors who have studied the WCI by analytical models widely used by the marine science community.