The characteristics of the mean velocity are presented by considering a closure scheme in the turbulent wave boundary layer by a one-equation model induced by nonlinear progressive and standing waves. The solutions are based on a single layer time-varying eddy viscosity, which is more realistic in the natural condition. First, the calculations are done by a one-equation model for the turbulent wave boundary layer induced by nonlinear progressive waves and the calculated profiles are compared with the experimental data of van Doom (1981). The validity of the model is well supported by the experimental data. Finally, the calculations are done by that model for the turbulent wave boundary layer induced by nonlinear standing waves. The characteristics of mean velocity, horizontal velocity and turbulent energy have been observed. The mean velocity is found quite different from the laminar boundary layer. In this paper, it is explained.
The mean velocity, or streaming in the boundary layer beneath surface water waves is of interest and importance to the coastal engineers and researchers in the field of sediment transport for many years. The mean velocity is important near the seabed where it influences to move sediment. A wide range of the works have been done on an oscillatory boundary layer, where the velocity is uniform and wave length is infinity like for the U-tube. Due to the nonlinearity in the waves, the magnitude of water particle velocity at the crest phase differs from at the trough phase and plays an important part to move the sediment near the seabed. The nonlinear wave develops a steady mean flow at a fixed position or streaming in the wave boundary layer and the sediments are moved by this streaming, which plays a very complicated role in the turbulent wave boundary.
