Modeling the turbulent boundary layer at the bottom of sea wave

We investigate the turbulent oscillatory flow generated by propagating surface waves close to the sea bottom focusing our attention on moderate values of the Reynolds number Rδ of the bottom boundary layer. For such moderate values of Rδ, turbulent fluctuations appear only during parts of the oscillation cycle and the flow recovers a laminar-like behaviour in the remaining parts. Different roughness sizes are considered and both the smooth and the rough flow regimes are analysed. The aim of the present investigation is to test the performance of different two-equation turbulence models to compute the flow field over both smooth and rough walls and for moderate values of the Reynolds number. The considered models are the e−ω model by Saffman and Wilcox (1974), two k−ω models (Wilcox (1988) and a model derived from Wilcox (1992)), a low-Reynolds number k−ε model (Foti and Scandura, 2004) and the model by Menter et al. (2003). To evaluate the performance of the models, the numerical predictions of the bottom shear stress are compared both with experimental measurements and with results of direct numerical simulations (DNS). All the models are found to provide fair results for high values of Rδ and for a smooth wall. For moderate values of Rδ, when turbulence is observed only during parts of the oscillating cycle, only one of the low-Reynolds number k−ω models is able to describe the rapid growth of the wall shear stress due to turbulence appearance. On the other hand, if a rough wall is considered, the performance of the models greatly depends on the size of the roughness.