RANS modelling of the turbulent boundary layer under a solitary wave

The flow field in the boundary layer at the bottom of a solitary wave is computed by means of the Reynolds averaged Navier–Stokes equations. Reynolds stresses are determined by means of the two-equation turbulence model by Saffman (Saffman, P.G., 1970. A model for inhomogeneous turbulent flow. Proceedings of the Royal Society of London. Series A: Mathematical and Physical Sciences 317 (1530), 417–433.) and Saffman and Wilcox (Saffman, P.G., Wilcox, D.C., 1974. Turbulence-model predictions for turbulent boundary layers. AIAA J. 12, 541–546.) which allows both the laminar and turbulent regime to be investigated along with the transition process. The results obtained for the smooth wall case show a fair agreement with the experimental measurements of Sumer et al. (Sumer, B.M., Jensen, P.M., Søerensen, L.B., Fredsøe, J., 2010. Coherent structures in wave boundary layers. Part 2. Solitary motion. J. Fluid Mech. 646, 207–231.) and with the direct numerical simulations of Vittori and Blondeaux (Vittori, G., Blondeaux, P., 2008. Turbulent boundary layer under a solitary wave. J. Fluid Mech. 615, 433–443.). The model allows to investigate the rough wall case, too. Attention is focused on the bottom shear stress and on its maximum positive (in the direction of wave propagation) and negative (in the direction opposite to the direction of wave propagation) values.