Bed slope effects on turbulent wave boundary layers: 1. Model validation and quantification of rough-turbulent results

A numerical model solving incompressible Reynolds-averaged Navier-Stokes equations, combined with a two-equation k-omega turbulence closure, is used to study converging-diverging effects from a sloping bed on turbulent (oscillatory) wave boundary layers. Bed shear stresses from the numerical model are first validated against hydraulically smooth and rough data from flat bed experiments in the form of wave friction factor diagrams. The results show that the model provides acceptable accuracy for wave orbital amplitude to roughness length ratios a/k(N) >= 20. Validation against experimental measurements for steady streaming induced by a skewed free stream velocity signal is also provided. We then simulate a series of experiments involving oscillatory flow in a convergent-divergent smooth tunnel, and a good match with respect to bed shear stresses and streaming velocities is achieved. The streaming is conceptually explained using analogies from steady converging and diffuser flows. A parametric study is undertaken to assess both the peak and time-averaged bed shear stresses in converging and diverging half periods under rough-turbulent conditions. The results are presented as friction factor diagrams. A local similarity condition is derived for relating oscillatory flow in a convergent-divergent tunnel, as considered herein, to shoaling shallow-water waves by matching spatial gradients in the free stream orbital length.