The flow over bedload sheets and sorted bedforms

• Flow over coastal and fluvial sorted bedforms.
• Turbulence structure over alternate bands of fine and coarse sediments.
• Steady recirculating cells over sorted bedforms.
• Saffman׳s turbulence model (two-equation turbulence model).

Field surveys show the existence of morphological patterns (named bed load sheets in fluvial enviroments and sorted bedforms in coastal environments) which consist of alternate bands of coarse and fine sediments and are characterized by a negligible spatial variation of the bottom elevation. Previous analyses show that these bottom patterns are self-organizing features which are originated by the interaction of poorly sorted sediments, fractional sediment transport and turbulence dynamics. Presently, we describe the results of an investigation of turbulence dynamics over a flat bottom but characterized by alternate bands of small and large roughness. Turbulence characteristics are obtained by means of the two-equation turbulence model of Saffman (1970) which is shown to provide a reliable description of turbulence structure both in steady and oscillatory flows, as those generated in coastal environments by surface wave propagation. Moreover, the turbulence model can describe both smooth and rough walls and provide fair results also at moderate values of the Reynolds number. The results are validated by comparing the predictions of the model with the experimental data of Jensen et al. (1989) and Fredsøe et al. (1993) who measured the velocity field and the bottom shear stress under a turbulent oscillatory flow over a plane bed with a uniform roughness and sudden spatial change of the roughness size, respectively. The measurements of Fredsøe et al. (1993) were simulated also by Fuhrman et al. (2011) by means of the k–ωk–ω turbulence model of Wilcox, 2006 and Wilcox, 2008 and an indirect comparison of the model results with the results of Fuhrman et al. (2011) can be made. The investigation shows that the streamwise advection of turbulence plays a significant role such that turbulence is more intense over the rough bottom than over the smooth bottom, if a region close to the bottom is considered. However, moving far from the bottom, an opposite trend is found. Moreover, the results clearly show that the streamwise variations of the horizontal velocity component induce a significant vertical component of the velocity which should be taken into account if an accurate description of transport phenomena is to be obtained.