Flow structure in fully developed open-channel flow over a mussel bed

Eddy-resolving numerical simulations are used to investigate the fully developed open-channel flow over an array of large-scale bed roughness elements placed on a rough or on a smooth surface that mimics freshwater mussels partially buried in a gravel or in a sand bed, respectively. The rough surface corresponds to the scanned surface of a gravel bed with uniformly distributed bed roughness. In this paper we analyse how the surface mussel coverage density, BC , the roughness of the bed surface on which the mussels are placed and the filtering activity of the mussels (i.e. the local mass exchange occurring through the mussels’ syphons) affect the double-averaged profiles of the streamwise velocity, turbulent kinetic energy, Reynolds and dispersive shear stresses, and the equivalent bed roughness height, $ K_{S} $ . Results show that similar to rough-bed boundary layers forming over sparse roughness elements in a deep environment (uniform free-stream velocity) and to those developing in a depth-limited environment (e.g. open channel), a multilayer analytical model can be used to approximate the double-averaged profile of the streamwise velocity over the flow depth, D , in the case of fully developed flow over a mussel bed. For similar values of BC and height of the protruding mussels, h , the scaling coefficient of the law-of-the-wake component supplementing the law-of-the-wall inside the inertial layer ( $h \lt z \lt D$ ) is found to be lower than values estimated for developing boundary layers over mussel beds. Results show that the equivalent roughness height increases monotonically with the surface mussel coverage density until BC ≈ 0.8, when the average distance between the mussels becomes sufficiently low for a skimming flow regime to develop over the top of the mussels. Bed roughness effects on the double-averaged variables are significant only for cases with $ \textit{BC} \lt 0.3$ . Results also show that mussel-induced velocity streaks are generated over the top of the mussels and the average transverse spacing of the streaks, λ , decays with increasing BC for constant h . The variation of $ \lambda / K_{S} $ with the non-dimensional distance from the bed surface is similar to that observed for fully developed flow over a rough bed with distributed roughness except for very low surface mussel coverage densities (i.e. $ \textit{BC} \lt 0.02 $ ) when λ remains constant (i.e. $ \lambda / K_{S} $ ≈ 10).