Difficulties are often encountered in estimating the bed shear stress in vegetated flows over a sediment bed due to complex interactions of the flow, sediment, and vegetation. Without involving any empirical partition of the bed friction and vegetation resistance, this study presents an analytical approach to evaluate the bed shear stress in the presence of vegetation in light of the phenomenological theory of turbulence. Then, the bed-load transport rate in vegetated flows is computed, with a result that agrees well with the bed-load transport formula developed for unvegetated flows. In addition, it is also shown that the present method is applicable not only to uniformly distributed vegetation but also to vegetation patches. However, further efforts are needed to extend the present model for flexible and submerged vegetation conditions.

In vegetated open channel flow, sediment transport is affected by both boundary shear and vegetation-induced turbulence. This study presents a theoretical derivation of the critical flow condition for incipient sediment motion, which is evaluated in the reach scale in the presence of emergent vegetation simulated with cylindrical rods. To take into account the combined effects of both mean flow and turbulence on sediment motion, a spatiotemporal average is applied to the force balance equation. The analysis shows that the critical condition can be formulated in terms of the dependence of the densimetric Froude number on the vegetation concentration for the condition of hydrodynamically rough turbulent flows. The derived theoretical formula is consistent with laboratory measurements reported in previous studies.

In the presence of vegetation in open channel flows, various physical processes, such as sediment transport, may be dominated by large-scale eddies, of which mechanisms are not well understood at present. In this study, we aimed to explore vegetation-affected turbulence from the perspective of energy spectral analysis. First, we conducted a series of laboratory experiments of open channel flows with submerged vegetation by varying the flow rate, water depth, and vegetation density. With flow velocities measured using the particle image velocimetry (PIV) technique, energy spectral analyses were then performed over several representative locations in the flow field. The results show that the Kelvin–Helmholtz (KH) vortices dominate the flow in the surface layer, while the shedding wake controls the flow in the vegetation layer, particularly downstream of individual vegetation stems. The normalized frequency of the KH vortices increases for flows with dense vegetation, of which the peak value, when normalized as the Strouhal number, has an average of 0.21. Furthermore, by applying Taylor's frozen turbulent hypothesis, it is shown that both the scale of the KH vortices and the penetration depth reduce when the vegetation becomes dense. Within the vegetation layer, the minimum of the peak streamwise wavelength is observed to be related to the shedding wake, while its maximum scales with the size of the penetrating KH vortices.

Local scour in a sediment bed varies depending on the type, size and shape of hydraulic structures, and the properties of approach flow and sediment particles. Published studies are hitherto confined primarily to empirical experiments based on particular types of hydraulic structure and there is almost no comparison of scour amongst different types of hydraulic structures. This study aims to provide an attempt to unify different types of clear‐water scour based on a new length scale, which is proposed to characterize the size of the large‐scale flow structure that governs scouring processes. The new length scale serves as a generalized hydraulic radius, which is applicable for all types of clear‐water scour related to junction flows at bridge piers and abutments, and wall jets including culverts. The analysis indicates that when normalized with the new length scale, the equilibrium scour depths can be described with a unified function of the densimetric Froude number, regardless of different scour types. In addition, this study also shows that the proposed function varies with the scour efficiency, in a fashion resembling the bedload function in the range of low to high transport regimes. This finding, which is founded on solid physical grounds, reveals that different kinds of local scour phenomena can be interpreted in unison rather than based on the individual type of hydraulic structures.