Optimisation of flow resistance and turbulent mixing over bed forms

Previous work on the interplay between turbulent mixing and flow resistance for flows over periodic rib roughness elements is extended to consider the flow over idealized shapes representative of naturally occurring sedimentary bed forms. The primary motivation is to understand how bed form roughness affects the carrying capacity of sediment-bearing flows in environmental fluid dynamics applications, and in engineering applications involving the transport of particulate matter in pipelines. For all bed form shapes considered, it is found that flow resistance and turbulent mixing are strongly correlated, with maximum resistance coinciding with maximum mixing, as was previously found for the special case of rectangular roughness elements. Furthermore, it is found that the relation between flow resistance to eddy viscosity collapses to a single monotonically increasing linear function for all bed form shapes considered, indicating that the mixing characteristics of the flows are independent of the detailed morphology of individual roughness elements.