Predicting bed form roughness: the influence of lee side angle

Flow transverse bedforms (ripples and dunes) are ubiquitous in rivers and coastal seas. Local hydrodynamics and transport conditions depend on the size and geometry of these bedforms, as they constitute roughness elements at the bed. Bedform influence on flow energy must be considered for the understanding of flow dynamics, and in the development and application of numerical models. Common estimations or predictors of form roughness (friction factors) are based mostly on data of steep bedforms (with angle-of-repose lee slopes), and described by highly simplified bedform dimensions (heights and lengths). However, natural bedforms often are not steep, and differ in form and hydraulic effect relative to idealised bedforms. Based on systematic numerical model experiments, this study shows how the hydraulic effect of bedforms depends on the flow structure behind bedforms, which is determined by the bedform lee side angle, aspect ratio and relative height. Simulations reveal that flow separation behind bedform crests and, thus, a hydraulic effect is induced at lee side angles steeper than 11 to 18° depending on relative height, and that a fully developed flow separation zone exists only over bedforms with a lee side angle steeper than 24°. Furthermore, the hydraulic effect of bedforms with varying lee side angle is evaluated and a reduction function to common friction factors is proposed. A function is also developed for the Nikuradse roughness (k s), and a new equation is proposed which directly relates k s to bedform relative height, aspect ratio and lee side angle.

Flow conditions, bed form dimensions and shear stress experiments

Large asymmetric bed forms commonly develop in rivers. The turbulence associated with flow separation that develops over their steep lee side is responsible for the form shear stress which can represent a substantial part of total shear stress in rivers. This paper uses the Delft3D modeling system to investigate the effects of bed form geometry and forcing conditions on flow separation length and associated turbulence, and bed form shear stress over angle-of-repose (30 lee side angle) bed forms. The model was validated with lab measurements that showed sufficient agreement to be used for a systematic analysis. The influence of flow velocity, bed roughness, relative height (bed form height/water depth), and aspect ratio (bed form height/length) on the variations of the normalized length of the flow separation zone, the extent of the wake region (where the turbulent kinetic energy (TKE) was more than 70% of the maximum TKE), the average TKE within the wake region and the form shear stress were investigated. Form shear stress was found not to scale with the size of the flow separation zone but to be related to the product of the normalized extent of the wake region (extent of the wake region/extent of water body above the bed form) and the average TKE within the wake region. The results add to understanding of the hydrodynamics of bed forms and may be used for the development of better parameterizations of smallscale processes for application in large-scale studies.