Predicting bed form roughness: the influence of lee side angle
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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.
KeywordsFriction Factor Flow Separation Relative Height Bedforms Form Friction
This study was funded through the DFG Research Center/Cluster of Excellence “The Ocean in the Earth System”. Alice Lefebvre appreciates the support of GLOMAR – Bremen International Graduate School for Marine Sciences. Data will be made available through the Publishing Network for Geoscientific & Environmental Data (PANGAEA, http://www.pangaea.de). The manuscript was improved following the suggestions of two anonymous reviewers and the journal editors.
Compliance with ethical standards
Conflict of interest
The authors declare that there is no conflict of interest with third parties.
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