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.

Hydraulic conductivity and experiments of sediment beds

In marine environments, sediments from different sources are stirred and dispersed, generating beds that are composed of mixed and layered sediments of differing grain sizes. Traditional engineering formulations used to predict erosion thresholds are however, generally for unimodal sediment distributions, and so may be inadequate for commonly occurring coastal sediments. We tested the transport behavior of deposited and mixed sediment beds consisting of a simplified two-grain fraction (silt (D50 = 55 µm) and sand (D50 = 300 µm)) in a laboratory-based annular flume with the objective of investigating the parameters controlling the stability of a sediment bed. To mimic recent deposition of particles following large storm events and the longer-term result of the incorporation of fines in coarse sediment, we designed two suites of experiments: (1) "the layering experiment": in which a sandy bed was covered by a thin layer of silt of varying thickness (0.2 - 3 mm; 0.5 - 3.7 wt %, dry weight in a layer 10 cm deep); and (2) "the mixing experiment" where the bed was composed of sand homogeneously mixed with small amounts of silt (0.07 - 0.7 wt %, dry weight). To initiate erosion and to detect a possible stabilizing effect in both settings, we increased the flow speeds in increments up to 0.30 m/s. Results showed that the sediment bed (or the underlying sand bed in the case of the layering experiment) stabilized with increasing silt composition. The increasing sediment stability was defined by a shift of the initial threshold conditions towards higher flow speeds, combined with, in the case of the mixed bed, decreasing erosion rates. Our results show that even extremely low concentrations of silt play a stabilizing role (1.4% silt (wt %) on a layered sediment bed of 10 cm thickness). In the case of a mixed sediment bed, 0.18% silt (wt %, in a sample of 10 cm depth) stabilized the bed. Both cases show that the depositional history of the sediment fractions can change the erosion characteristics of the seabed. These observations are summarized in a conceptual model that suggests that, in addition to the effect on surface roughness, silt stabilizes the sand bed by pore-space plugging and reducing the inflow in the bed, and hence increases the bed stability. Measurements of hydraulic conductivity on similar bed assemblages qualitatively supported this conclusion by showing that silt could decrease the permeability by up to 22% in the case of a layered bed and by up to 70% in the case of a mixed bed.