Experimental study on toe scouring at sloping walls with gravel foreshores

Sea defences, such as urban seawalls can fail due to the development of a scour hole at the toe of the structure. The scour depth or the information on ground levels at the structure toe is required for the sustainable management of coastal defences, due to its influence on the structural performance. This research reports and summarises the main findings of a new laboratory study on toe scouring at a smooth sloping wall with permeable gravel foreshore. A set of small-scale laboratory experiments of wave-induced scouring at sloping seawalls were conducted. Two gravel sediments of prototype d50 values of 13 mm and 24 mm were used to simulate the permeable 1:20 (V:H) gravel beach configurations in the front of a smooth 1 in 2 sloping wall. Each experiment comprised of a sequence of around 1000 random waves of a JONSWAP energy spectrum with a peak enhancement factor of 3.3. The relationship of the scour depth with toe water depth, Iribarren number, and wall slope were investigated from the test results of this work and through a comparison with available datasets in the literature. The results of this study showed that the relative toe water depth and Iribarren number influence the relative toe scour depth at a sloping structure on a shingle beach. Within the experimental limitations, the maximum toe scour depths were observed for the experiments under spilling and plunging wave attack

Wave overtopping and toe scouring at a plain vertical seawall with shingle foreshore : a physical model study

This paper describes a physical model study to investigate the wave overtopping and toe scouring at a plain vertical wall with a shingle foreshore. A matrix of 180 experimental test conditions were performed in a 2D wave flume, with an approximate scale of 1:50. The study investigates the baseline overtopping characteristics at a plain vertical wall on an impermeable 1:20 foreshore slope and compares the results with two permeable 1:20 shingle beach foreshores with prototype d50 values of 13 mm, and 24 mm respectively. For impulsive wave conditions, it was found that the mean overtopping rate was reduced by factor 3 for the d50 of 13 mm, and a factor of 4 for the d50 of 24 mm. For non-impulsive waves, the reduction factors were 1.5 for d50 of 13 mm and 2 for d50 of 24 mm. Prior to this study, limited design guidance was available to predict the mean overtopping discharges and mean sediment rates at vertical seawalls on permeable shingle foreshores. Therefore, a new set of prediction formulae are proposed in this study, based on the new laboratory test results, and a comparison with the available prediction methods in literature for vertical seawalls subjected to both impulsive and non-impulsive wave conditions

Inclusion of seasonal variation in river system microbial communities and phototroph activity increases environmental relevance of laboratory chemical persistence tests

Regulatory tests assess crop protection product environmental fate and toxicity before approval for commercial use. Although globally applied laboratory tests can assess biodegradation, they lack environmental complexity. Microbial communities are subject to temporal and spatial variation, but there is little consideration of these microbial dynamics in the laboratory. Here, we investigated seasonal variation in the microbial composition of water and sediment from a UK river across a two-year time course and determined its effect on the outcome of water-sediment (OECD 308) and water-only (OECD 309) biodegradation tests, using the fungicide isopyrazam. These OECD tests are performed under dark conditions, so test systems incubated under non-UV light:dark cycles were also included to determine the impact on both inoculum characteristics and biodegradation. Isopyrazam degradation was faster when incubated under non-UV light at all collection times in water-sediment microcosms, suggesting that phototrophic communities can metabolise isopyrazam throughout the year. Degradation rate varied seasonally between inoculum collection times only in microcosms incubated in the light, but isopyrazam mineralisation to 14CO2 varied seasonally under both light and dark conditions, suggesting that heterotrophic communities may also play a role in degradation. Bacterial and phototroph communities varied across time, but there was no clear link between water or sediment microbial composition and variation in degradation rate. During the test period, inoculum microbial community composition changed, particularly in non-UV light incubated microcosms. Overall, we show that regulatory test outcome is not influenced by temporal variation in microbial community structure; however, biodegradation rates from higher tier studies with improved environmental realism, e.g. through addition of non-UV light, may be more variable. These data suggest that standardised OECD tests can provide a conservative estimate of pesticide persistence end points and that additional tests including non-UV light could help bridge the gap between standard tests and field studies

Vertical variation of mixing within porous sediment beds below turbulent flows

River ecosystems are influenced by contaminants in the water column, in the pore water and adsorbed to sediment particles. When exchange across the sediment-water interface (hyporheic exchange) is included in modelling, the mixing coefficient is often assumed to be constant with depth below the interface. Novel fibre-optic fluorometers have been developed and combined with a modified EROSIMESS system to quantify the vertical variation in mixing coefficient with depth below the sediment-water interface. The study considered a range of particle diameters and bed shear velocities, with the permeability Péclet number, image between 1,000 and 77,000 and the shear Reynolds number, image between 5 and 600. Different parameterisation of both an interface exchange coefficient and a spatially variable in-sediment mixing coefficient are explored. The variation of in-sediment mixing is described by an exponential function applicable over the full range of parameter combinations tested. The empirical relationship enables estimates of the depth to which concentrations of pollutants will penetrate into the bed sediment, allowing the region where exchange will occur faster than molecular diffusion to be determined

Laboratory investigation of overtopping at a sloping structure with permeable shingle foreshore

The vast majority of overtopping data applied in EurOtop (2018) has been made from small-scale measurements with impermeable foreshore slopes. This article describes a comprehensive two-dimensional experimental study conducted in a small-scale 1:50 wave flume. Results are presented for the overtopping performance at a 1 to 2 sloping wall, undertaken on both impermeable and permeable foreshore slopes. Within experimental limitations, the results demonstrated that the mean overtopping rate is reduced by up-to a factor of 4, when compared to the predictions reported for the impermeable slope. However, when comparing maximum individual wave-by-wave overtopping volumes, no significant differences were observed. These results are intended for practitioners and researchers predicting wave overtopping characteristics at sloping structures with permeable gravel foreshores

Application of smoothed particle hydrodynamics in evaluating the performance of coastal retrofit structures

This study develops an accurate numerical tool for investigating optimal retrofit configurations in order to minimize wave overtopping from a vertical seawall due to extreme climatic events and under changing climate. A weakly compressible smoothed particle hydrodynamics (WCSPH) model is developed to simulate the wave-structure interactions for coastal retrofit structures in front of a vertical seawall. A range of possible physical configurations of coastal retrofits including re-curve wall and submerged breakwater are modelled with the numerical model to understand their performance under different wave and structural conditions. The numerical model is successfully validated against laboratory data collected in 2D wave flume at Warwick Water Laboratory. The findings of numerical modelling are in good agreement with the laboratory data. The results indicate that recurve wall is more effective in mitigating wave overtopping and provides more resilience to coastal flooding in comparison to base-case (plain vertical wall) and submerged breakwater retrofit

Singular Continuous Spectrum for the Laplacian on Certain Sparse Trees

We present examples of rooted tree graphs for which the Laplacian has singular continuous spectral measures. For some of these examples we further establish fractional Hausdorff dimensions. The singular continuous components, in these models, have an interesting multiplicity structure. The results are obtained via a decomposition of the Laplacian into a direct sum of Jacobi matrices

Densities of short uniform random walks

We study the densities of uniform random walks in the plane. A special focus is on the case of short walks with three or four steps and less completely those with five steps. As one of the main results, we obtain a hypergeometric representation of the density for four steps, which complements the classical elliptic representation in the case of three steps. It appears unrealistic to expect similar results for more than five steps. New results are also presented concerning the moments of uniform random walks and, in particular, their derivatives. Relations with Mahler measures are discussed.Comment: 32 pages, 9 figure