Scour at the head of a vertical-wall breakwater

This paper presents the results of an experimental investigation on the near-bed flow patterns, the bed shear stress amplification and scour around the head of a vertical-wall breakwater, using regular waves. The Keulegan-Carpenter number (KC), based on the diameter of the breakwater head, is found to be the major parameter that governs the flow and the equilibrium scour depth. Basic flow structures are identified as function of KC. The scour depth is found to increase with increasing the Keulegan-Carpenter number. The necessary extent of the conventional stone protection is studied. An empirical formula is worked out for the width of the protection layer as function of KC. Also, the effects of head shape, the angle of attack and the presence of a co-directional current are investigated. The results indicate that the scour depth is increased considerably in the presence of a current. Likewise, the scour depth is increased when the head shape is changed from a round shape to a sharp-edged one. It is found that the angle of attack is also an influencing factor as regards the scour depth.     

A note on the deflection of a baroclinic current by a continental shelf

The deflection, at a step-shelf fronted coast, of a constant potential vorticity current in a reduced-gravity, inviscid model ocean is studied theoretically. The step shelf, with a depth smaller than the reservoir depth, forces the uplifting of the approaching current and causes water column foreshortening, leading to relative vorticity generation that enhances current deflection to the right (facing the coast). As a consequence, in comparison to the case of a vertical wall coast, the proportion of the transport to the right is increased. For normal incidence for a shelf-depth/reservoir-depth ratio of 0.3 and shelf width to deformation radius ratio of 1.5, more than 90% of the approaching current transport goes to the right and less than 10% to the left. In addition, the (barotropic) dynamic pressure at the coast is low to the right and high to the left (with the highest pressure at the stagnation point). In the vertical wall case, the wall pressures on the flank are equal. For oblique incidence from the left, the deflection to the left is drastically reduced. In fact, there is practically no steady-state flow diverted to the left (less than 2%) when the approach angle is greater than 60° to the left of normal. In the vertical wall case, the same angle would have to be 90° for the flow to the left to vanish, namely only when the approach current is parallel to the coast to the right.     

Probabilistic modelling of long-term beach evolution near segmented shore-parallel breakwaters

This paper presents a new framework for probabilistic modelling of long-term beach evolution in the vicinity of detached breakwaters. The study focuses on the key physical processes contributing to beach variability over a range of spatial and temporal scales. Based on a one-line model, the framework is enhanced with sophisticated solutions for beach-wave-structure interaction, diffraction together with a treatment of varying tide level. The sediment transport rate is calibrated at regional and local levels using data from bespoke field campaigns and site-specific coefficients are proposed. Monte Carlo simulation is conducted for long-term shoreline simulation under a sequence of time varying sequence of waves, currents and tidal levels. The results of the Monte Carlo simulation give an insight into the statistical characteristics of beach behaviour within the defence system. In particular, regions within the scheme that are relatively stable and those that exhibit greater natural fluctuations are identified.     

Processes affecting deposition of sediment in a small, morphologically complex lake

Devil Lake is morphologically complex as a result of Pleistocene glacial erosion of the Frontenac Axis of the Canadian Shield. In order to assess the processes causing highly variable sedimentation in the lake, we monitored currents, suspended sediment and temperature in the lake before and during autumn overturn in 2002. Strong summer thermal stratification (stability number to 0.11 s^–1 declining with the approach of overturn) was insufficient to prevent a dynamic response in the hypolimnion to wind forcing. Superimposed on a gradual increase in suspended sediment concentration in the last weeks of stratification from less than 2 g/l to about 30 g/l were shorter-term rises lasting up to several days. Associated with these events was an increase in particle size of the sediment from a mode of 40–50 to 150–200 m ascribed to flocculation from primary particles. These events culminated in rapid (<1 h) clearing of the water associated with strong, sustained winds over the lake, especially from the southwest. After overturn, the events were more frequent, and flocculation was unable to develop as well in the more vigorous circulation. However, currents in the hypolimnion occurred throughout the period before, during and after overturn with speed related to wind speed, but direction largely independent of wind direction. The results represent an approach to understanding the nature of sedimentary processes and thus to strengthening the use of sedimentary records as proxy in environmental and paleoenvironmental assessment.     

A dataset of global ocean surface currents for 1999-2007 derived from Argo float trajectories: Comparison with surface drifter and TAO measurements

A dataset of surface current vectors with error estimate from 1999 to 2007 is derived from the trajectories of the Array for Real-time Geostrophic Oceanography （Argo） drifting on surface over the global ocean. The error of the estimated surface currents is about 4.7 cm s-1 which is equivalent to the accuracy of the currents determined from the surface drifters. Geographically, the Argo-derived surface currents can fill many gaps left by the Global Drifter Program due to the greater number of floats, and can provide a complementary in situ observational system for monitoring global ocean surface currents. The surface currents from the Argo floats are compared with the surface drifter-derived currents and the Tropical Atmosphere Ocean program （TAO） measurements. The comparisons show good agreement for both the current amplitude and the direction of surface currents. Results indicate the feasibility of obtaining ocean surface currents from the Argo array and of combining the surface currents from Argo and the ocean surface drifters for in situ mapping of the global surface currents. The authors also make the dataset available to users of interest for many types of applications.     

Onset of scour below pipelines and self-burial

This paper summarizes the results of an experimental study on the onset of scour below and self-burial of pipelines in currents/waves. Pressure was measured on the surface of a slightly buried pipe at two points, one at the upstream side and the other at the downstream side of the pipe, both in the sand bed. The latter enabled the pressure gradient (which drives a seepage flow underneath the pipe) to be calculated. The results indicated that the excessive seepage flow and the resulting piping are the major factor to cause the onset of scour below the pipeline. The onset of scour occurred always locally (but not along the length of the pipeline as a two-dimensional process). The critical condition corresponding to the onset of scour was determined both in the case of currents and in the case of waves. Once the scour breaks out, it will propagate along the length of the pipeline, scour holes being interrupted with stretches of soil (span shoulders) supporting the pipeline. As the span shoulder gets shorter and shorter, more and more weight of the pipeline is exerted on the soil. In this process, a critical point is reached where the bearing capacity of the soil is exceeded (general shear failure). At this point, the pipe begins to sink at the span shoulder (self-burial). It was found that the self-burial depth is governed mainly by the Keulegan–Carpenter number. The time scale of the self-burial process, on the other hand, is governed by the Keulegan–Carpenter number and the Shields parameter. Diagrams are given for the self-burial depth and the time scale of the self-burial process.     

Modelling the wave-current interactions in an offshore basin using the SWAN model

The theoretical background of the wave-current interactions, including the transformation of the wave spectrum and breaking waves due to currents, are first presented in this work. In the next part of the work, experimental data resulted from studies performed in an offshore wave basin of the Danish Hydraulic Institute concerning the wave-current interactions were presented in parallel with some wave model simulations performed in similar conditions. SWAN, which is presently the state-of-the-art spectral model for the wave transformations, was adopted for performing numerical simulations. In general, a good agreement was encountered between the experimental data and the simulation results.     

Long-term evolution of sand waves in the Marsdiep inlet. II: Relation to hydrodynamics

A discussion is presented about the mechanisms that govern the spatial and seasonal variability in sand-wave height and migration speed in the 4 km wide Marsdiep tidal inlet, the Netherlands. Since 1998, current velocities and water depths have been recorded with an ADCP that is mounted under the ferry ‘Schulpengat’. In this paper, the current measurements were used to explain the sand-wave observations presented in Buijsman and Ridderinkhof [this issue. Long-term evolution of sand waves in the Marsdiep inlet. I: high-resolution observations. Continental Shelf Research, doi:10.1016/j.csr.2007.10.011]. Across nearly the entire inlet, the sand waves migrate in the flood direction. In the flood-dominated southern part of the inlet, the ‘measured’ (i.e. based on sand-wave shape and migration speed) and predicted bedload transport agree in direction, magnitude, and trends, whereas in the ebb-dominated northern part the predicted bedload and suspended load transport is opposite to the sand-wave migration. In the southern part, 55% of the bedload transport is due to tidal asymmetries and 45% due to residual currents. In addition to the well-known tidal asymmetries, asymmetries that arise from the interaction of _M2${\mathrm{M}}_2$ and its overtides with _S2${\mathrm{S}}_2$ and its compound tides are also important. It is hypothesised that in the northern part of the inlet the advection of suspended sand and lag effects govern the sand-wave migration. The relative importance of suspended load transport also explains why the sand waves have smaller lee-slope angles, are smaller, more rounded, and more three-dimensional in the northern half of the inlet. The sand waves in this part of the inlet feature the largest seasonal variability in height and migration speed. This seasonal variability may be attributed to the tides or a seasonal fluctuation in fall velocity. In both cases sediment transport is enhanced in winter, increasing sand-wave migration and decreasing sand-wave height. The influence of storms and estuarine circulation on the sand-wave variability is negligible.     

Modelling the Gibraltar Strait/Western Alboran Sea ecohydrodynamics

The ecohydrodynamics of the Gibraltar Strait and the Western Alboran Sea is investigated using a 3-D, two-way nested, coupled hydrodynamic/plankton ecosystem model, exploiting the MEDATLAS climatological database. A high-resolution model (~1 km) of the Gibraltar/Western Alboran region embedded within a coarse-resolution model of the West Mediterranean (~5 km) is implemented. The model seasonal climatology of the 3-D circulation and the flow characteristics at the Gibraltar Strait and the Alboran Sea are discussed, and their impact on the plankton ecosystem evolution is explored. An important ecohydrodynamic feature produced by the model is a permanent upwelling zone in the northwestern part of the Alboran Sea in agreement with observations. Model results show that both horizontal and vertical current intensity of the Atlantic Jet increases progressively at the strait to obtain maximum values in the northeastern Mediterranean entrance, inducing an upward displacement of the nitracline. The nutrient-rich water transport through the strait along with the generation of cyclonic vorticity in the northwestern Alboran Sea result in the accumulation of nutrients there and thus induce a permanent fertilisation of this area.