Bailard's sediment transport formulation in shelf sea conditions: comparison with observations using a clustering technique

A previously published wave-averaged version of Bailard's sediment transport formulation, intended for use in a numerical model of shelf sand transport, is compared against available field observations from literature. The objective was to test the performance of the transport relation over the wide range of hydrodynamical conditions that can occur at sea. A modified data analysis method was used to assess the reliability of the field observations. The modification consists of a method to cluster the data into classes to enable statistical analysis. The sediment transport formulation is part of the classification method. The method is in principle also suitable to reduce the size of data sets of non-cohesive sediment transport obtained with modern electronic equipment. The results show that the quality of the published field observations is fair, and that the wave-averaged Bailard formulation performs well for low and medium transport regimes in both currents and waves. For those conditions, it yields a slight overprediction of the transports, and a nearly uniform behaviour as a function of the conditions. The formulation underestimates transport rates for very high flow velocities in absence of waves, which is in agreement with earlier findings. The present version of Bailard's wave averaged sediment transport formulation is suitable for computing the local transport rates of fine to coarse sand on continental shelves in conditions ranging from small currents to moderate currents combined with non-breaking waves.     

Tidal eddies in a semi-enclosed basin: a model study

A modeling study has been carried out to support a Marine Management Plan for the Gulf of Kachchh, India and here the hydrodynamic part of the programme is described. The hydrodynamic model accurately predicts the tides and tidal currents present in the Gulf and these have been validated with the measured data, albeit at only a few locations. The time averaged residual currents obtained from the model for one lunar cycle clearly reproduce the complex, small-scale, topographically induced flows with several eddies. The existence of a dynamic barrier along Sikka-Mundra section, which divides the Gulf into two distinct dynamic systems, is very evident. The model is further used to predict the movement of surface floating particles launched at different locations in the Gulf, as an aid to determining floating pollutants. The results indicate that industries discharging wastes upstream of the barrier should use extreme caution, as these will remain in the vicinity for at least one lunar cycle.     

Long-term ferry-ADCP observations of tidal currents in the Marsdiep inlet

A unique, five-year long data set of ferry-mounted ADCP measurements in the Marsdiep inlet, the Netherlands, obtained between 1998 and 2003, is presented. A least-squares harmonic analysis was applied to the water transport, (depth-averaged) currents, and water level to study the contribution of the tides. With 144 tidal constituents, maximally 98% of the variance in the water transport and streamwise currents is explained by the tides, whereas for the stream-normal currents this is maximally 50%. The most important constituent is the semi-diurnal M₂ constituent, which is modulated by the second-largest S₂ constituent (about 27% of M₂). Compound and overtides, such as 2MS₂, 2MN₂, M₄, and M₆, are important in the inlet. Due to interaction of M₂ with its quarter-diurnal overtide M₄, the tidal asymmetry in the southern two thirds of the inlet is flood dominant. The amplitudes of all non-astronomic constituents are largest during spring tides, strongly distorting the water level and velocity curves. The M₂ water transport is 40° ahead in phase compared to the M₂ water level, reflecting the progressive character of the tidal wave in the inlet. The currents are strongly rectilinear and they are sheared vertically and horizontally, with the highest currents at the surface above the deepest part of the inlet. During spring tides, near-surface currents can be as large as 1.8 m s^− 1. Due to the relative importance of inertia compared to friction, the M₂ currents near the centre (surface) lag maximal 20° (3°) in phase with the currents near the sides (bottom). The tidal-mean currents are directed into the basin in the shallower channel to the south and out of the basin in the deeper channel to the north.     

The reflection of water waves by shear currents

The refraction and reflection of linear water waves entering a following jet-type current is considered. A short-wave asymptotic solution is presented and the reflection coefficient found. This varies continuously from zero when the waves are normal to the current to unity when they are very oblique to it. The trapping of waves by an opposing current is also considered.     

A velocity projection framework for inferring shallow water currents from surface tracer fields

To the extent that sea surface temperature and colors can be considered passive tracers, their motions can be tracked to estimate the current velocities, or a conservation equation can be invoked to relate their temporal variations to the velocities. We investigate the latter, the so-called tracer inversion problem, with a particular focus on (1) the conditions under which the problem can be rendered over-determined for least squares solutions, (2) the possibility of using the tracer conservation equation within the “velocity projection” framework to estimate subsurface current profiles in shallow coastal waters, and (3) the accuracy of the tracer inversion calculation in terms of the data resolution and noise. The velocity projection framework refers to relating surface motion, either measured directly or made visible by tracers, to the subsurface current motion through the equations of motion. The accuracy of the tracer inversion calculation is quantified in terms of the spatial and temporal resolution of the tracer distribution. In the presence of irreducible tracer noise, the accuracy of the inversion rapidly degrades, and it is shown that the inversion with velocity projection can help improve accuracy. The tracer inversion method developed in this study is applied to the satellite sea surface temperature data, and the velocity result is compared to the velocity measurements made with the shore-based HF Coastal Current Radar. The potential of improving the velocity estimation with the present approach is indicated.     

Advances in the Study of Moving Sediments and Evolving Seabeds

Sands and mud are continually being transported around the world’s coastal seas due to the action of tides, wind and waves. The transport of these sediments modifies the boundary between the land and the sea, changing and reshaping its form. Sometimes the nearshore bathymetry evolves slowly over long time periods, at other times more rapidly due to natural episodic events or the introduction of manmade structures at the shoreline. For over half a century we have been trying to understand the physics of sediment transport processes and formulate predictive models. Although significant progress has been made, our capability to forecast the future behaviour of the coastal zone from basic principles is still relatively poor. However, innovative acoustic techniques for studying the fundamentals of sediment movement experimentally are now providing new insights, and it is expected that such observations, coupled with developing theoretical works, will allow us to take further steps towards the goal of predicting the evolution of coastlines and coastal bathymetry. This paper presents an overview of our existing predictive capabilities, primarily in the field of non-cohesive sediment transport, and highlights how new acoustic techniques are enabling our modelling efforts to achieve greater sophistication and accuracy. The paper is aimed at coastal scientists and managers seeking to understand how detailed physical studies can contribute to the improvement of coastal area models and, hence, inform coastal zone management strategies.     

Suspended sediment transport in the German Wadden Sea—seasonal variations and extreme events

The German Wadden Sea (southern North Sea) sediments are composed of both cohesive and non-cohesive deposits. The spatial distribution patterns are mainly driven by wind-induced waves and tidal currents. Transport intensity and duration depend on the hydrodynamic conditions, which vary over time. In this paper, the transport of suspended sediment was investigated on seasonal, tidal and hourly time scales in the back-barrier system of Spiekeroog Island. Long- and short-term data of fair weather periods and two storm events were investigated based on stationary and mobile measurements of currents and waves by Acoustic Doppler Current Profiler (ADCP), in situ particle size and suspended sediment concentration (SSC) measurements by laser in situ scattering and transmissometry (LISST) as well as wind records. The ADCP backscatter intensities were calibrated by means of LISST volume concentration data in order to quantify longer term SSCs and fluxes in the back-barrier system. Values up to 120 mg l⁻¹ were recorded, but concentrations more commonly were below 60 mg l⁻¹. The long-term results confirm former observations of a balanced budget during low-energy (fair weather) conditions in the study area. In general, SSCs were higher during spring tides than during neap tides. The data also clearly show the remobilisation of sediment by tidal current entrainment. The records include two severe storm events, “Britta” (1st November 2006) and “Kyrill” (18th January 2007). The data reveal very complex temporal flow and transport patterns. During both storm events, the export of material was mainly controlled by the interaction of wind, waves and tidal phase. The typical ebb-dominance occurring during fair-weather conditions was temporarily neutralised and even reversed to a flood-dominated situation. During “Kyrill”, the wind and high-waves setup in conjunction with the tidal phase was even able to compress the duration of two successive ebb cycles by over 70%. Although SSCs increased during both storms and higher turbulence lifted particle clouds upwards, an export of suspended matter towards the North Sea was only observed under the conditions taking place during “Britta”. Such fluxes, however, are currently still difficult to quantify because the backscatter intensity during high energy events includes a substantial amount of noise produced by the high turbulence, especially near the water surface.     

Interaction of waves,currents and tides,and wave-energy impact on the beach area of Sylt Island

Erosion due to waves is an important and actual problem for most coastal areas of the North Sea. The objective of this study was to estimate the impact of wave action on the coastline of Sylt Island. From a 2-year time series (November 1999 to October 2001) of hydrological and wave parameters generated with a coupled wave–current modelling system, a period comprising storm ‘Anatol’ (3–4 December 1999) is used to investigate the effects of waves on currents and water levels and the input of wave energy into the coastline. The wave-induced stress causes an increase of the current velocity of 1 m/s over sand and an additional drift along the coast of about 20 cm/s. This produces a water level increase of more than 20 cm in parts of the tidal basin. The model system also calculates the wave energy input into the coastline. Scenario runs for December 1999 with a water level increase of 50 cm and wind velocity increased by 10% show that the input of the wave energy into the west coast of Sylt Island increases by 30% compared to present conditions. With regard to the forecasted near-future (Woth et al., Ocean Dyn 56:3–15, 2006) increase of strong storm surges, the scenario results indicate an increased risk of coastal erosion in the surf zone of Sylt Island.     

Radiation stress due to ocean waves and the resulting currents and set-up/set-down

The authors have developed a model to predict the radiation stresses in the coastal zone and to estimate currents and set-up/set-down of mean sea level. The values of radiation stress are calculated from velocity potential, which can be obtained by analytical means or from a finite element model of the elliptic extended mild slope equation depending on the complexity of the situation in question. The values of radiation stress are then input into a hydrodynamic model which gives the resulting set-up/set-down and currents caused by these stresses. The developed model includes convective acceleration and bottom friction. The radiation stress results of the model have been compared with analytical results and published values. Results for set-up/set-down and currents have been compared with published results for seven other similar models. The model has been compared with published results for set-up/set-down and currents created in the vicinity of a detached breakwater and also around a conical island. The results of the authors’ model compare well with the analytical results, and published results for similar models. An erratum to this article can be found at     

Analysis of directional wave fields using X-band navigation radar

The aim of this work is to present an approach to describe complex sea states including the ones consisting of superpositions of swell and wind sea components, using a nautical radar in X-band as a remote sensing technique. In the present article, the inversion method to obtain the spectral representation of the wave fields is described. The method is applied to analyse data obtained from simulation techniques, as well as from measurements obtained during oceanographic campaigns in the Bay of Biscay and North Sea.