Wave-induced Bed Shear Stress Research Articles

Spatio-Temporal Variation in Suspended Sediment during Typhoon Ampil under Wave–Current Interactions in the Yangtze River Estuary

Suspended sediment plays a major role in estuary morphological change and shoal erosion and deposition. The impact of storm waves on sediment transport and resuspension in the Yangtze River Estuary (YRE) was investigated using a 3D coupling hydrodynamic-wave model with a sediment transport model during Typhoon Ampil. This model has been validated in field observations of water level, current, wave, and sediment concentration. The model was run for tide only, tide + wind, tide + wind and wave forcing conditions. It was found that: (1) typhoons can increase the suspended sediment concentration (SSC) by enhancing bed shear stress (BSS), especially in the offshore area of the YRE, and there is hysteresis between SSC and BSS variation; (2) exponential and vertical-line types are the main vertical profile of the SSC in the YRE and typhoons can strengthen vertical mixing and reconstruct the vertical distribution; and (3) waves are the dominating forcing factor for the SSC in the majority of the YRE through wave-induced BSS which releases sediment from the seabed. This study comprehensively investigates the spatio-temporal variation in SSC induced by Typhoon Ampil in the main branch of the YRE, which provides insights into sediment transport and resuspension during severe storms for estuaries around the world.

Wave, flow, and suspended sediment dynamics under strong winds on a tidal beach

Tidal beaches are shaped by intense wave-current interactions, leading to dynamic sediment erosion and accretion, which can be further complicated by strong winds. In this study, field observations were conducted on a tidal beach at the junction of Yangtze Estuary and Hangzhou Bay (China), to investigate the dynamics of wave, flow, and suspended sediment under strong winds. Observations were carried out synchronously at two sites on the middle and lower intertidal beach covering 4 semidiurnal tides (52 h) including a ∼20 h-long strong wind period. During the strong wind period, wave motions and flood currents were significantly enhanced, leading to a high combined wave-current bed shear stress (τcw). The wave-induced bed shear stress (τw) greatly exceeded current-induced bed shear stress (τc). Breaking waves generated turbulence at the surface and amplified the near-bed turbulent Reynolds stress (−u′w′‾ and −v′w′‾) at the shallow, middle intertidal beach. The intense hydrodynamics and turbulence kept sediments in suspension and hindered any settling, resulting in net erosion of the intertidal beach. These findings provide valuable insights into the complex interplay among waves, currents, and sediment dynamics under short-duration strong winds on tidal beaches. A key emphasis is placed on the significant role of breaking waves, underscoring the critical importance of their contribution to near-bed turbulence.

Optimal wave reflection as a mechanism for seagrass self-organization

Ecosystems threatened by climate change can boost their resilience by developing spatial patterns. Spatially regular patterns in wave-exposed seagrass meadows are attributed to self-organization, yet underlying mechanisms are not well understood. Here, we show that these patterns could emerge from feedbacks between wave reflection and seagrass-induced bedform growth. We derive a theoretical model for surface waves propagating over a growing seagrass bed. Wave-induced bed shear stress shapes bedforms which, in turn, trigger wave reflection. Numerical simulations show seagrass pattern development once wave forcing exceeds a critical amplitude. In line with Mediterranean Sea field observations, these patterns have half the wavelength of the forcing waves. Our results raise the hypothesis that pattern formation optimizes the potential of seagrass meadows to reflect wave energy, and a clear direction for future field campaigns. If wave-reflecting pattern formation increases ecosystem resilience under globally intensifying wave climates, these ecosystems may inspire nature-based coastal protection measures.

Sensitivity of sheltered mudflats to wind events

The impact of waves on the morphological changes of sheltered mudflats is less well studied compared to that on open flats. To investigate the sensitivity of low-energy sheltered mudflats to hydrodynamics such as waves, we carried out in situ measurements of bed level, currents, and waves on the middle flat of a sheltered mudflat in a bay in southern China. Two 1-month measurements, March 26–26 April 2021, and July 8–8 August 2021, were performed for repetition. We found that the sheltered system was not as stable as it appeared. The maximum intratidal bed-level variation, ΔZ, was <5 mm in calm conditions. However, wind speeds slightly highly than 3.0 m/s, under which significant wave height was approximately 0.1 m, triggered significant bed-level variation patterns, with ΔZ reaching up to 2 cm. Intratidal bed-level change patterns depend on the relative dominance of waves and currents: low τc (current-induced bed shear stress) and high τw (wave-induced bed shear stress) promote the generation and migration of bed ripples; comparable τc and τw, with medium-to-high values, lead to non-cyclic bed-level change patterns; high τc and high τw result in bed accumulation/degradation superimposed by bed ripple migration. From a long-term perspective, i.e. in the time scale of month to year, sheltered mudflats are stable systems, and their high sensitivity causes short-term significant bed-level variation. The sensitivity and stability of sheltered mudflats must be further investigated to explore the effects of human intervention and global climate change.

The effect of waves in hydrodynamics, stratification, and salt wedge intrusion in a microtidal estuary

Waves have been found to modulate circulation, stratification, and sediment dynamics in several estuaries, mainly near the mouth. This study analyzes the effects of waves on the hydrodynamics, stratification process, and dynamics of the salt wedge in an estuary with a microtidal range, high fluvial and sediment discharges, and dominated by waves: the Magdalena River estuary (MRE). It is, under low flow conditions, a highly stratified, salt wedge type. Field measurements and the MOHID 3D modeling system, 2D coupled with the SWAN model, were used for this purpose. The low flow seasons of 2018 (February-March) and 2020 (March) were taken as case studies. Results show that when considering wave effects in the numerical simulations, more realistic conditions are reproduced in the circulation patterns and salinity distribution in the outer estuary. Variations in velocity patterns and salinity distribution are found between the mouth and 2 km upstream of the mouth when comparing the simulations with and without waves, especially in the mixing layer. These variations in hydrodynamics and stratification may be associated with increased wave-induced bed shear stress, variations in barotropic and baroclinic acceleration, and increased vertical mixing. At 2 km into the river channel, the reduction in wave height energy of 95% and changes in salinity distribution are already lower than 2%. In addition, it was observed that waves do not generate significant changes in the dynamics of the salt wedge, which is mainly affected by the diurnal tidal cycle, presenting variations in the length of the intrusion of up to 1 km, and in the magnitude of the longitudinal salinity gradient at the salt front, presenting low salinities at high tide when the wedge enters, and high salinities at low tide, in its retreat.

Real-time and long-term monitoring of waves and suspended sediment concentrations over an intertidal algal reef

Suspended sediment concentration (c) has been considered a critical environmental factor in reef habitats; however, the values and variations of c are not evident in a unique reef mainly created by crustose coralline algal concretions compared to abundant studies in coral reefs. The results of real-time and long-term monitoring of waves and c over the intertidal algal reef are reported because of the construction of an offshore industrial harbor near the reef. The real-time monitoring systems were based on techniques, including optical backscatter sensors (OBSs) for measuring c, pressure sensors for measuring waves, data loggers, and wireless networks for data transmission. The instruments sampled every hour and ran continuously and automatically for years. The OBS measurement was compared and validated with biweekly water sampling. A good correlation between the results of the two methods was observed. Nevertheless, more calibrations of OBSs in different seasons reduced the variance between the two methods over a year-long timescale. The year-long data showed a remarkable seasonal variation in c. The average c was approximately 140 mg/l during the winter season, while it was only approximately 70 mg/l during the summer season. The observed c was higher than that in other coral reef environments; the elevated and highly variable c, ranging from approximately 0 to 500 mg/l, may be one factor that creates the unique algae reef environment. The year-long measurement of waves and c showed that the variation in c was mainly due to the variation in waves in different seasons and was well correlated with the wave-induced bed shear stress. The real-time and long-term data measured by the system will aid in better understanding and providing useful environmental data for accessing future environmental changes and protecting reef habitats.

The role of a remote tropical cyclone in sediment resuspension over the subaqueous delta front in the Changjiang Estuary, China

This study investigates the sediment resuspension and the resultant morphological changes over the subaqueous delta front in the Changjiang Estuary (CJE). An in-situ observation platform equipped with multi-sensor instruments was deployed in the CJE to measure the currents, waves, and suspended sediment concentrations (SSC) when a typical remote tropical cyclone, Sanba, passed through the waters over 540 km away from the CJE from September 15 to 17 in 2012. In addition, a current-wave-coupled numerical model was employed to simulate the spatial and temporal variations of the waves, currents, and sediment transport. The numerical simulation accurately captures the sharp increases in wave-induced bed shear stress and associated SSC, as indicated in the field measurements during the tropical cyclone period. Remarkable erosional patterns are observed over the subaqueous delta, which highlight the role of the remote tropical cyclone in sediment suspension and short-term morphological changes in the CJE. Moreover, the simulated erosional pattern agrees well with the sediment coarsening area observed between the 2 and 10 m isobaths. Analyses of the wave spectrum suggest that the bed shear stresses induced by the swells prevail over those induced by the wind waves during the tropical cyclone period. In addition, two simulation runs with ideal wind fields were performed to clarify the contribution of the swells propagated from the outer sea to the sediment transport. Overall, this study suggests that the erosion trends of the subaqueous deltas observed in the CJE are largely determined by the waves, and the swells produced by tropical cyclone events can significantly facilitate such a trend.

Erosion of the coastal Mekong delta: Assessing natural against man induced processes

The Lower Mekong Delta Coastal Zone (LMDCZ) is emblematic of the coastal erosion problem facing many tropical deltas. Over the last 3500 years, large river sediment fluxes expanded the delta seaward, and waves and currents formed the Ca Mau Peninsula to the southwest. Since the middle of the 20th century, the LMDCZ is affected by various human activities that include reduction of river fluxes due to damming and sand mining, land subsidence due to groundwater extraction, and reduction of protective coastal mangroves in favor of agriculture and aquaculture. Coastal erosion is observed along many sections of the delta, with a rate of up to 50 m per year in some areas. However, the role of human activities remains difficult to assess because of its complexity. The present modeling study is designed to sort out the contribution of natural hydrodynamic redistribution of sediments from man-induced erosion. The modeling system used is based on CROCO, forced by global reanalyses at the boundaries and at the surface, including wave statistics (required by the sediment transport model). Tides and realistic river forcing are also included. Calibration and validation relies on a combination of in situ and remotely-sensed observations, and laboratory experiments. Once validated, coastal dynamics are investigated by performing sensitivity experiments for both the hydro- and sediment dynamics. The results suggest that while wind is the main factor driving the coastal currents, the sediment dynamics is essentially the result of re-suspension due to wave-induced bed shear stress. The suspended sediments are then redistributed by coastal currents that are not limited to the nearshore zone. Strong seasonality of the process is observed with the northeast winter monsoon being the season of strongest re-suspension and sediment redistribution. The annual sediment budget is characterized by important local disequilibrium, with alongshore patterns that are in agreement with the observed shoreline evolution. The effect of a decrease in river sediment supply is difficult to evaluate because the estuarine zone is still in accretion, apart from the particular case of Go Cong shores. Far from the estuarine zone, subsidence is an additional strong candidate to explain erosion in areas that should naturally be accreting. Synthesizing these results, the study proposes a first attempt at a “taxonomy and geography” of processes along the coastal Mekong delta that can explain the recent observations of shoreline changes and help design protection measures.

Field investigation of bedform morphodynamics under combined flow

Fieldwork was conducted at the Red Cliff sandbar located in the upper Humber Estuary in order to investigate bedform dynamics under different hydrodynamic conditions related to combinations in tidal and wave-generated currents. A fixed mooring was deployed to obtain current flow and wave properties across the sand bar site at both spring and neap tidal flows and during conditions of high wind generated waves. A terrestrial laser scanner was used to scan the sandbar during low water across the various forcing conditions, acquiring detailed information of ripple geometries. Under spring tide and calm wave conditions, two-dimensional asymmetrical ripples with straight crest lines were generated on the sandbar. Surveys were also conducted during strong winds. Prior to high-wind-waves, two-dimensional symmetrical and washed-out ripples were observed, during spring and neap tidal conditions respectively. The lengths of these ripples were almost the same as those generated under current only conditions, but their heights were relatively smaller. After the strong wind periods, 2D current-induced ripples were replaced by flatbed conditions and 2D symmetrical wash-out ripples, which indicates wave-induced bed shear stress is enhanced by the presence of a tidal current. Most pertinently our study reveals discrepancies between field observations and existing predictions of bed configurations that are largely based on laboratory investigations. This is likely due to a larger grain size distribution in field conditions and due to turbulence dampening by high concentrations of suspended clay particles. The study thus highlights a need to extend a range of field investigations that explore the current deficiencies in our abilities to predict bedforms and bedform dynamics in estuarine systems.

Bed shear stress and turbulence characteristics under unsteady flows

A series of laboratory experiments were conducted to investigate the turbulence and bed shear stress characteristics under solitary waves and dam break flows. The Laser Doppler velocimetry (LDV) systems were used to measure the velocity profile very near the bottom. A method was developed to find the wave-induced bed shear stress over a smooth bed from the measured velocities within or near the viscous sub-layer. A unified 2D numerical model was developed to simulate the entire flow field from bottom to free surface. The model solves the Reynolds Averaged Navier-Stokes (RANS) equations, with the BSL k-ω turbulence closure model that can capture the turbulence inside and outside of boundary layer. The numerical results were compared to the experimental data and available theories in terms of free surface displacement, mean velocity, turbulence intensity, and bed shear stress. Discussions were made on the effects of the turbulence characteristics on changing the patterns of mean velocity profile and bed shear stress. Further efforts were made to revisit the existing boundary layer theories, trying to quantifying the role of free stream velocity and acceleration as well as eddy viscosity in modifying the response properties of the bed shear stress under unsteady flows. A formula was proposed to calculate the instantaneous bed shear using the free stream velocity and acceleration. The results using the present formula are compared to those from the earlier works for solitary wave, dam break wave, and saw-tooth wave.

Numerical Modeling of Long-Term Biogeochemical Processes and Its Application to Sedimentary Bed Formation in Tokyo Bay

Even though models of water quality have become increasingly detailed over time, their applicability to analyze long-term effect on sedimentary bed formation is yet to be clarified. Hence, an integrated, layer-resolved, process-based, sediment–water coupled, long-term robust, three-dimensional (3D) ecosystem model, including realistic sedimentary and pelagic processes, was developed. The constituents of the integrated model included a multi layered ecosystem model, a quasi-three dimensional hydrodynamic model, a wave hindcasting model, and a sediment deposition and erosion model. Because numerical modeling difficulties arise in setting the initial conditions, especially for a sedimentary bed, this novel modeling approach suggests to initiate the model with the simplest initial conditions of no particulate organic carbon content (POCC) and uniform inorganic sediment distribution. The model was applied to Tokyo Bay and quasi-steady state POCC in the sediment was obtained through long-term computation with realistic sedimentary and pelagic processes. Wave induced bed shear stress (WBSS) is critical for sediment erosion and spatial movement of sediment pollution, while a stable morphology is determined by the balance between the current induced bed shear stress (CBSS) and WBSS in Tokyo Bay. This novel modeling approach, with the simplest sedimentary initial conditions and realistic sedimentary and pelagic processes, provides a great tool for long-term ecosystem modeling in future studies.

Bed shear stress estimation on an open intertidal flat using in situ measurements

Accurate estimations for the bed shear stress are essential to predict the erosion and deposition processes in estuaries and coasts. This study used high-frequency in situ measurements of water depths and near-bed velocities to estimate bed shear stress on an open intertidal flat in the Yangtze Delta, China. To determine the current-induced bed shear stress (τc) the in situ near-bed velocities were first decomposed from the turbulent velocity into separate wave orbital velocities using two approaches: a moving average (MA) and energy spectrum analysis (ESA). τc was then calculated and evaluated using the log-profile (LP), turbulent kinetic energy (TKE), modified TKE (TKEw), Reynolds stress (RS), and inertial dissipation (ID) methods. Wave-induced bed shear stress (τw) was estimated using classic linear wave theory. The total bed shear stress (τcw) was determined based on the Grant–Madsen wave–current interaction model (WCI). The results demonstrate that when the ratio of significant wave height to water depth (Hs/h) is greater than 0.25, τcw is significantly overestimated because the vertical velocity fluctuations are contaminated by the surface waves generated by high winds. In addition, wind enhances the total bed shear stress as a result of the increases in both τw and τc generated by the greater wave height and reinforcing of vertical turbulence, respectively. From a comparison of these various methods, the TKEw method associated with ESA decomposition was found to be the best approach because: (1) this method generates the highest mean index of agreement; (2) it uses vertical velocities that are less affected by Doppler noise; and (3) it is less sensitive to the near-bed stratification structure and uncertainty in bed location and roughness.

Erosion of an intertidal mussel bed by ice- and wave-action

The persistence of intertidal mussel beds is governed by both biotic and abiotic processes. Many studies have shown that waves and currents are able to erode mussels from an intertidal mussel bed, but here it is demonstrated that in temperate regions ice action can be important as well. These findings result from a 27-month-long monitoring campaign on a mature intertidal mussel bed in the Dutch Wadden Sea. Daily camera observations revealed two periods in which significant erosion occurred. The first event occurred in a period during which the bed was covered by ice. Ice action resulted in an initial decrease of 19% in mussel covered area around the monitoring station. The losses were concentrated in three erosion hotspots of which the largest two were located close to the beds’ edge. Around these hotspots, up to 0.3m high ridges of piled up mussels had formed, with the highest ridges located westward of these erosion gaps. The observed topographic changes support the view that the mechanism by which the bed was damaged was, at least partly, due to physical disturbance by scouring ice. Recovery of mussel cover was limited in the 19 months following the ice action event. Due to sedimentation and reorganization of the mussels, initial relief inside the mussel bed was reduced again and mussels spread out over a larger area. Height differences between uncovered parts and mussel covered parts increased as a result of sedimentation in mussel covered areas. Wave action during a storm period caused a further reduction in mussel cover. Especially areas that were previously elevated by ice action suffered from large losses. Wave erosion occurred during multiple wind events, causing initially small erosion gaps to expand outward and increase in extent. The results suggest a twofold impact of wave and ice action on mussel bed cover: firstly, by directly eroding mussels from mussel beds; secondly, by indirectly increasing the exposure of mussel beds to wave induced bed shear stresses.

Feedbacks between flow, sediment motion and microbial growth on sand bars initiate and shape elongated stromatolite mounds

Elongated stromatolites are often used as indicators of current direction and shoreline orientation, especially in paleoenvironmental reconstructions. However, mechanisms that create shore-parallel, m-scale elongated stromatolite mounds in carbonate sand are not well understood. We propose that this geometry is initiated by microbial growth on the parts of sand bars that experience low wave-induced bed shear stresses. We test this idea by growing microbial mats on carbonate sand bars in a laboratory wave tank. Cyanobacterial mats grow on the bar runnels, where sediment motion is negligible, but are absent from the bar ridges, where the waves generate migrating ripples. When microbially-promoted lithification reinforces and preserves this initial pattern, elongated stromatolites should initiate in the runnels of sand bars, with long wavelengths (5–100 m) and small width-to-wavelength ratios (∼0.3). These dimensions are consistent with modern shore-parallel stromatolites in Hamelin Pool, Western Australia, and with patterns of microbial colonization in other sandy sediments. This model of elongated stromatolite mounds can inform paleoenvironmental reconstructions by clarifying and quantifying feedbacks among waves, sediment transport and microbial growth.

Numerical study on wave dynamics and wave-induced bed erosion characteristics in Potter Cove, Antarctica

Wave generation, propagation, and transformation from deep ocean over complex bathymetric terrains to coastal waters around Potter Cove (King George Island, South Shetland Islands, Antarctica) have been simulated for an austral summer month using the Simulating Waves Nearshore (SWAN) wave model. This study aims to examine and understand the wave patterns, energy fluxes, and dissipations in Potter Cove. Bed shear stress due to waves is also calculated to provide a general insight on the bed sediment erosion characteristics in Potter Cove.A nesting approach has been implemented from an oceanic scale to a high-resolution coastal scale around Potter Cove. The results of the simulations were compared with buoy observations obtained from the National Data Buoy Center, the WAVEWATCH III model results, and GlobWave altimeter data. The quality of the modelling results has been assessed using two statistical parameters, namely the Willmott’s index of agreement D and the bias index. Under various wave conditions, the significant wave heights at the inner cove were found to be about 40–50 % smaller than the ones near the mouth of Potter Cove. The wave power in Potter Cove is generally low. The spatial distributions of the wave-induced bed shear stress and active energy dissipation were found to be following the pattern of the bathymetry, and waves were identified as a potential major driving force for bed sediment erosion in Potter Cove, especially in shallow water regions. This study also gives some results on global ocean applications of SWAN.

Field observations and modeling of wave attenuation over colonized beachrocks

Beachrocks are common coastal formations, constructed through the lithification of beach sediments by carbonate cements. The objectives of the present contribution were to (a) assess the impacts of beachrock benthic communities on nearshore wave dynamics; (b) present a numerical model, developed to simulate wave propagation over shallow nearshore waters characterized by both loose sediment beds and colonized/non-colonized beachrocks; and (c) discuss the structure and dynamics of beachrock macro-benthic communities in an E. Mediterranean micro-tidal beach (Vatera, Lesbos Island, NE Aegean Sea), as well as their interactions with the wave forcing. Field measurements of wave height and flow velocity were processed to assess shoaling wave energy dissipation due to bottom friction from the colonized beachrock outcrops. The equivalent Nikuradse hydraulic roughness of the beachrock surface, estimated through spectral wave attenuation calculations, was found to be around kN=0.13m. The corresponding wave friction factors were incorporated into a wave propagation model to obtain estimates of the wave-induced bed shear stress τw acting on the beachrock benthic communities. Information about the structure and characteristics of the latter was obtained through the collection and analysis of samples from 15 stations along a beach transect, during two months of the year (April and September) and the results showed that benthic communities at the beachrock habitat were very similar to the ones typically found at NE Mediterranean hard substrates. Wave-induced bed shear stress τw values were able to explain cross-shore variations in population density and biomass, both decreasing significantly above water depths of about h=1.8–2m. The latter values corresponded, for the studied conditions, to shear stresses of about τw=2.2Nt/m2. The present findings clearly show that nearshore wave patterns not only control to a certain extent the spatial structure of the beachrock habitats, but can be also influenced by them. Thus, hydrodynamics and beachrocks habitats constitute a complex system which remains very little understood and demands for further investigation.

Wave–current interaction at an angle 2: theory

A theoretical model is presented to describe the current velocity within and outside a wave–current boundary layer and to quantify the associated bed shear stresses for wave–current interaction at an arbitrary angle. The model assumes that the wave-induced bed shear stress in the combined flow varies sinusoidally with time while the current-induced bed shear stress follows an eddy viscosity concept. The computational procedure is given for both depth-averaged and reference-point current-based computations. Unlike other analytical models proposing different coefficients for different problems, the present model uses the same set of equations and coefficients to describe wave–current flows at any angle under any flow regime. This model agrees better with both field measurements and laboratory data than existing theoretical models. The model indicates that the wave–current interaction angle is not significant for wave–current flow properties.

Evolution of bed shear stress distribution over the northwest European shelf seas during the last 12,000 years

Due to changes in relative sea level of order 100 m, the contribution of tides and waves to net bed shear stress in shelf sea regions has varied considerably over the Late Glacial and Holocene. Understanding the spatial and temporal distribution of this ratio leads to a deeper understanding of the erosion and deposition of sediments over the shelf seas throughout this time period. Tidal and wave models are here applied to palaeo time slices of the northwest European shelf seas over the last 12,000 years. The model simulations include a series of sensitivity tests to account for the influence of interannual variability in wind conditions on the resulting bed shear stress. The results show that there has been a significant decrease over the last 12,000 years in shelf-scale mobilisation of coarse sediment. Since there was a lower magnitude of wave orbital velocity penetrating to the sea bed as a result of increasing relative sea level, this reduction in sediment mobilisation was primarily controlled by a shelf-scale decrease in wave-induced bed shear stress over the last 12,000 years. The predictions of mean and residual bed shear stress for the modelled palaeo time slices are a useful tool with which to inform site-selection and subsequent interpretation of sediment cores. In addition, the modelled reconstructions of palaeo tidal range over the shelf seas demonstrates the potential errors associated with assuming a present-day tidal range when correcting palaeo sea-level proxies from their deposited datum (e.g. palaeo mean high water spring tide) to palaeo mean sea level.

Bed shear stress in the southern North Sea as an important driver for suspended sediment dynamics

This paper addresses the spatial and temporal patterns of drivers for sediment dynamics in coastal areas. The basic assumption is that local processes are dominating. The focus is put on the bed shear stress in the southern part of North Sea giving the basic control for deposition–sedimentation and resuspension–erosion. The wave-induced bed shear stress is formulated using a model based on the concept that the turbulent kinetic energy associated with surface waves is a function of orbital velocity, the latter depending on the wave height and period, as well as on the water depth. Parameters of surface waves are taken from simulations with the wave spectrum model WAM (wave model). Bed shear stress associated with currents is simulated with a 3D primitive equation model, Hamburg Shelf Ocean Model. Significant wave height, bed shear stress due to waves and currents, is subjected to empirical orthogonal functions (EOF) analysis. It has been found that the EOF-1 of significant wave height represents the decrease of significant wave height over the shallows and, due to fetch limitation, along the coastlines. Higher order modes are seesaw-like and, in combination, display a basin-scale rotational pattern centred approximately in the middle of the basin. Similar types of variability is also observed in the second and third EOF of bed shear stress. Surface concentrations of suspended matter derived from MERIS satellite data are analysed and compared against statistical characteristics of bed shear stress. The results show convincingly that the horizontal distribution of sediment can, to a larger extent, be explained by the local shear stress. However, availability of resuspendable sediments on the bottom is quite important in some areas like the Dogger Bank.

Numerical simulation of wave-induced laminar boundary layers

The three-dimensional numerical model with σ-coordinate transformation in the vertical direction is applied to the simulation of surface water waves and wave-induced laminar boundary layers. Unlike most of the previous investigations that solved the simplified one-dimensional boundary layer equation of motion and neglected the interaction between boundary layer and outside flow, the present model solves the full Navier–Stokes equations (NSE) in the entire domain from bottom to free surface. A non-uniform mesh system is used in the vertical direction to resolve the thin boundary layer. Linear wave, Stokes wave, cnoidal wave and solitary wave are considered. The numerical results are compared to analytical solutions and available experimental data. The numerical results agree favorably to all of the experimental data. It is found that the analytical solutions are accurate for both linear wave and Stokes wave but inadequate for cnoidal wave or solitary wave. The possible reason is that the existing analytical solutions for cnoidal and solitary waves adopt the first-order approximation for free stream velocity and thus overestimate the near bottom velocity. Besides velocity, the present model also provides accurate results for wave-induced bed shear stress.