Grain size dependency in the occurrence of sand waves

Sandy shallow seas, like the North Sea, are very dynamic. Several morphological features are present on the bed, from small ripples to sand waves and large tidal sandbanks. The larger patterns induce significant depth variations that have an impact on human activities taking place in this area. Therefore, it is important to know where these large-scale features occur, what their natural behaviour is and how they interact with human activities. Here, we extend earlier research that compares the results of an idealized model of large-scale seabed patterns with data of seabed patterns in the North Sea. The idealized model is extended with a grain size dependency. The adaptations lead to more accurate predictions of the occurrence of large-scale bed forms in the North Sea. Therefore, grain size dependency and, in particular, critical shear stress are important to explain the occurrence of sand waves and sandbanks in the North Sea. Responsible Editor: Alejandro Souza     

On the parameterization of biological influences on offshore sand wave dynamics

The bed of the North Sea is covered by sand waves and houses a great number of macrobenthic animals. These bio-engineers are known to have a significant influence on the stability of the bed and thereby on the geomorphology of the seabed. This paper proposes a parameterization of these bio-geomorphological interactions. Given the abundance of three dominant bio-engineers on the Dutch Continental Shelf, the predicted occurrence of sand waves, in which the parameterization is included, shows significantly better results, compared to the prediction for the default case without biology. Therefore, the inclusion of biological activity could be important to predict the occurrence of sand waves.     

The influence of tides, wind and waves on the net sand transport in the North Sea

Large-scale redistribution of sand by hydrodynamical processes in shelf seas is important for basin and coastal evolution on time scales of a thousand to tens of thousands of years. The influence of tides on the large-scale net sand-transport patterns in the North Sea has received much attention, but the influence of wind-driven flow and wind waves has hardly been investigated. Here, to establish the present-day situation and to develop a method that can also be used for palaeo-situations and forecasts for different sea levels, this influence is assessed for the present southern North Sea using a numerical flow model, a parametric wave model and a wave-averaged sand-transport formulation. Various forcing combinations are used to identify the dominant transport mechanisms: tides only, tides and wind, tides and waves, and combined tides, wind and waves. Wind forcing is applied in two ways to find an efficient, but still representative, method of incorporating this stochastic process: a statistical wind climatology and an observed time series. The results show that (i) the wind climatology yields a good approximation of the sand transport computed using the time series; (ii) wind-driven flow and waves only contribute significantly to the net sand transport by tides when acting together where tidal currents are small; and (iii) various combinations of forcings dominate the net sand transport in different regions of the southern North Sea: (a) tides dominate in the southern, middle and northwestern parts of the Southern Bight and in the region of The Wash; (b) tides, wind-driven flow and waves all are important in the northeastern part of the Southern Bight; and (c) wind-driven flow and waves dominate north of the Friesian Islands, in the German Bight and on the Dogger Bank. Qualitative comparison with observations shows good agreement.     

An enhanced depth-averaged tidal model for morphological studies in the presence of rotary currents

A simple and efficient method to improve morphological predictions using depth-averaged tidal models is presented. The method includes the contribution of secondary flows in sediment transport using the computed flow field from a depth-averaged model. The method has been validated for a case study using the 3D POLCOMS model and ADCP data. The enhanced depth-averaged tidal model along with the SWAN wave model are applied to morphological prediction around the Lleyn Peninsula and Bardsey Island as a case study in the Irish Sea. Due to the presence of a headland in this area two asymmetrical tidal eddies are developed in which the cyclonic eddy is stronger as a result of Coriolis effects. The results show that the enhanced model can effectively predict formation of sand banks at the centre of cyclonic eddies, while the depth-averaged model, due to its inability to accommodate secondary flow, is inadequate in this respect.     

A parameterization of the wavelength of tidal dunes

The idealized model of Besio et al. (On the formation of sand waves and sand banks. Journal of Fluid Mechanics 2006; 557: 1–17) is used to predict the wavelength of tidal dunes (sand waves) generated by tidal currents in estuaries and shallow seas. The predictions are then analysed and a formula is proposed to estimate the wavelength of tidal dunes as a function of the parameters of the problem. The wavelength of the dunes is found to increase when the water depth is increased and/or the strength of the tidal current is decreased. On the other hand, the size of the bottom material (if medium sand is considered) and the tidal ellipticity are found to have a relatively small influence on the length of the bottom forms. The formula proposed provides results which are consistent with field observations of different authors. Copyright © 2011 John Wiley & Sons, Ltd.     

Simulating the temporal and spatial dynamics of the North Sea using the new model GETM (general estuarine transport model)

Here we present results of a 1-year realistic North Sea simulation from the new model GETM (general estuarine transport model) and assess the capabilities of this model by comparing them to model results from the well-known HAMSOM (Hamburg shelf sea and ocean model) model, in situ data from the North Sea project and satellite-derived sea-surface temperature data. The annual cycle and the spatial variability of stratification and mixing in the North Sea is simulated. It is shown that the new model is successful in reproducing the general temporal and spatial dynamics of the North Sea. The major advantages of GETM for achieving improved results in this simulation are the implementation of general vertical coordinates, of a state-of-the-art turbulence model and of higher-order advection schemes. By exploiting the full capabilities of these features a more realistic simulation could be achieved. We found that the greatest differences in the model results are produced by applying advection schemes of different complexity. Here we are able to demonstrate that better advection schemes lead to stronger horizontal gradients and stronger vertical stratification during summer. When comparing these results to measurements from the North Sea project and to satellite data, we find that these stronger gradients are more realistic. Therefore, we consider it as essential to use such high-order advection schemes if the spatial variability of estuarine or shelf seas like the North Sea is to be resolved adequately. The advanced turbulence closure scheme also contributed to more realistic simulation of the vertical stratification. Finally, general vertical coordinates better resolve the shallow regions, but are also useful for the deeper regions, as they allow a better estimation of sea-surface temperature compared to traditional coordinates.Responsible Editor: Phil Dyke     

Comparison of numerical hindcasted severe waves with Doppler radar measurements in the North Sea

Severe sea states in the North Sea present a challenge to wave forecasting systems and a threat to offshore installations such as oil and gas platforms and offshore wind farms. Here, we study the ability of a third-generation spectral wave model to reproduce winter sea states in the North Sea. Measured and modeled time series of integral wave parameters and directional wave spectra are compared for a 12-day period in the winter of 2013–2014 when successive severe storms moved across the North Atlantic and the North Sea. Records were obtained from a Doppler radar and wave buoys. The hindcast was performed with the WAVEWATCH III model (Tolman 2014) with high spectral resolution both in frequency and direction. A good general agreement was obtained for integrated parameters, but discrepancies were found to occur in spectral shapes.     

Computing near coastal tidal dynamics from observations and a numerical model

A two-dimensional vertically integrated model of the North Sea is used to compute the distribution of M₂ and M₄ tidal elevations and currents over the region. Comparison of computed and observed elevations and currents in the area shows that the model can accurately reproduce the M₂ tide in the North Sea, although there are difficulties with the M₄ tide particularly in the northern North Sea.Comparison between model and a large number of observations collected in a shallow water region off the east coast of England, revealed that the model can accurately reproduce the tides even in near coastal regions, where model resolution problems can occur. Comparisons of computed and observed M₂ tidal energy fluxes in this region, show that model and observations agree to within the order of 10% (the error associated with the necessary interpolation of the observations in order to compute the energy flux).The problem of computing energy dissipation in the area by subtracting the energy fluxes into and out of the region is shown to be ill-conditioned in that the energy dissipation in the area is comparable to the error in the energy flux. Consequently for the sea region considered here it is not meaningful to compare this energy budget with energy dissipation due to bottom friction.Energy dissipation for the whole of the North Sea is computed using the numerical model and the geographical distribution of dissipation due to bottom friction is given for the M₂ tide.     

南海北部沙波运移的观测与理论分析

针对南海北部海域特点建立了模拟该区域小尺度沙波运移过程的准三维力学模型.以多波束海底地貌扫描数据和水文资料为基础,预测了研究区域沙波的运移,其结果在沙脊脊沟处与实际观测一致,而在脊背上与实际观测值存在差异.分析表明,本文所提出的物理模型可以用于预测南海海域以推移质泥沙运动为主的小尺度沙波运移规律.这一结果对该区域海底管线等工程设计是很有意义的.     

Assessment of the atmospheric nitrogen and sulphur inputs into the North Sea using a Lagrangian model

The atmospheric chemistry and deposition model has been applied for calculation of nitrogen and sulphur depositions to the entire North Sea area for the year 1999. The total atmospheric nitrogen and sulphur depositions to the North Sea area were determined to 709 kton (kt) N and 551 kt S, respectively. Since the North Sea area was calculated to be 747,988 km², this is equivalent to an average deposition of 0.9 ton N km^?2 and 0.7 ton S km^?2, respectively. The depositions decrease strongly from the south end (about 2–3 kt N km^?2) to the north end (about 0.2 kt N km^?2) of the North Sea, due to increasing distance to the large source areas in the northern part of the European continent. The territorial waters of Belgium, the Netherlands and Germany receive about 50% higher deposition densities than the average value for the entire North Sea area. For the remaining territorial waters of the North Sea the depositions follow more or less the fraction of the area. The results furthermore show that about 60% of the total nitrogen deposition is related to emissions from combustion sources (nitrogen oxides) and about 40% from emissions related to agricultural activities (ammonia).     

Growth of large-scale bed forms due to storm-driven and tidal currents: a model approach

An idealized morphodynamic model is used to gain further understanding about the formation and characteristics of shoreface-connected sand ridges and tidal sand banks on the continental shelf. The model consists of the 2D shallow water equations, supplemented with a sediment transport formulation and describes the initial feedback between currents and small amplitude bed forms. The behaviour of bed forms during both storm and fair weather conditions is analyzed. This is relevant in case of coastal seas characterized by tidal motion, where the latter causes continuous transport of sediment as bed load.The new aspects of this work are the incorporation of both steady and tidal currents (represented by an M₂ and M₄ component) in the external forcing, in combination with dominant suspended sediment transport during storms. The results indicate that the dynamics during storms and fair weather strongly differ, causing different types of bed forms to develop. Shoreface-connected sand ridges mainly form during storm conditions, whereas if fair weather conditions prevail the more offshore located tidal sand banks develop. Including the M₄ tide changes the properties of the bed forms, such as growth rates and migration speeds, due to tidal asymmetry. Finally a probabilistic formulation of the storm and fair weather realization of the model is used to find conditions for which both types of large-scale bed forms occur simultaneously. These conditions turn out to be a low storm fraction and the presence strong tidal currents in combination with strong steady currents during storms.     

A convection-conduction model for analysis of the freeze-thaw conditions in the surrounding rock wall of a tunnel in permafrost regions

The results of simulated tidal current field, wave field and storm-induced current field are employed to interpret the depositional dynamic mechanism of formation and evolution of the radial sand ridges on the Yellow Sea door. The anticlockwise rotary tidal wave to the south of Shandong Peninsula meets the following progressive tidal wave from the South Yellow Sea, forming a radial current field outside Jianggang. This current field provides a necessary dynamic condition for the formation and existence of the radial sand ridges on the Yellow Sea seafloor. The results of simulated “old current field (holocene)” show that there existed a convergent-divergent tidal zone just outside the palaeo-Yangtze River estuary where a palaeo-underwater accumulation was developed. The calculated results from wave models indicate that the wave impact on the topography, under the condition of high water level and strong winds, is significant. The storm current induced by typhoons landing in the Yangtze River estuary and turning away to the sea can have an obvious influence, too, on the sand ridges. The depmitional dynamic mechanism of formation and evolution of the radial sand ridges on the Yellow Sea seafloor is “tidal current-induced formation—storm-induced chang—tidal current-induced recovery”. Project supported by the National Natural Science Foundation of China (Grant No. 49236120).     

Effects of pore aspect ratios on velocity prediction from well‐log data

We develop a semi‐empirical model which combines the theoretical model of Xu and White and the empirical formula of Han, Nur and Morgan in sand–clay environments. This new model may be used for petrophysical interpretation of P‐ and S‐wave velocities. In particular, we are able to obtain an independent estimation of aspect ratios based on log data and seismic velocity, and also the relationship between velocities and other reservoir parameters (e.g. porosity and clay content), thus providing a prediction of shear‐wave velocity. To achieve this, we first use Kuster and Toksöz's theory to derive bulk and shear moduli in a sand–clay mixture. Secondly, Xu and White's model is combined with an artificial neural network to invert the depth‐dependent variation of pore aspect ratios. Finally these aspect ratio results are linked to the empirical formula of Han, Nur and Morgan, using a multiple regression algorithm for petrophysical interpretation. Tests on field data from a North Sea reservoir show that this semi‐empirical model provides simple but satisfactory results for the prediction of shear‐wave velocities and the estimation of reservoir parameters.     

Integrated environmental management: The Dutch Governmental view

In the last 10 years concern for the economic and ecological value of the North Sea has increased. Many different users are putting increasing pressure on the resources of the North Sea and its adjacent estuaries. Its uses include shipping, fisheries, the oil and gas industry, mineral extraction, and—along its shores—recreation. The North Sea suffers pollution directly from some of these sources, but also indirectly from discharges from land, from rivers and from the atmosphere. The resilience of the North Sea ecosystem puts limits on the human use. These limits have in a number of cases been exceeded. It is necessary to define and assess the sustainable use of the North Sea ecosystem. The sustainable use may be defined as the long-term use of current and future potential while ensuring sustainable conservation of the ecological value of the North Sea and adjacent vulnerable water systems. Integrated environmental management for the North Sea implies that policy-makers assess all interests and resolve any conflicts which arise. This paper considers the problem of input of organic substances into the North Sea. It considers a target scenario of sustainable use and ecological health, in relation to what concentrations of organic substances are permissible. Secondly, it considers a target percentage reduction in current inputs. Thirdly, it is necessary to give the measures to be taken to deal with the major sources of the pollution, i.e. to define target groups. Finally, the paper gives examples of the statutory instruments available to implement the chosen policy.     

Modelling offshore sand wave evolution

We present a two-dimensional vertical (2DV) flow and morphological numerical model describing the behaviour of offshore sand waves. The model contains the 2DV shallow water equations, with a free water surface and a general bed load formula. The water movement is coupled to the sediment transport equation by a seabed evolution equation. Using this model, we investigate the evolution of sand waves in a marine environment. As a result, we find sand wave saturation for heights of 10–30% of the average water depth on a timescale of decades. The stabilization mechanism, causing sand waves to saturate, is found to be based on the balance between the shear stress at the seabed and the principle that sediment is transported more easily downhill than uphill. The migration rate of the sand waves decreases slightly during their evolution. For a unidirectional steady flow the sand waves become asymmetrical in the horizontal direction and for a unidirectional block current asymmetrical in the vertical. A sensitivity analysis showed the slope effect of the sediment transport plays an important role herein. Furthermore, the magnitude of the resistance at the seabed and the eddy viscosity influence both the timescale and height of sand waves. The order of magnitudes found of the time and spatial scales coincide with observations made in the southern bight of the North Sea, Japan and Spain.     

Wave climate and long-term changes for the Southern North Sea obtained from a high-resolution hindcast 1958–2002

An analysis of the extreme wave conditions in 1958–2002 in the North Sea as obtained from a regional model hindcast is presented. The model was driven by hourly wind fields obtained from a regional atmosphere model forced with reanalysis data from the National Center for Environmental Prediction (NCEP/NCAR). Furthermore, observed sea ice conditions from the Norwegian Meteorological Institute have been accounted for in the simulation. It is shown that the model is capable of reproducing extreme wave height statistics at a reasonable degree of approximation. The analysis of severe wave height events reveals that for much of the Southern North Sea, their number has increased since the beginning of the simulation period (1958), although the increase has attenuated later and leveled off around about 1985. On the other hand, the intensity and duration of severe wave height events decreased within the last few years of the simulation so that annual 99%-ile wave heights have also reduced since about 1990–1995. For the UK North Sea coast, a different behavior was found characterized by a reduction in severe wave conditions over much of the hindcast period.     

Downscaling a twentieth century global climate simulation to the North Sea

The regional ocean model system (ROMS) is used to downscale a 26-year period of the twentieth century 20C3M experiment from the global coupled Bergen climate model (BCM) for the North Sea. Compared to an observational-based climatology, BCM have good results on the mean temperature, except for too low winter temperature. This is connected to a too weak inflow of Atlantic water. The downscaling gives added value to the BCM results by providing regional details, doubling the Atlantic inflow, and improving the mean winter temperature. For mean salinity, BCM has values very close to the climatology, whereas the downscaling becomes too fresh. The downscaling, however, improves the sea surface salinity, the vertical structure, and the Norwegian Coastal Current. It is concluded that the downscaling procedure as presented here is a suitable tool for assessing the future Atlantic inflow and sea temperature in the North Sea based on a global climate projection.