N
ATURAL AND
H
UMAN
I
NDUCED
S
EABED
E
VOLUTION
The occurrence of large-scale bed patterns and the effects of
human activities on the North Sea seabed
Samenstelling promotiecommissie:
prof. dr. F. Eising Universiteit Twente, voorzitter, secretaris
prof. dr. S.J.M.H. Hulscher Universiteit Twente, promotor
ir. H.J.M. Beurskens Energieonderzoek Centrum Nederland
prof. dr. P. Blondeaux University of Genua
prof. dr. H.W.M. Hoeijmakers Universiteit Twente
prof. dr. ir. G.A.M. van Kuik Technische Universiteit Delft
dr. ir. J.S. Ribberink Universiteit Twente
prof. dr. ir. J.A. Roelvink Unesco-IHE
drs. A. Stolk Rijkswaterstaat
This research is supported by:
EU-project HUMOR (EVK3-CT-2000-000037)
PhD@Sea, which is substantially funded under the BSIK-programme of the Dutch Government and supported by the consortium WE@Sea.
Cover: ‘Annoy the stewardess’ Photo courtesy of Judith Janssen.
Copyright © 2008 by Henriët van der Veen, Enschede, The Netherlands
All rights reserved. No part of this publication may be reproduced, stored in a retrieval system, or transmitted, in any other form or by any means, electronic, mechanical,
N
ATURAL AND
H
UMAN
I
NDUCED
S
EABED
E
VOLUTION
T
HE OCCURRENCE OF LARGE
-
SCALE BED PATTERNS AND THE
EFFECTS OF HUMAN ACTIVITIES ON THE
N
ORTH
S
EA SEABED
PROEFSCHRIFT
ter verkrijging van
de graad van doctor aan de Universiteit Twente, op gezag van de rector magnificus,
prof. dr. W.H.M. Zijm,
volgens het besluit van het College voor Promoties in het openbaar te verdedigen
op donderdag 21 februari 2008 om 15:00 uur
door
Hennie Henriët van der Veen geboren op 31 augustus 1978
Dit proefschrift is goedgekeurd door de promotor: prof. dr. S.J.M.H. Hulscher
Contents
VOORWOORD ... 9 SUMMARY...11 SAMENVATTING ...13 CHAPTER 1 INTRODUCTION...15 1.1GENERAL...15 1.2THE NORTH SEA...15 1.2.1 General ...151.2.2 Large scale bed forms in the North Sea...16
1.2.3 Human activities in the North Sea ...17
1.3STATE OF THE ART...18
1.4CENTRAL RESEARCH THEME OF THIS THESIS...19
1.5OUTLINE...21
CHAPTER 2 GRAIN SIZE DEPENDENCY IN THE OCCURRENCE OF SAND WAVES ...23
2.1INTRODUCTION...23
2.2THE BED PATTERN MODEL...26
2.2.1 The theoretical model to predict large-scale bed forms ...26
2.2.2 Inclusion of a grain size dependency ...28
2.2.3 The GIS and datalayers ...30
2.3RESULTS AND COMPARISON WITH OBSERVATIONS...31
2.3.1 Results...31
2.3.2 Comparison with observations ...32
2.3.3 Comparison of predictions with and without grain size dependency...33
2.4DISCUSSION...34
2.5CONCLUSION...35
CHAPTER 3 PREDICTING SAND BANKS IN THE NORTH SEA ...37
3.1INTRODUCTION...37
3.2MODEL...39
3.2.1 The model to predict large-scale bed forms ...39
3.2.2 Data ...43
3.3RESULTS...43
3.3.1 Model results ...43
3.4SENSITIVITY ANALYSIS OF THE VISCOSITY VARIATION PARAMETER AND THE LEVEL OF ZERO INTERCEPT
...44
3.4.1 Viscosity variation parameter (ε) ...45
3.4.2 Level of zero intercept (z0) ...45
3.5DISCUSSION...47
3.6CONCLUSION...49
CHAPTER 4 LARGE-SCALE SAND EXTRACTION IN THE NORTH SEA ...51
4.1INTRODUCTION...51
4.2MODEL IMPLEMENTATION...52
4.2.1 The morphodynamic model...52
4.2.2 Solution method ...55
4.2.3 Interpretation of the model results...56
4.2.4 GIS implementation ...58
4.2.5 Data ...61
4.3RESULTS...61
4.3.1 Sand pit evolution ...62
4.3.2 Sensitivity analysis...63
4.3.3 Case study: sand extraction to facilitate the enlargement of the Rotterdam harbour ...64
4.3.4 North Sea overview...66
4.4DISCUSSION...67
4.5CONCLUSION...69
APPENDIX A: SOLUTION METHOD SAND PITS ...70
CHAPTER 5 LARGE-SCALE SEABED MORPHODYNAMICS DUE TO OFFSHORE WIND FARMS ...73
5.1INTRODUCTION...73
5.2OFFSHORE WIND FARMS IN EUROPE...74
5.3THE MORPHODYNAMIC MODEL...75
5.3.1 Representation of a wind farm in the morphodynamic model ...75
5.3.2 The morphodynamic model...78
5.3.3 Data ...83
5.4 RESULTS...83
APPENDIX B: SOLUTION METHOD WIND FARMS ...90
CHAPTER 6 DISCUSSION, CONCLUSIONS AND RECOMMENDATIONS...95
6.1DISCUSSION...95
6.1.1 Model to predict large scale bed forms ...95
6.1.2 Idealized model...96 6.1.3 Data ...98 6.1.4 Validation ...98 6.2CONCLUSIONS...99 6.3RECOMMENDATIONS...102 COLOR FIGURES ...105 CHAPTER 2...105 CHAPTER 3...107 CHAPTER 4...109 CHAPTER 5...110 NOMENCLATURE ...111 REFERENCES ...113
Voorwoord
De ene keer zit je uren te denken zonder dat je ook maar iets te binnen schiet en een andere keer bereik je precies hetzelfde in nog geen vijf minuten… - Herman Finkers
...en zo verging het mij ook bij het schrijven van het proefschrift. Toch is het er nu dan van gekomen en daarom wil ik graag de volgende mensen bedanken.
Ten eerste Suzanne Hulscher die mij ‘overhaalde’ om een promotie te gaan doen. Halverwege werd ze niet alleen mijn professor maar ook mijn dagelijks begeleider, Suzanne dank voor je kritische vragen en bemoedigende woorden op momenten dat ik ze nodig had.
Graag wil ik ook Blanca Pérez Lapeña bedanken die halverwege het project als GIS specialist aan het project werd toegevoegd. Blanca, door jou komst kreeg mijn onderzoek de vaart die het daarvoor gemist had en was het mogelijk om het onderzoek af te ronden. Ook wil ik René Buijsrogge bedanken voor zijn ondersteuning op het gebied van alle computer perikelen. Pieter Roos wil ik bedanken voor de vele tijd die hij stak in het kritisch doorlezen en becommentariëren van dit proefschrift.
Mijn collega’s van WEM bedank ik voor hun belangstelling en gezellige lunchwandelingen, in het bijzonder Lisette, Judith, Saskia, Jolanthe, Fenneke, Rolien, en mijn kamergenotes Tanya en Christina, kortom de WEM-dames.
Anke en Brigitte wil ik graag bedanken voor hun secretariële ondersteuning en Hillie die het laatste stukje voor mij regelde. Ook wil ik graag Joke bedanken die, altijd aanwezig, vaak als vraagbaak diende.
Ook wil ik graag mijn vrienden bedanken voor alle gezellige tijden; De WBW-allstars omdat het er tenslotte niet toe doet wie je bent of wat je doet, maar wie je vrienden zijn ;-) De surfcrew voor de relaxte weekjes en wie niet in één van de voorgaande categorieën valt voor de gezellige etentjes en avondjes.
Zoals u misschien al opgevallen is, hebben mijn paranimfen dezelfde achternaam, maar daar heb ik ze niet op uitgekozen. Fenneke van der Meer, mede-promovenda, leerde ik kennen
in een zwembad in Mexico (zwaar werk die conferenties!) of eigenlijk net daarvoor toen ze in de wachtkamer van de GGD zat bij te komen van de benodigde vaccinaties. Het klikte meteen en ondertussen zijn er al veel ‘appel-momentjes’ geweest om frustraties en triomfen te delen. Mijn andere paranimf is Tanja van der Meer, haar ken ik al sinds PIP’97 toen meisjes nog in de minderheid waren op de UT. Samen hebben we veel trainingsrondjes en baantjes afgelegd, en met onze conditie groeide ook onze vriendschap. Dames, ik ben heel blij dat jullie twee bij me op het podium staan tijdens de laatste loodjes.
Ten slotte wil ik graag mijn familie bedanken. Ruud en Monica, het is altijd weer fijn om op zaterdagmiddag de benen onder jullie eettafel te kunnen steken, pannekoeken te eten en gezellig te kletsen, mijn dank daarvoor.
AB en Matthea, terwijl ik dit schrijf klinkt op de radio, “we are family, I got all my sisters with me” en zo is het maar net!
Heit en mem, bedankt voor jullie vertrouwen dat het allemaal wel goed zou komen met dit MAVO-meisje. Zonder jullie steun en vertrouwen had ik hier nooit gestaan.
Als één iemand in een huishouden promoveert zal het zo af en toe moeilijk zijn, maar met z’n tweeën is het hilarisch! Daan, dank je voor alle peptalks en schop-onder-de-kont speeches op de momenten dat ik ze nodig had. “I love you, pumpkin...” (Pulp Fiction, 1994).
Summary
The North Sea is a highly dynamic area, where a tidal current flows over a sandy seabed. It is an intensively used area where various human activities take place. The seabed is rich in oil and gas and there are a lot of oil and gas platforms connected to the shore with pipelines that are mostly buried below the seabed. Telephone and data cables are placed up and in the seabed running from one country to another. Also, since the North Sea is a biological rich area, a lot of fishery takes place. The sand of the seabed is mined and used for large infrastructural projects. As important harbours face the North Sea, intensive shipping takes place and there are many shipping lanes which have to be dredged. Also, large areas are reserved for offshore wind farms and other functions like military terrains.
The seabed of the North Sea is not flat, but is shaped in several wavy patterns, ranging from small ripples to large sand banks. Sand banks have a wave length between 1 and 10 km and can have a height of several tens of meters. Somewhat smaller features are sand waves. Their length varies between 100 and 800 m and they can be up to 10 m high from trough to crest.
As the North Sea is a very dynamic area, both in natural and a morphological sense, and as many human activities take place here, it is important to know what the large-scale effects of human activities on the seabed will be. Therefore, in this thesis we develop a system that can predict the large-scale effects of human activities on the North Sea seabed on a long timescale. We do this by implementing idealized morphodynamic models in a GIS (Geographical Information System) that also contains data on the North Sea environment.
We predict the occurrence of sand banks and sand waves in the North Sea and compare the results with observations of these large-scale bed forms. The results show that in large parts of the North Sea, we are able to correctly predict the occurrence of sand banks and sand waves. (chapter 2 and 3).
The models that predict the morphological effects of human activities (chapter 4 and 5) cannot be validated yet. But they are based on the same principles as the models that we use to predict the occurrence of sand banks and sand waves of which the results are compared with observations of large-scale bed forms in the North Sea.
It is assumed that the models that predict the effects of human activities, do not show any morphological evolution, if the model that predicts the occurrence of sand banks (chapter 3) does not predict the occurrence of sand banks at this particular location. This because, the
underlying mechanism of the models on human activities are based on the same 2DH flow conditions that are necessary for sand bank development.
We connect idealized morphodynamic models to the GIS to create a tool that can be used to predict the effects of human activities on the North Sea seabed. The models use site-specific input to give predictions for an arbitrary location in the North Sea.
The first application of this system is large-scale sand extraction. Due to large construction projects like the enlargement of the Rotterdam harbour, the demand for sand is rising and more offshore resources will be used to fulfill the need. This means that more large-scale sand pits will be created in the North Sea. The North Sea is a shallow shelf sea where the tide flows over a sandy bed. Therefore, the presence of sand pits can influence the morphological behaviour of this seabed (chapter 4).
The second application is offshore wind farms. We investigate the influence of offshore wind farms on the large-scale morphodynamics of the seabed. The need for sustainable energy is rising, and at the moment wind energy is one of the forms of renewable energy that can be harvested efficiently. We develop a morphodynamic model to investigate the effect of offshore wind farms on the seabed. By implementing the model in the GIS environment, the model allows us to calculate the effects of a wind farm using site-specific and farm design input parameters (chapter 5).
By implementing idealized morphodynamic models in a GIS environment we are able to predict the occurrence of large-scale bed forms on the North Sea seabed. Also, by implementing models that predict the effects of human activities in the GIS system, we are able to give an indication of the large-scale morphological effects of these human activities in the North Sea, thereby providing a rapid assessment tool to predict the morphological effects of human activities on the seabed
Samenvatting
De Noordzee is een dynamisch gebied, getij en golven zorgen voor een dynamische zandige bodem. De Noordzee wordt intensief gebruikt, er bevindt zich veel olie en gas in de bodem en er zijn veel olie- en gasplatforms. Deze zijn met de kust verbonden door in de zeebodem liggende pijpen waarmee olie en gas onshore worden getransporteerd. Ook lopen er data- en telefoonkabels door en over de zeebodem van het ene land naar het andere. Omdat de Noordzee ook biologisch heel rijk is, vindt er veel visserij plaats. Zand uit de bodem wordt gebruikt voor grootschalige bouwprojecten. Vanwege de grote havens aan de Noordzee, is er een intensief scheepsverkeer en moeten de scheepsroutes regelmatig worden gebaggerd. Verder worden er grote gebieden gereserveerd voor offshore wind parken en andere activiteiten zoals militaire oefenterreinen.
De bodem van de Noordzee is niet vlak maar bestaat uit golvende patronen variërend in schaal van kleine ribbels tot grote getijde zandbanken. Zandbanken hebben een golflengte tussen 1 en 10 km en kunnen tot enkele tientallen meters hoog worden. Wat kleiner zijn de zandgolven, hun golflengte varieert van 100 tot 800 m en van dal tot top kunnen ze 10 m hoog worden.
Omdat de Noordzee een dynamisch gebied is en er tegelijkertijd veel menselijke activiteiten plaatsvinden is het belangrijk om te weten wat de effecten van menselijke activiteiten op de zeebodem zijn. In dit proefschrift ontwerpen we een systeem dat de effecten van menselijke activiteiten op de bodem op lange termijn kan voorspellen. Hiervoor koppelen we geïdealiseerde morfologische modellen aan een GIS (Geografisch Informatie Systeem) waarin zich ook data van de Noordzee bevindt.
We voorspellen het voorkomen van zandbanken en zandgolven in de Noordzee en vergelijken de modelresultaten met observaties van deze grootschalige bodemvormen. De resultaten laten zien dat we in grote delen van de Noordzee in staat zijn om het al dan niet voorkomen van grootschalige bodemvormen correct te voorspellen (hoofdstuk 2 en 3).
De modellen die de effecten van menselijke activiteiten voorspellen, kunnen nog niet gevalideerd worden door metingen. Maar ze zijn gebaseerd op dezelfde principes als de modellen die gebruikt worden om grootschalige bodemvormen te voorspellen en waarvan de resultaten vergeleken zijn met observaties van zandbanken en zandgolven.
We nemen aan dat de modellen die effecten van menselijke activiteiten voorspellen geen morfologische effecten laten zien, als er geen zandbanken voorspeld worden in een bepaald
gebied in de Noordzee. Dit omdat het model dat effecten van menselijke activiteiten voorspelt, gebaseerd is op dezelfde 2DH stroming die noodzakelijk is voor zandbank evolutie. We implementeren geïdealiseerde modellen om de morfologische effecten van menselijke activteiten te voorspellen, in een GIS van de Noordzee. Hierdoor wordt een tool gecreëerd die gebruikt kan worden om de morfologische effecten op de Noordzeebodem te voorspellen. De modellen gebruiken site-specifieke input parameters om een voorspelling te geven voor een specifieke locatie in de Noordzee.
De eerste toepassing van dit systeem is grootschalige zandwinning. Door grootschalige bouwprojecten zoals de uitbreiding van de haven van Rotterdam, stijgt de vraag naar zand. Steeds meer zal hiervoor zand uit offshore bronnen worden gebruikt. Dit betekent dat er meer en grotere putten gecreëerd worden in de Noordzee. Omdat de Noordzee een dynamisch gebied is, waar de getijdestroom over een zandige bodem stroomt, kan de aanwezigheid van een zandwinput het grootschalige morfologische gedrag van een zeebodem beïnvloeden (hoofdstuk 4).
De tweede toepassing zijn offshore wind parken. Omdat de ruimte om grootschalige wind parken op land aan te leggen beperkt is, zijn er veel plannen om in de nabije toekomst offshore wind parken te bouwen. We onderzoeken de invloed van grote offshore wind parken op de grootschalige morfologie van de Noordzeebodem. We ontwikkelen een model om de morfodynamische effecten ten gevolge van wind parken te onderzoeken en implementeren dit in de GIS omgeving (hoofdstuk 5).
Door geïdealiseerde morfodynamische modellen te implementeren in een GIS van de Noordzee, zijn we in staat om het al dan niet voorkomen van grootschalige bodemvormen op de Noordzeebodem te voorspellen. Door modellen te implementeren die de morfologische gevolgen van menselijke activiteiten op de Noordzeebodem kunnen voorspellen, zijn we in staat om een indicatie te geven van de morfologische gevolgen van deze activiteiten. Hierdoor kan het ontworpen systeem (GIS + modellen) dienen als rapid assessment tool om morfologische effecten van menselijke activiteiten te voorspellen.
Chapter 1
Introduction
1.1 General
Shallow shelf seas stretch from the coastline to the shelf break. Most of them are bounded at one side by land and some, like the North Sea are semi enclosed. Most shallow shelf seas have a bottom consisting of a thick layer of sediment, which is composed of relict and modern sediments. Nowadays, rivers and coastal erosion are the most important sources of sediment for shallow shelf seas. Most of the tidal energy is dissipated in these shallow seas and this leads to an intensive reworking of the sediments (Brown et al., 1999).
In contrast to the world’s vast oceans, shallow shelf seas are brimming with activity, as many human activities take place in these areas. Besides these activities, shallow shelf seas are also important marine habitats, where much life in the underwater environment and numerous birds are present.
1.2 The North Sea
1.2.1 General
In this thesis the focus will be on the North Sea. This is a highly dynamic area where a tidal current flows over a sandy seabed. Also, the North Sea is a valuable habitat for different kind of animals. Furthermore, the North Sea is one of the most intensively used seas in which shipping, extraction of minerals and numerous other human activities take place. This combination of factors means that it is important to know what the large-scale effects of human activities on the seabed will be.
The southern part of the North Sea is a shallow shelf sea. A prominent shoal in this area is the Dogger Bank in the North. In the western part, a deeper channel runs towards the Strait of Dover (see Figure 1.1). The tides in the southern bight of the North Sea are semi-diurnal and along the coast the M2 tidal amplitude is dominant. The seabed of the North Sea mainly consists of fine to medium sands (125-500µm) but along the British coast and in the Strait of Dover large parts of the seabed are covered with gravel. The seabed sediments show a gradual fining towards the north-east (Jarke, 1956).
Figure 1.1: Left: General overview of the North Sea. right: Bathymetry of the North Sea (ICONA, 1992).
1.2.2 Large scale bed forms in the North Sea
Several sand bank systems are present in the area, and large parts of the seabed are covered with sand waves. Sand banks have a wavelength between 1 and 10 km and can have a height of several tens of meters (Dyer and Huntley, 1999). Sand banks can either be formed by the tide or can be remains of relict features which can be reworked by the tidal currents. Banks that are formed by the tide can be either actively maintained or moribund. Actively maintained sand banks are formed by the modern (late Holocene) tidal regime. Moribund banks were formed during periods of lower sea levels, they occur in deeper water where the present tidal current is too weak to form sand banks (no sediment transport occurs under the present tidal current) (Collins et al., 1995). Sand waves cover large parts of the North Sea seabed (Figure 1.2). These features are much smaller than sand banks. The spacing of sand waves varies between 100 and 800 m, they can be up to 10 m high from trough to crest, and
Figure 1.2: An overview of the southern part of the North Sea. The gray areas denote sand wave areas and the black lines show the locations of sand banks. Courtesy of F. van der Meer and B. Pérez Lapeña.
The evolution of sand banks and sand waves can be modeled using idealized morphological models. Such models represent wavy bed patterns developing as free instabilities of the system. The model studies the behaviour of a small bottom perturbation evolving on a basic state consisting of a tidal flow over a flat sandy seabed. Friction and Coriolis forces cause a net sediment transport towards the crest of the bed pattern, resulting in growth of the bed feature. Huthnance(1982a), (1982b) was the first to treat the tidal current and the erodible sand bed as a coupled system, and predicts a preferred initial growth of bed form perturbations with their crests turned slightly anti-clockwise with respect to the current direction. De Vriend (1990) extended this research by including suspended sediment transport and the influence of wave effects. Hulscher et al.(1993) adapted the model by allowing for elliptical tidal currents (Huthnance used a unidirectional tide).
The model that predicts sand waves is based on the same principle that was first studied by Huthnance (1982a), (1982b) to predict tidal sand banks, where it is investigated if certain regular patterns develop as free instabilities of the system. In addition to Huthnance who used a depth-averaged flow velocity, Hulscher (1996) included vertical circulation and found that the model also predicted sand waves, while the model of Huthnance only predicted sand banks.
1.2.3 Human activities in the North Sea
Many activities take place in the North Sea. The seabed is rich in oil and gas and there are many oil and gas platforms, connected to the shore with pipelines that are mostly buried just below the seabed. Telephone and data cables are placed up and in the seabed from one
country to another. Also, since the North Sea is a biologically rich area, intensive fishing takes place. The sand of the seabed is mined and used for large infrastructural projects and building activities. As important harbours face the North Sea there is intensive shipping and there are many shipping lanes which have to be dredged regularly. Also, the demand for durable forms of energy is increasing, and more and more offshore areas are reserved for offshore wind farms. Figure 1.3 shows an overview of the activities that take place in the Dutch part of the North Sea.
Figure 1.3: Human activities in the Dutch part of the North Sea (Ministerie_van_VROM et al., 2006).
1.3 State of the art
Different models have been developed to predict the effect of human activities on the North Sea seabed (see also Hommes et al. (2007)):
• Roos and Hulscher (2004), developed an idealized morphodynamic model to predict the effects of offshore sand pits. Also, different design options for sand pits are included in this model.
• Fluit and Hulscher (2002), did research on the effects of gas mining on the seabed using an idealized morphodynamic model.
• Delft3D is an integrated numerical model in which different modules (hydrodynamics, sediment transport etc.) are linked up together to calculate the morphological change of the bed. Klein (1999) did research on the behaviour of large-scale pits with Delft3D. • TELEMAC is another numerical model, it uses algorithms based on the finite-element
method. Idier and Astruc (2003) showed that the model is accurate enough to study the dynamics of the seabed. However, no sand pits have been modeled yet.
The aforementioned models forecast seabed evolution at scales typically of 1 to 10 km but do not give calculations on a North Sea scale. The idealized models (Roos and Hulscher, De Swart and Calvete, Fluit and Hulscher and Morelissen et al.) use a more general environment as input for their model. The numerical models (Delft3D, TELEMAC) have a long calculation time and at the moment can only carry out calculations for small portions of the seabed.
1.4 Central research theme of this thesis
As the North Sea is a very dynamic area both in a natural and in a morphological sense and as many human activities take place here, it is important to know what the large-scale effects (i.e. southern bight of the North Sea scale) of human activities on the seabed will be. To predict this, a reliable prediction tool is needed. In this research we want to develop a system
that can predict the large-scale effects of human activities on the North Sea seabed on a long timescale. The human activities that are explicitly treated in this thesis are sand extraction and offshore wind farms. This is because there are multiple plans to build large offshore wind farms in the North Sea and to create large sand pits to provide sediment for large construction plans (e.g. Rotterdam main port). This aim is reached by combining a Geographical Information System (GIS) that contains data of the North Sea with idealized models that predict the large-scale effects of human activities for a long period of time.
In this thesis we will use a GIS to store the environmental data on the North Sea. A GIS is particularly suitable for this, since it is especially designed to handle geo-referenced data and can easily transform data that has a different spatial reference system. Also, the GIS has a database structure to handle large amounts of data.
We choose not to use numerical models like Delft3D (option 1) as they have a long calculation time for detailed calculations on a North Sea scale and it is difficult to represent the actual environmental data for the whole North Sea in the model. We use the term
numerical models to denote models that are spatially and temporally discretized. Also, we did not include a numerical model in the GIS (option 3) since it is difficult to connect such a complicated model to the GIS due to the strict input parameter format that they need and the difficulties to make the raster of the model and that of the GIS compatible.
Since the GIS cannot calculate morphological development by itself a morphodynamic model has to be added to the GIS. Here we connect an idealized morphodynamic model to the GIS (option 2) since they can readily be embedded in the GIS and because these models help to gain insight in the processes that are important for bed evolution due to human activities. See also Figure 1.4 for an overview of the approach.
Figure 1.4: Overview of the research method
The idealized model is not directly included in the GIS but connected to it by a DLL (Dynamic Link Library), this is a set of autonomous functions that can be used by any application. Since the code of the morphodynamic model is quite straightforward it can readily be transformed into a DLL that is connected to the GIS. Also, the GIS environment is designed to easily facilitate the use of DLL’s.
Two scales are prominent in this research, the first is the southern bight of the North Sea basin scale, on which the variation in effects of human activities is investigated. The second scale is the scale of the disturbance (sand pit, wind farm). In this research, we do not take into account the ‘local’ effects of the human activities, like head and tail effects of sand pits or
start by investigating if this model is able to predict the occurrence of these large-scale bed forms for a North Sea environment correctly (research questions 1 and 2). The results can increase trust in the models that predict the effects of human activities (research questions 3, 4 and 5).
The research questions that are answered are:
1. What is the role of sediment size in the prediction of the occurrence of sand waves in the North Sea?
2. Can we use an idealized model to predict the occurrence of sand banks in the North Sea?
3. What is the variation in large-scale morphological effects of sand pits over the southern North Sea?
4. What are the large-scale effects of offshore wind farms on the North Sea seabed and how do these effects differ for different design options for the wind farm and for different sites in the southern North Sea?
5. Can the results of this thesis be used by North Sea managers, and if yes, how?
1.5 Outline
In Chapter 2 we use the model of Hulscher (1996) to predict the occurrence of sand waves in the North Sea and compare the model predictions with observations of sand waves. We include a grain size dependency in the form of a critical shear stress, to see if this improves the prediction of sand wave occurrence in the North Sea.
In Chapter 3 we use the same model that is used in Chapter 2 to investigate if we can predict the occurrence of sand banks in the North Sea.
The results of the prediction of sand bank occurrence in the North Sea are used in chapter 4 and 5 to determine whether the model that predicts the morphodynamic effects of human activities (sand pits and offshore wind farms) is valid for a certain area in the North Sea. When sand bank occurrence is not predicted at a certain location, this means that the (2DH) flow conditions that determine sand bank evolution do no occur in that part of the North Sea. Since the models that predict the large-scale morphological effects of human activities on the seabed, are based on the model that describes the evolution of sand banks (2DH flow conditions), this implies that at these locations also no morphodynamics due to human activities are expected. However, at these locations, it is possible that the pit size slowly
increases while its depth decreases, due to diffusive behaviour. We do not take this process into account in the present research.
In this chapter we also carry out a sensitivity analysis of two model input parameters, namely a viscosity variation parameter (ε) and the level of zero intercept (z0). The results for
different values of these parameters are compared with observations of sand banks in the North Sea to find the optimal parameter values to predict the occurrence of sand banks in a North Sea environment.
In Chapter 4 we use the model of Roos et al. (2008) to predict the morphological effects of sand pits. We implemented this model in a GIS of the North Sea to create a tool that can be used to predict the effects of a sand pit on the North Sea seabed as the model uses site-specific input to give predictions for a certain location in the North Sea.
In Chapter 5 we develop a morphodynamic model to investigate the influence of offshore wind farms on the seabed. This model is implemented in the GIS to allow calculation of the effects of offshore wind farms on the North Sea seabed using site-specific and farm design input parameters.
In Chapter 6 the answers to the research questions are presented. Furthermore, this chapter contains the discussion and recommendations for further research.
Chapter 2
Grain size dependency in the occurrence of sand waves
1Abstract
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 sand banks. 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 critical shear stress depending on the sediment grain size. The adaptations lead to more accurate predictions of the occurrence of sand waves in the North Sea. Therefore, grain size dependency and in particular critical shear stress are important to explain the occurrence of sand waves and sand banks in the North Sea.
2.1 Introduction
Shelf seas are very important areas, they are biologically highly active and provide most of the worlds main fisheries. Often, the seabed contains high concentrations of oil and gas supplies and most shelf seas are very busy shipping areas. In most shelf seas sediment is widely abundant and is shaped into a range of bed forms due to the fact that in these areas the largest part of the tidal and wave energy is dissipated. The smallest of these forms are ripples and somewhat larger are megaripples. Here we focus on the large-scale offshore bed forms: sand waves and sand banks.
The spacing of sand waves varies between 100 and 800 m, they can be up to 10 m high (from trough to crest) and their crests are aligned almost perpendicular to the direction of the main tidal flow. Sand waves can be active and migrate with speeds up to 5 m per year (Neméth et al., 2002). Tidal sand banks have a spacing of about 5 km, their height can be up
1
This chapter is slightly adapted after: Van der Veen, H. H., S. J. M. H. Hulscher and M. A. F. Knaapen (2006). Grain size dependency in the occurrence of sand waves. Ocean Dynamics 56: 228-234. doi: 10.1007/s10236-005-0049-7.
to 40 m, up to a few meters below the water surface, and their crests are aligned at a small angle with respect to the direction of the main tidal current.
The North Sea is a shallow shelf sea. The tides in the Southern part are semi-diurnal and the tidal amplitudes ranges from 2.4 meter in the Strait of Dover to 0.6 meter more to the North (Davies et al., 1997). At spring tide, the flow velocities at the surface vary from 1.4 m/s in the western and southern part to 0.7 m/s along the Dutch coast and the northern part (Hydrographical_Survey, 2000). The seabed consists mainly of fine to medium sands, ranging from 125 to 500 µm, but at some places, in the Strait of Dover and in front of the coast of East Anglia (UK), patches of gravel have been observed (Jarke, 1956). On the seabed a variety of large-scale bed forms such as sand banks and sand waves are present.
Bed forms interact with human activities, as the North Sea is intensively used for different purposes. User functions that are affected by the large-scale morphology are navigation, telecommunication cables, oil and gas transportation (pipelines), oil and gas mining, sand extraction, artificial islands and offshore wind farms. For safety reasons, it is important to know where the bed forms occur, what their natural behaviour is and how they interact with human activities.
Here we predict the occurrence of large-scale bed forms in the southern part of the North Sea using an idealized model of Hulscher (1996) and compare the predictions for sand waves with observations. Hulscher and Van den Brink (2001) were the first to compare the model of Hulscher (1996) against observations of sand wave occurrence in the North Sea. In Hulscher and Van den Brink (2001) the spatial variation of sediment characteristics were not accounted for. Furthermore, effects of critical stress were neglected, so even at very low tidal velocities bed pattern formation was allowed.
Belderson (1986) showed (Figure 2.1) that the magnitude of tidal currents and the occurrence of sand waves are related. This supports the idea that a critical treshold has to be exceeded before sand waves will form.
Figure 2.1: Areas where the mean spring near-surface peak tidal currents are stronger than 50 cm/s (gray) and where sand waves occur (within the thick dashed line) (Belderson, 1986).
In the present research we include the above mentioned effects of spatial variations of sediment characteristics and critical stress. All data were gathered in a Geographical Information System (ARCGIS). A GIS is a digital map with extended capabilities to manipulate and analyze geographical data (Heywood et al., 1998). Within this GIS, the new results are compared to observations of sand waves in the North Sea.
In section 2.2 the theoretical bed pattern model, the effects of inclusion of a grain size dependency, and the GIS are discussed. The results and comparison with observations and with earlier predictions without grain size influence can be found in section 2.3. Section 2.4 contains the discussion and section 2.5 presents the conclusions.
2.2 The bed pattern model
2.2.1 The theoretical model to predict large-scale bed forms
The three-dimensional model of Hulscher (1996) explains how tidal currents form rhythmic bed patterns in sandy beds. The model is based on the three-dimensional shallow-water equations, applied to a tidal flow. An empirical bedload transport, which includes slope effects, models the sediment transport and the bed level changes are calculated using the sediment balance. In Hulscher (1996), tide and seabed are regarded as a coupled system. The bed patterns are assumed to be free instabilities of this system. A linear stability analysis is performed to study pattern dynamics, which means that only small amplitude perturbations are considered. The model calculates growth rates for every wavelength and orientation which characterize the spatial structure of the pattern. If all growth rates are negative, all bed patterns are damped and such a flat bed is stable. In this research we define a flat bed as a bed on which no large-scale bed forms occur. However, if at least one bed pattern has a positive growth rate, the situation with the flat bed is unstable and a wavy bed pattern occurs. The wavelength with the fastest growing mode is considered to represent the occurring bed form (Figure 2.2).
Figure 2.2: Characteristic bed forms predicted by the three-dimensional shallow-water model as a function of the resistance
parameter (Sˆ) and the Stokes number (Ev) (Hulscher, 1996).
Figure 2.3: Discretized Ev-S scheme. FB flat bed, SB sand banks, SB & SW sand banks and sand waves, SW sand waves.
The values of the resistance parameter ( Sˆ ) and the Stokes number (Ev) are estimated by
fitting the partial slip model used in Hulscher (1996) to a more realistic turbulence model including a no-slip condition at the bed and a parabolic eddy viscosity (Hulscher and Roelvink, 1997), which leads to the following expressions:
A B H u Ev 2 4 3 κ σ π = (2.1)
(
13)
4 3 ˆ 2 − = AB A B H u S κ σ π (2.2) Where:(
)
− − + − − − + − = ε ε ε ε ε ε ε ε ln1 1 1 1 ln 1 1 ln 2 0 0 H z z H A (2.3) 6 2 3− ε = B (2.4)In which, κ (0.41) is the von Kármán constant, u is the depth-averaged flow velocity, H is the local mean depth, σ is the tidal frequency, ε is the dimensionless viscosity variation parameter (which denotes the influence of waves). In the case of a moderate resistance (small
Sˆ and large Ev), the Stokes boundary layer is much thicker than the water depth and the
vertical shear in the horizontal velocities is small. Then the flow resembles the depth-averaged flow in the sand bank model of Hulscher (1996). The parameter z0denotes the level
z0 is defined analogous to Hulscher and Van den Brink (2001) and references herein and is defined by: 4 . 1 0 2 ∆ ∆ = r r r z λ (Soulsby, 1983) (2.5)
In which ∆r =αmrH and λr =βmrH(Van Rijn, 1993) where αmr (0.03) and βmr (0.5) are
dimensionless coefficients for the megaripple regime in the North sea (Tobias, 1989).
Figure 2.4: Bed form prediction made by Hulscher and Van den Brink (2001). (For a color version see p105.)
Hulscher and Van den Brink (2001) tested the model of Hulscher (1996) against observations of sand wave occurrence on the North Sea basin scale.
Figure 2.4 shows the predictions of Hulscher and Van den Brink (2001). They conclude that for the southern part of the North Sea the parameters that denote the level of zero intercept (z0) and the viscosity variation parameter (ε) differ enough to distinguish between
possible bed forms. With respect to sand waves, the model can predict the outline of a sand wave field but is unable to explain the smaller scale variations in the area. Therefore, they conclude that there must be other factors that are not included in the model, which influence the occurrence of sand waves. One of these factors may be the type of bed deposit.
2.2.2 Inclusion of a grain size dependency
(
)
d50g s
cr
cr θ ρ ρ
τ = − (2.6)
Where g is the gravitational acceleration (9.81 (m/s2)), ρ is the density of seawater (1025 kg/m3),ρs is the sediment density (2650 kg/m3), d50is the median grain size (m) and θcris the
dimensionless critical Shields parameter which is calculated using the equation of Soulsby and Whitehouse (1997):
(
)
[
*]
* 020 . 0 exp 1 055 . 0 2 . 1 1 30 . 0 D D cr + − − + = θ (2.7)In which D* is the dimensionless sediment parameter, denoted by:
3 1 2 50 * ∆ = υ g d D (2.8)
Where ∆ is the relative density and υis the kinematic viscosity of water (1.36·10-6(m2/s)).
0.2 0.3 0.4 0.5 0.6 0.7 0.8 0.9 1 0 0.05 0.1 0.15 0.2 0.25 0.3 0.35 0.4 0.45 0.5 flow velocity [m/s] b e d s h e a r s tr e s s [ N /m 2] White-Colebrook Dawson Soulsby Strickler Critical shear stress
Figure 2.5: Bed shear stress plotted against the flow velocity for different relations from literature. The vertical line denotes the critical flow velocity (0.5 m/s). The grain size is 200 µm and the water depth is 20m.
Figure 2.5 shows the bed shear stress (τb) for varying flow velocity for four typical grain
size dependent bed shear stress equations. The grain size d50 is set at 200µm, which is a
typical grain size found in sand waves. Belderson (1986) showed (Figure 2.1) that the occurrence of sand waves depends on the magnitude of the flow velocity. Above the critical value of 0.5 m/s sand waves are observed. Note that Belderson (1986) uses the near surface velocity, while we use the depth-averaged flow velocity. This means that the boundary value that Belderson denotes might be lower if we use the depth-averaged flow velocity. We choose
to use an equation that exceeds the critical bed stress (τcr) closest to 0.5 (m/s) i.e. Soulsby
(1997), which is denoted by:
2
u CD
b ρ
τ = (2.9)
In which u is the depth-averaged flow velocity and CD is defined by: 7 2 0 0415 . 0 = H z C skin D (2.10)
In which z0 skin is the level of zero intercept due to grain size only:
12 50 0
d
z skin = (2.11)
The bed shear stress and the critical bed shear stress are calculated using location specific parameters (grain size, water depth and flow velocity) as input parameters. In the model we assume that sediment transport takes place when the bed shear stress (τb) exceeds the critical
bed shear stress (τcr):
∇ − = → > = → ≤ h S S b b b b b cr b b cr b v v v v v v λ τ τ τ α τ τ τ τ 0 (2.12)
We use a general sediment transport equation taking into account bed load, which is assumed to be dominant in offshore tidal regimes (Hulscher, 1996). Parameter b denotes the non-linearity of transport in relation with the bed shear stress, λ is a bed-slope correction term, h denotes the height of the bed form and αis a bed load transport proportionality parameter.
2.2.3 The GIS and datalayers
In this research we use a GIS environment to calculate predictions for the southern part of the North Sea. Site-specific parameters are used as model input (Figure 2.6), which results in site-specific predictions for the occurrence of sand waves. The model that is used to predict large-scale bed forms is connected to the GIS using a Dynamic Link Library (DLL).
Figure 2.6: Input layers in the GIS. (For a color version see p105.)
The data on the velocity of the M2 tidal component is interpolated from a grid of points provided by the RIKZ (Rijksinstituut voor Kust en Zee) and is derived from runs of the ZUNOWAQ model (Van Dijk and Plieger, 1988). The water depth (H) data was taken from Hulscher and van den Brink (2001) and originated from Boon and Gerritsen (1997) and Ten Brummelhuis (1997). The median grain size (d50) distribution of the Southern North Sea was
taken from different geographical maps (Rijks_Geologische_Dienst, 1984; Hydrographer_of_the_Navy, 1992). Additional data on d50 for the dutch part of the North Sea
was provided by TNO-NITG.
The data on the occurrence of sand waves is digitized from different geographical maps (Rijks_Geologische_Dienst, 1984; Hydrographer_of_the_Navy, 1992).
2.3 Results and comparison with observations
2.3.1 Results
The bed pattern predictions, after inclusion of grain size dependency, are shown in Figure 2.7. In a large area sand banks and sand waves are predicted. Furthermore, there is a small area where only sand banks are predicted.
When we compare the results of the model to the grain size data, we observe that in the north-east of the research area the presence of fine sediment is combined with low flow velocities, which causes the prediction of a flat bed (i.e. no large-scale bed forms) at this location.
2.3.2 Comparison with observations
Figure 2.8: Comparison of the prediction with observations of sand waves. (For a color version see p105.)
The comparison between the prediction of the model and observations of sand waves in the North Sea is given in Figure 2.8. The model gives a correct prediction in the north of the research area, where a flat bed (no large-scale bed forms are present) is both predicted and observed. Also, along the Dutch coast the prediction of a flat bed agrees with the observations. In the middle of the southern North Sea sand waves are both predicted and observed. The model gives an over-prediction of the area in which sand waves occur, especially along the British coast. Here, only patches of sand waves are observed, but the model predicts a large area of sand waves. The model gives a correct pattern occurrence prediction in 62% of the research area.
Figure 2.9: Discretized scheme (after Figure 2.3) wherein the occurrence of sand waves is plotted. (FB flat bed (i.e. no large-scale bedforms), SB sand banks, SB & SW sand banks and sand waves, SW sand waves).
In Figure 2.9 the discretized Ev -S
)
scheme is plotted that is used to calculate the bed form prediction at a specific location in the North Sea. The black lines denote the calculated Ev and
S )
value pairs for locations in the North Sea where sand waves are observed. As can be seen from the figure, most of the Evand S
)
values of locations where sand waves occur in the North Sea correspond with values where the model predicts sand waves and sand banks. A small part of the sand wave occurrence in the North Sea corresponds with an area in the model where a flat bed is predicted or where no prediction can be given. Note that in this figure, the critical bed shear stress that has to be exceeded is not taken into account.
2.3.3 Comparison of predictions with and without grain size dependency
The model results are also compared to the results without grain size influence (Figure 2.10). When grain size is taken into account in the model, larger areas of flat bed are predicted. This is caused by the fact that the bed shear stress and the critical bed shear stress are influenced by the grain size. When the grain size increases, the bed shear stress and the critical shear stress increase too, but as the critical bed shear stress increases more rapidly than the bed shear stress, at a certain grain size the bed shear stress does not exceed the critical bed shear stress anymore. So, if the bed material is coarser than that critical size, no sediment transport takes place anymore and a flat bed is predicted. A flat bed (no large-scale bed forms) is also predicted along the Belgian and Dutch coast, although the grain size is equal to the grain size in a large part of the North Sea where the occurrence of sand waves is predicted. This difference in prediction is caused by the flow velocity which is lower in front
of the Belgian and Dutch coast. The critical bed shear stress is not exceeded, no sediment transport takes place and hence, no large-scale bed forms are predicted.
Figure 2.10: Comparison between the results of Hulscher and van den Brink (2001) and the model in which a grain size dependency is included.
When a grain size dependency is included in the model, the area where a correct prediction is given increases from 51% to 62%.
2.4 Discussion
The quality and availability of data influences the results strongly. The grain size data is digitized on a grid with a certain size, the size of the grid is such, that patchiness of alternating gravel and sand is not picked up. This might be the case in front of the British coast, where the model predicts a large sand wave area, but observations show only small patches of sand waves. This patchiness may be due to the presence of gravel patches which are not included in the grain size data.
When the critical shear stress is exceeded and sediment transport occurs, this sediment transport is calculated without further taking into account the influence of the critical shear stress. So, the calculation of sediment transport is made using τ instead ofb
(
τb−τcr)
. Thismeans that the calculated sediment transport may be higher than the actually occurring transport. This has no effect on the type of bed form that is predicted but does influence the evolution time of the different bed patterns. As in this chapter we are only interested in the type of bed form that occurs in an equilibrium situation, this way of calculating sediment
class. This can cause errors in the prediction since the actual occurring grain size can be larger or smaller.
Here, we calculated the occurrence of bed patterns using observed grain sizes. In reality, the grain size distribution is coupled to the bed forms. Walgreen et al. (2004) show that the bed forms cause a sorting of the sediment. In general however, these variations are small. The resolution of the grain size data is too coarse to take this effect into account.
Figure 2.11: Prediction of the model, when the bed shear stress equation of Strickler is included. (For a color version see p105.)
In the new prediction, the area where sand waves occur is over-predicted. In Figure 2.5 we see that at the critical flow velocity proposed by Belderson (1986) (0.5 m/s), the bed shear stress equation of Soulsby (1997) has already exceeded the critical bed shear stress and sediment transport is already taking place. Also, Belderson (1986) uses the near surface velocity while we use the depth-averaged velocity, which means that the boundary value of the flow velocity might actually be lower. The only equation that is still below the critical shear stress at a flow velocity of 0.5 m/s is the equation of Strickler. However, this equation gives a large under-prediction of the sand wave area, as can be seen in Figure 2.11. From the results, it can be concluded that the bed shear stress equation that is chosen, has a large influence on the results of the model. As most expressions for the critical bed shear stress and the bed shear stress contain empirical parameters, which are estimated using datasets that are mostly acquired from laboratory experiments, these parameters can be less suited for offshore conditions and adapting these parameters could yield a better result.
2.5 Conclusion
Including a grain size dependency in the model, improves the predictions of the model. Large areas are predicted in which sand banks and sand waves occur, in some smaller areas
only sand banks are predicted. Along the Belgian and Dutch coast and in the north east of the research domain areas of flat bed are predicted. There are large areas in which sand waves are both predicted and observed. When the predictions that include a grain size dependency are compared to predictions without sediment influence, larger areas of flat bed are predicted and the overall correct prediction increases from 51% to 62%. This means that inclusion of a grain size dependency is important in order to predict the occurrence of sand waves.
Chapter 3
Predicting sand banks in the North Sea
Abstract
Sandy shallow seas, like the North Sea are very dynamic. Several morphological features are present on the seabed, from small ripples to sand waves and large tidal sand banks. Sand banks have a wavelength between 1 and 10 km and can have a height of several tens of meters. They can induce significant depth variations and have an impact on human activities that take place in the North Sea. Therefore, it is important to know where sand banks occur and what their natural behaviour is. Here we use an idealized model to predict the occurrence of sand banks in the North Sea. Also, we carry out a sensitivity analysis of two model parameters, namely the viscosity variation parameter (ε) and the level of zero intercept (z0), to
investigate their influence on the model results. The results show that the model is able to predict the occurrence of sand banks in the North Sea in 64,8% of the area and that the value of the level of zero intercept has a large influence on the results.
3.1 Introduction
Shelf seas like the North Sea are areas that are biologically highly active and provide most of the world’s main fisheries. Often, the seabed contains high concentrations of oil and gas supplies and most shelf seas are very busy shipping areas. In most shelf seas, sediment is widely abundant and due to the fact that in these areas the largest part of the tidal and wave energy is dissipated, the bed is shaped in a range of bed forms by the tidal flow over the erodible bed. (Brown et al., 1999) The smallest of these forms are ripples, with a height in the order of cm’s and somewhat larger are megaripples, here we focus on the largest offshore bed forms: sand banks. An overview of sand bank occurrence in the North Sea is given in Figure 3.1.
Figure 3.1: An overview of the southern part of the North Sea. The black lines denote sand bank occurrence adapted after Dyer and Huntley (1999). The gray areas denote the digitized areas that we used to compare to the model results.
Sand banks can either be formed by the tide or are relict features. Banks that are formed by the tide can be either actively maintained or moribund. Actively maintained sand banks are formed by the modern (late Holocene) tidal regime. Moribund sand banks were formed during periods of lower sea levels, they occur in deeper water where the present tidal current is too weak to form sand banks (no sediment transport occurs under the present tidal current) (Collins et al., 1995). Moribund banks are not covered with sand waves and have more rounded crests than active sand banks. Also, their slopes are gentler, in the order of 1˚. These banks are mostly separated by a sandy or muddy seafloor. Relict sandbanks are not formed by (present or former) flow-topography interaction, but can e.g. be left overs from old coastal dunes. They can be intensively reworked by the present regime. Banks often store large amounts of sand and they appear to be hydraulically maintained. The most common situations that lead to accumulation of sediment are a reversal in the sand transport direction involving bedload convergence or a reduction in shear stress (Dyer and Huntley, 1999).
The North Sea is a shallow shelf sea. The tides in the southern part are semi-diurnal and the tidal amplitudes ranges from 2.4 m in the Strait of Dover to 0.6 m more to the North (Davies et al., 1997). At spring tide, the flow velocities at the surface vary from 1.4 m/s in the western and southern part to 0.7 m/s along the Dutch coast and the northern part (Hydrographical_Survey, 2000). The seabed consists mainly of fine to medium sands, ranging
telecommunication cables, oil and gas transportation (pipelines), oil and gas mining, sand extraction, artificial islands and offshore wind farms. For safety reasons, it is important to know where the bed forms occur or might be generated and which parameters are crucial herein. The model underlying the prediction of sand waves, i.e. Hulscher (1996), is also capable to predict sand banks. In Chapter 2 we successfully predicted the occurrence of sand waves in the North Sea. In this chapter, we investigate if the same model can be used to predict the occurrence of sand banks in the North Sea. The research question that we want to answer is: to what extent is the model able to predict the occurrence of sand banks in the North Sea?
This chapter is organized as follows, in Section 3.2 the idealized model (Hulscher, 1996) is described. In section 3.3 model results are listed and we compare these results with observations of sand banks. In section 3.4 we investigate the sensitivity of two model parameters, which determine the turbulence model, namely the viscosity variation parameter (ε) and the level of zero intercept (z0). Section 3.5 contains the discussion and in section 3.6
the conclusions are listed. 3.2 Model
3.2.1 The model to predict large-scale bed forms
The three-dimensional model of Hulscher (1996) explains how tidal currents form rhythmic bed patterns in sandy beds. The model is based on the three-dimensional shallow-water equations, applied to a tidal flow. An empirical bed load transport, which includes slope effects, models the sediment transport and the bed level changes are calculated using a sediment balance. In Hulscher (1996), tide and seabed are regarded as a coupled system. The bed patterns are assumed to be free instabilities of this system. A linear stability analysis is performed to study pattern dynamics, which means that only small amplitude perturbations are considered. The model calculates growth rates for every wavelength and orientation which characterize the spatial structure of the pattern. If all growth rates are negative, all bed patterns are damped and so the flat bed is stable. In this research we define a flat bed as a bed where no large-scale bed forms occur. However, if at least one bed pattern has a positive growth rate, the flat bed is unstable and a wavy bed pattern develops. For a more elaborate description of the model, see Van der Veen et al. (2006).
In this chapter we used the model to predict the occurrence of tidal sand banks in the North Sea. In the case of a moderate resistance (small Sˆ and large Ev), the Stokes boundary layer is
much thicker than the water depth and the vertical shear in the horizontal velocities is small. Then the flow resembles the depth-averaged (2DH) flow in the sand bank model of Hulscher et al. (1993).
The values of the resistance parameter (Sˆ) and the Stokes number (E ) are estimated by v
fitting the partial slip model used in Hulscher (1996) to a more realistic turbulence model including the no-slip condition at the bed and a parabolic eddy viscosity distribution (Hulscher and Roelvink, 1997), which leads to the following expressions:
A B H u Ev 2 4 3 κ σ π = (3.1)
(
13)
4 3 ˆ 2 − = AB A B H u S κ σ π (3.2) Where:(
)
− − + − − − + − = ε ε ε ε ε ε ε ε ln1 1 1 1 ln 1 1 ln 2 0 0 H z z H A (3.3) 6 2 3− ε = B (3.4)In which, κ (0.41) is the von Kármán constant, u is the depth-averaged flow velocity, H is the local mean depth, σ is the tidal frequency and ε is the viscosity variation parameter (which denotes the influence of waves), which may vary between 0 and 1, where ε = 1 represents a parabolic distribution over the water column and a rigid lid approach and ε = 0 represents a linear increase of the eddy viscosity (Soulsby, 1990), and resembles the situation in which there is influence of waves and wind on the eddy viscosity, which is denoted by:
0 10 20 0 5 10 15 20 25 30 ε =0 w a te rd e p th [ m ] 0 10 20 0 5 10 15 20 25 30 ε =0.25 0 10 20 0 5 10 15 20 25 30 ε =0.5 eddy-viscosity (ν) [m2/s] 0 10 20 0 5 10 15 20 25 30 ε =0.75 0 10 20 0 5 10 15 20 25 30 ε =1
Figure 3.2: Eddy viscosity (ν) as function of the water depth for different values of the viscosity variation parameter ε.
The parameter z0denotes the level of zero-intercept (the level above the seabed, where the
flow velocity is zero). The value of z0 varies with grain size and can also be influenced by the
occurrence of bed forms like ripples and megaripples. To predict the occurrence of sand banks in the North Sea, we used values of z0 based on the characteristics of megaripples in the
North Sea (Tobias, 1989). This is analogous to Hulscher and Van den Brink (2001) and references herein and is defined by:
4 . 1 0 2 ∆ ∆ = r r r z λ (Soulsby, 1983) (3.6)
In which ∆r =αmrH and λr =βmrH(Van Rijn, 1993) where αmr (0.03) and βmr (0.5) are
dimensionless coefficients for the megaripple regime in the North sea (Tobias, 1989).
A grain size dependency is included in the model. The grain size of the sediment influences the initiation of motion of the grains. Sediment transport takes place if the bed shear stress (τb) exceeds the critical shear stress (τcr).
The critical bed shear stress τcr is denoted by:
(
)
d50g s
cr
cr θ ρ ρ
τ = − (3.7)
Where g is the gravitational acceleration (9.81 (m/s2)), ρ is the density of seawater (1025 kg/m3),ρs is the sediment density (2650 kg/m3), d50 is the median grain size and θcris the
critical Shields parameter which is calculated using the equation of Soulsby and Whitehouse (1997):
(
)
[
*]
* 020 . 0 exp 1 055 . 0 2 . 1 1 30 . 0 D D cr + − − + = θ (3.8)In which D* is the dimensionless sediment parameter, denoted by:
3 1 2 50 * ∆ = υ g d D (3.9)
Where ∆ is the relative density and υis the kinematic viscosity of water (1.36·10-6(m2/s)). The bed shear stress is denoted by:
2
u CD
b ρ
τ = (3.10)
In which u is the depth-averaged flow velocity and CD is defined by: 7 2 0 0415 . 0 = H z C skin D (Soulsby, 1997) (3.11)
In which z0 skin is the level of zero intercept due to grain size only:
12 50 0
d
z skin = (3.12)
The bed shear stress τb and the critical bed shear stress τcr are calculated using the
site-specific parameters (grain size, water depth and flow velocity) as input parameters. In the model we assume that sediment transport takes place if the bed shear stress exceeds the critical bed shear stress:
∇ − = → > = → ≤ h S S b b b b b cr b b cr b v v v v v v λ τ τ τ α τ τ τ τ 0 (3.13)
We use a general sediment transport equation and only take into account bed load, which is assumed to be dominant in offshore tidal regimes (Hulscher, 1996). Parameter b (~3) denotes the non-linearity of transport in relation with the bed shear stress, λ (usually 2) is a bed-slope correction term, h denotes the height of the bed form and α is a bed load transport
3.2.2 Data
The data on the velocity of the M2 tidal component is interpolated from a grid of points provided by the RIKZ (Rijksinstituut voor Kust en Zee) and is derived from runs of the ZUNOWAQ model (Van Dijk and Plieger, 1988). The water depth (H) data was taken from Hulscher and van den Brink (2001) and originated from Boon and Gerritsen (1997) and Ten Brummelhuis (1997). The median grain size (d50) distribution of the Southern North Sea was
taken from different geographical maps (Rijks_Geologische_Dienst, 1984; Hydrographer_of_the_Navy, 1992). Additional data on d50 for the dutch part of the North Sea
was provided by TNO-NITG.
The data on sand bank occurrence is adapted from Dyer and Huntley (1999) and is digitized by manually selecting the areas where sand banks occur. Following, a corridor of 5km around the original areas is selected, which is assumed to be on average half the wavelength of a sand bank. Where the different areas overlap each other, they are merged, thus arriving at the sand bank occurrence in the southern part of the North Sea as is depicted in Figure 3.1.
3.3 Results
3.3.1 Model results
Figure 3.3 shows the prediction (with default values ε= 0.5), of sand bank occurrence in the North Sea.
As can be seen in Figure 3.3 the occurrence of sand banks is predicted in a large part of the southern North Sea. In a small area in the middle of the southern North Sea, between the British coast and the Dutch coast, sand banks are predicted exclusively. In the northern part of the North Sea a flat bed is predicted. Note that also sand waves are predicted by the model, but here we only focus on the prediction of sand banks and do not discuss the prediction of sand waves.
3.3.2 Comparison of model results with observations of sand banks
Figure 3.4 shows the comparison between the model results and observations of sand banks.
Figure 3.4: Comparison of model predictions with observations of sand banks. (For a color version see p107.)
The categories “predicted and observed” and “not predicted and not observed” represent the cases for which the model gives a correct prediction.
As can be seen, there is an over-prediction in the occurrence of sand banks (predicted but not observed). Also, the sand bank area in the northern part of the North Sea, off the coast of the Dutch Wadden isles is not predicted correctly by the model. Quantitatively, the model gives a correct prediction in 64.5% of the area and an incorrect prediction in 32.5% of the area (in 3% of the area, the model does not give a prediction).
