Wave dissipation over vegetation fields

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Wave Dissipation Over

Vegetation Fields

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Wave Dissipation Over

Vegetation Fields

Proefschrift

ter verkrijging van de graad van doctor aan de Technische Universiteit Delft,

op gezag van de Rector Magnificus prof.ir. K.C.A.M. Luyben, voorzitter van het College voor Promoties,

in het openbaar te verdedigen

op maandag 30 mei 2011 om 12.30 uur

door

Tomohiro SUZUKI

Master of Engineering, Saitama University, Japan geboren te Mito, Japan

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Prof.dr.ir. M.J.F. Stive, Prof.dr.ir. W.S.J. Uijttewaal

Samenstelling promotiecommissie:

Rector Magnificus voorzitter

Prof.dr.ir. M.J.F. Stive Technische Universiteit Delft, promotor Prof.dr.ir. W.S.J. Uijttewaal Technische Universiteit Delft, promotor

Prof.dr. Peter M.J. Herman Het Nederlands Instituut voor Ecologie (NIOO-KNAW) Prof.dr.ir. Arnold W. Heemink Technische Universiteit Delft

Prof.dr.ir. Julien De Rouck Universiteit Gent

Dr. Taro Arikawa Port and Airport Research Institute Dr.ir. Marcel Zijlema Technische Universiteit Delft

Prof.dr.ir. Guus Stelling Technische Universiteit Delft, reservelid

This research has been financially supported by the Rotary Foundation, Het Lam-mingafonds, the Water Research Center Delft and Delft University of Technology.

Keywords: Wave dissipation, bulk drag coefficient, vegetation, CADMAS-SURF/3D, Large-Eddy Simulation, Immersed Boundary Method, SWAN-VEG.

This thesis should be referred to as: Suzuki, T.(2011). Wave Dissipation Over Vege-tation Fields. Ph.D. thesis, Delft University of Technology.

ISBN 978-94-91211-44-7

Copyright c 2011 by Tomohiro Suzuki

Printed by PrintPartners Ipskamp B.V., the Netherlands.

All rights reserved. No part of the material protected by this copyright notice may be reproduced or utilized in any form or by any means, electronic or me-chanical, including photocopying, recording or by any information storage and retrieval system, without written permission of the author.

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Summary

It has been widely recognized that ongoing climate change, most likely due to human interference with nature, may accelerate sea level rise and increase storm intensity. It is therefore urgent to design countermeasures to alleviate the im-pact of climate change on coastal regions. Apart from the view point of coastal protection, it is also very important for coastal engineers to keep an eye on en-vironmental issues in the coastal region. In this context, vegetation fields such as salt marshes, sea grasses and mangrove forests in coastal regions have started to attract the attention of coastal engineers due to their function as wave atten-uator. However, the wave attenuation function of a vegetated field is not well understood yet. To utilize coastal vegetation fields as a part of coastal manage-ment in practice, it is crucial to accumulate more knowledge about the physical processes, especially the hydraulic processes, and these need to be modeled in a practical sense. Hence, this thesis is intended as an investigation of the process of wave dissipation over vegetation fields through various approaches, specifically theoretical, physical and numerical studies.

Prior to practical modeling of wave attenuation, theoretical background and literature reviews are conducted at the beginning of this research. Basic theories and major research efforts on the drag force are introduced indicating the impor-tance of obtaining the bulk drag coefficient in different conditions. In the end formulations for wave dissipation over a multiple-cylinder field are developed, based on the literature. In the physical experiments, hydrodynamics around a salt marsh are investigated. Five different configurations of a salt marsh includ-ing two different density conditions for rigid cylinders and a real vegetation case are tested in a wave flume in terms of wave dissipation, wave reflection, velocity fields and pressures acting on the cliff. After the physical experiments, a 2DV spatial averaged model is developed. This model is validated by the physical model results. It can simulate wave dissipation appropriately by incorporating the defined porosity and surface permeability for artificial vegetation and natural vegetation, even in a strongly varying topography. Also velocities and pressures acting on a cliff are reproduced well. In the case studies, impact on a dyke in different wave conditions, impact on seedlings from a view point of vortices and impact on cliff erosion are discussed.

Even when the model is appropriate, it is often difficult to choose an appropri-v

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ate bulk drag coefficient to estimate vegetation induced wave attenuation. This is partly due to the complexity of the turbulence structure over the vegetated field. To understand the bulk drag coefficients, a three dimensional numerical sim-ulation model CADMAS-SURF/3D is further developed incorporating an Im-mersed Boundary Method and a Large Eddy Simulation technique. From the validation, all the results obtained show good agreement with the reference data in literature. After the validation, case studies were conducted with regard to the bulk drag coefficient. From the study, it was concluded that the drag reduction is not just a function of density but also a function of the parameter 2a/S, where 2a is the stroke of the motion and S is the cylinder spacing. When 2a is less than S, the effect of the density is neglected because the wake does not reach the other cylinders even when the density is high. Additionally it was found that the drag reduction is not only related to 2a/S and but also to β, which is a frequency pa-rameter described as Re/KC or D2/νT. In this study it was not possible to define a clear relationship quantitatively between wave conditions and cylinder array condition because of data limitations. However, a certain tendency was obtained. For the engineering practice of wave dissipation simulation, it is important to develop a computationally less expensive model. A 2DH model based on a third generation action balance wave model (SWAN) with vertical schematization of the vegetation is developed in this thesis. This is the most detailed implementa-tion of wave dissipaimplementa-tion of vegetaimplementa-tion in a 2D numerical model to date. After the implementation and the validation, sensitivity analyses are conducted in terms of frequency spectrum shape, directional spreading (directional spectrum shape) and layer schematization. This model is capable of calculating not only the effect of horizontal variation of vegetation but also of wave diffraction around tion patches. This is quite important when the wave height behind the vegeta-tion patch is of importance. Subsequently two practical engineering applicavegeta-tions based on the developed SWAN model developed are presented. One is about the effectiveness of mangroves in attenuating cyclone-induced waves including a quantitative case study for a mangrove island near the upcoming Dhamra Port in Orissa, India. The other is about wave attenuation by a field of willows in front of a river dike in the Dutch Noordwaard polder. In both cases, wave attenua-tions in extreme condiattenua-tions are calculated and some conclusions are drawn. The first focuses on wave propagation with different vegetation factors and hydraulic conditions in a practical topography while the latter focuses on the capability of a willow field to attenuate waves in a specific condition and discusses uncertain-ties and model limitations which can be also very important to a practical design. Finally, each model developed in this thesis is evaluated in terms of its ap-plicability. In practice, many effects related to wave dissipation over vegetation fields have to be considered. In general, the 2DH model in this study (SWAN) is most suitable to a practical application compared to the other models devel-oped in this thesis (2DV and 3D model) when applied to fields due to computa-tional resources needed and applicability to wave characteristics. However, the

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Summary vii

2DH model has more limitations than the other models. For instance, the model has difficulties in modeling in a situation of strongly varying topography. Often cliffs, which are common and important features of most salt marshes, can be seen at the edge of the salt marsh and experiencing erosion. Thus it is important to know the hydrodynamics around the cliff, not only in terms of wave dissipa-tion but also velocity fields, pressures to the cliff and forces to the cylinders, in view of eco-engineering and sustainable coastal management applications. The 2DV model is capable of producing these results. In the 3D model, wake interfer-ence which is important to obtain the bulk drag coefficient in a multiple cylinder field, is calculated. Therefore, it is important to use different models depending on the purpose of the calculations.

Practical models and a relationship between the bulk drag coefficient and wave parameters are developed in this thesis, but further investigation is still necessary on wave dissipation over vegetation fields. Specifically for a better understanding of the effective bulk drag coefficient, experimental flume studies with a wide range of parameters are highly recommended since there are not enough data for such an analysis.

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Samenvatting

Het is algemeen erkend dat de huidige klimaatverandering, meest waarschijnlijk te wijten aan menselijk ingrijpen in de natuur, tot een verhoogd risico op zee-spiegelstijging en een verhoogde intensiviteit van stormen leidt. Het is daarom dringend noodzakelijk om tegenmaatregelen te ontwerpen om de gevolgen van de klimaatverandering voor kustregio’s te verlichten. Naast kustbescherming is het ook zeer belangrijk voor de kustingenieurs om het milieu in het kustge-bied in het oog te houden. In dit verband beginnen natuurlijke vegetaties zoals zoutmoerassen, zeegrassen en mangrovebossen in kustregio’s nu meer aandacht te krijgen in hun functie als golfdemper. Echter, de werking van golfdemping in een begroeid veld is nog niet goed begrepen. Voor het gebruik van kustvegetaties als onderdeel van het beheer van kustgebieden in de praktijk, is het van cruci-aal belang om meer kennis te vergaren over de fysische processen, met name de hydraulische processen. Het is van belang dat deze processen ook praktisch ge-modelleerd worden. Deze dissertatie betreft het onderzoek van het proces van ”golf-dissipatie ¨over diverse vegetaties door verschillende benaderingen, in het bijzonder in theoretische, fysische en numerieke studies.

Voorafgaand aan de praktische modellering van golfdemping, is een theore-tische achtergrond- en een literatuuronderzoek uitgevoerd. De basistheorieen en de meest belangrijke onderzoekresultaten met betrekking tot de stromingsweer-stand worden geintroduceerd, die het belang onderstrepen in het verkrijgen van de weerstandscoefficient onder verschillende omstandigheden. Vervolgens wor-den op basis van de literatuurgegevens formuleringen voor de golf-dissipatie over een veld van meerdere cilinders ontwikkeld. In de fysische experimenten wordt de hydrodynamica rond schorren onderzocht. Vijf verschillende configu-raties van een schor met inbegrip van twee verschillende dichtheden voor starre cilinders en een met echte vegetatie worden in een golfgoot getest op groothe-den als golfdissipatie, golfreflectie, snelheidsveld en druk op de klif. Volgend op deze experimenten, is een 2DV ruimtelijk gemiddelde model ontwikkeld. Dit model is gevalideerd met de fysische resultaten van het model. Het model kan de golf-dissipatie op juiste wijze simuleren door de integratie van de gedefinieerde porositeit en permeabiliteit van de oppervlakte voor kunstmatige en natuurlijke vegetatie, zelfs voor een sterk varierende topografie. De snelheden en drukken op een klif worden goed weergegeven. Bij toepassingen in de case-studies wordt

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het effect op een dijk bij verschillende golf condities behandeld alsook het effect op de zaailingen uit een oogpunt van wervelingen, en het effect op de klif erosie. Zelfs wanneer het model geschikt is, is het vaak moeilijk om een passende bulk weerstandscoefficient te kiezen waarmee de door de vegetatie-geinduceerde golfdemping geschat kan worden. Dit is deels te wijten aan de complexiteit van de structuur van de turbulentie over de vegetatie. Om de weerstandscoefficien-ten te begrijpen is een drie dimensionaal numeriek simulatiemodel

CADMAS-SURF/3D verder ontwikkeld, waarin een ”Immersed Boundary Method”gecombineerd wordt met een ”Large Eddy Simulation”techniek. Bij de validatie tonen alle

ver-kregen resultaten goede overeenkomst met de referentiegegevens in de litera-tuur. Na de validatie, werden case studies uitgevoerd met betrekking tot de weerstandscoefficient. Uit de studie kan worden geconcludeerd dat de weer-standsvermindering niet alleen een functie is van dichtheid, maar ook een func-tie is van de parameter 2a/S, waar 2a is de afgelegde weg van de beweging is en S de afstand tussen de cilinders is. Wanneer 2a kleiner is dan S, kan het effect van de dichtheid verwaarloosd worden, omdat het zog de andere cilinders niet be-reikt, zelfs wanneer de dichtheid hoog is. Bovendien bleek dat de vermindering van de weerstand niet alleen gerelateerd is aan 2a/S en maar ook aan β; een fre-quentie parameter beschreven als Re/KC of D2/νT. In deze studie was het niet mogelijk om een duidelijke kwantitatieve relatie te definieren tussen golfcondi-ties en cilinder configuragolfcondi-ties vanwege de beperkingen van gegevens. Echter, een bepaalde tendens is wel zichtbaar geworden.

Voor de technische toepassing van golf-dissipatie simulatie is het belangrijk om een minder rekenintensief model te ontwikkelen. In dit proefschrift is een 2DH model ontwikkeld met een verticale schematisatie van de vegetatie, geba-seerd op een derde generatie ’action balance’ golfmodel (SWAN). Dit is de meest gedetailleerde implementatie van golf-dissipatie van vegetatie in een 2D nume-riek model tot nu toe. Na de implementatie en validatie, zijn gevoeligheidsana-lyses uitgevoerd met betrekking tot de vorm van het spectrum, richtingsprei-ding en schematisatie per laag. Dit model is in staat om niet alleen de gevolgen van horizontale variatie van vegetatie te berekenen, maar ook van golf diffrac-tie rondom vegetadiffrac-tie. Dit is vooral van belang wanneer de golfhoogte achter de vegetatie er toe doet. Vervolgens worden twee praktische waterbouwkun-dige toepassingen op basis van het ontwikkelde SWAN model gepresenteerd. Een gaat over de doeltreffendheid van mangroves bij de demping van cyclone-geinduceerde golven met inbegrip van een kwantitatieve case study voor een mangrove eiland in de buurt van de toekomstige haven van Dhamra in Orissa, India. De andere gaat over golfdemping door een veld van wilgen voor een rivierdijk in de Nederlandse Noordwaardse polder. In beide gevallen, wordt golfdemping onder extreme condities berekend en worden daaruit conclusies getrokken. De eerste studie richt zich op golfvoortplanting met verschillende ve-getatie kenmerken en hydraulische omstandigheden in een specifieke topografie, terwijl de tweede studie zich richt op het vermogen van een wilgen vegetatie om

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Samenvatting xi

golven onder een bepaalde omstandigheden te verzachten en komen de onze-kerheden en model beperkingen ter sprake die belangrijk zijn in de toepassing van het ontwerp.

Tot slot, elk model ontwikkeld in dit proefschrift wordt geevalueerd in ter-men van de toepasbaarheid ervan. In de praktijk zullen veel effecten met be-trekking tot golf-dissipatie over vegetatie in acht moeten worden genomen. In het algemeen is het 2DH-model in deze studie (SWAN) het meest geschikt voor een praktische toepassing met vegetatie, in vergelijking met de andere modellen ontwikkeld in deze thesis (2DV en 3D-model) als gevolg van de benodigde re-kenkracht en toepasbaarheid voor de golven karakteristieken. Echter, het 2DH model heeft meer beperkingen dan de andere modellen. Bijvoorbeeld, het model is problematisch bij een sterk varierende bodemligging. Vaak ondervinden klif-fen, een veelvoorkomend en belangrijk kenmerk van de meeste schorren, erosie aan de rand van het schor. Het is dus belangrijk om de hydrodynamische pro-cessen rond de klif te kennen, niet alleen in termen van golf- dissipatie maar ook in termen van snelheid, druk op de klif en krachten op de cilinders, met het oog op toepassingen in eco-engineering en duurzame beheer van kustgebieden. Het 2DV model is in staat om deze resultaten te genereren. In het 3D-model is zog in-teractie berekend welke belangrijk is voor het verkrijgen van de weerstandscoef-ficient voor een veld met meerdere cilinders. Het is belangrijk om verschillende modellen te gebruiken, afhankelijk van het doel van de berekeningen.

In dit proefschrift zijn praktische modellen en een relatie tussen de bulk sleep coefficient en golf- parameters ontwikkeld, maar nader onderzoek is nog steeds nodig met betrekking tot golf-dissipatie over vegetatie. Specifiek om een betere inzicht in de effectieve weerstandscoefficient te krijgen worden experimentele goot-studies met een ruime variatie van de parameters sterk aanbevolen omdat er niet voldoende gegevens zijn voor een dergelijke analyse.

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Chapter 1 Introduction

1.1 Background

It has been widely recognized that ongoing climate change, most likely due to human interference with nature, may accelerate sea level rise and increase storm intensity. In fact, sea level rise for the past century has been about 18 cm (Dou-glas, 1997), and is estimated to be at least 18-59 cm in the next century (IPCC, 2007). A recent study (Rahmstorf, 2007) indicates that maximum sea level rise in 2100 can be up to 1.4 m above 1990 levels. With regard to the increase of storm intensity, IPCC (2007) reports that ’It is likely (>66%) that we will see increases in hurricane intensity during the 21st century’. In line with this, Saad-Lessler and Tselioudis (2010) show based on climate change models that storm intensity will increase while storm frequency will decrease in the United States. These esti-mates indicate great threats for those areas located in the low-lying lands. There are many other challenging issues in coastal regions other than climate change. For example, coastal recessions and environmental issues are problems which have been a focus of constant attention in coastal regions. Coastal recessions oc-cur not only due to sea level rise (e.g. Bruun, 1962) but also due to other factors such as human economic activities which disturb the equilibrium of nature. The environmental issues are also strongly related to human interference with the ecosystem. Thus, most of the problems at coasts are anthropogenic induced on one level or another.

The negative impacts on nature have made civil engineers aware of the im-portance of keeping the balance of natural ecosystems, and the trend of civil en-gineering works has been shifting from ’hard’ to ’soft’ in the last few decades. For instance, this trend can be seen in a project ’Building with Nature’ in the Nether-lands. This project programme states that ’The focus is on developments with policy-makers, designers, project contractors and project managers teaming up to bring together factors such as safety, natural values, economic potential, qual-ity of life and sustainabilqual-ity in ways that generate mutual benefits’(http://www. ecoshape.nl). Thus, the Netherlands tries to develop sustainable infrastructure at

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the waterfront. As another example, in Japan, a law related to coastal manage-ment (Coast Law) has been revised in 1999. In the revision, two new concepts have been added to the original law which was only aimed at coastal protection from coastal disasters such as tsunamis and storm surges. These newly-added concepts are 1) the maintenance and conservation of coastal environments and 2) the development of the coastline for public use. Thus, current civil engineers have been trying to find ways to intervene in harmony with nature. In this con-text, it would become more important than before to explore sustainable and cost-effective methods to protect the shoreline considering the impacts on the entire ecosystem.

In the above context, vegetation fields such as salt marshes, sea grasses and mangrove forests in the coastal region have started to attract the attention of civil engineers. In fact, salt marshes used to be regarded as waste lands in the past. However, salt marshes have come to be appreciated after they came to be consid-ered as effective for protection from coastal disasters. Specifically, plants in salt marshes play an important role in wave attenuation (M ¨oller et al., 1999; M ¨oller, 2006) in extreme storm events. Similarly, it has been known that mangroves can be used as buffer zones against storm surges, a fact that was not appreciated be-fore. Besides the wave attenuation function, vegetation fields promote sediment deposition (Bouma et al., 2005) by reducing the velocity of the water in the veg-etation canopy. According to van de Koppel et al. (2005), salt marshes can raise the level of the land, at rates which correspond with the rate of sea level rise. In other words, vegetation fields work to maintain the balance of nature much like an on site field engineer. Other than these physical characteristics, vegeta-tion fields have large ecological values. The Ramsar Convenvegeta-tion is a well known international law established in order to preserve the wetlands for migrant birds. Because of migrant birds, the salt marsh is used as places for wildfowl. Man-grove forests are also being used as recreation places (Ahmad, 2009). Last but not least, vegetation itself has a function to reduce carbon dioxide by the process of photosynthesis.

Thus, coastal managements using vegetation fields can be a key for the sus-tainable and cost-effective coastal protection in this age. However, research on physical processes in coastal vegetation have been less than in geochemical and biological processes where scientists have long viewed these as intrinsically inter-esting environments (Allen and Pye, 1991). To utilize coastal vegetation fields as a part of coastal management in practice, it is crucial to accumulate more knowl-edge about the physical processes, especially the hydraulic processes, and they need to be modeled in a practical sense. Hence, this thesis is intended as an inves-tigation of wave dissipation over vegetation fields to quantify border conditions at sea defences. Several specific topics on wave dissipation over vegetated fields will be discussed in this thesis.

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1.2. Problem description 3

1.2 Problem description

Vegetation model and bulk drag coefficient

As stated above, coastal vegetation such as mangrove forests and salt marshes act as a coastal protection by reducing wave energy. An important process is wave energy dissipation due to the cylindrical structures that the vegetation forms. The vegetation imposes drag and friction forces on the water motion, which re-sults in energy loss in waves. Understanding the hydraulic processes in the veg-etation fields is important for the protection of highly populated areas behind it, for the preservation of the vegetation, as well as for the estimation of erosion potential in and around the vegetation.

Although there have been studies (e.g. Asano et al., 1993; Kobayashi et al., 1993; M ¨oller et al., 1999; M´endez and Losada, 2004) about hydraulic processes especially for wave dissipation over vegetation fields, a lot of work is still needed to apply them to a practical estimation. Models of wave dissipation by vegeta-tion are various, and it needs to be decided which models are suitable for the physical representation. Also vegetation fields have a spatial distribution of dif-ferent vegetation species each with a difdif-ferent structure. Most of the existing models are based on 1D estimations, hence, it is difficult to calculate wave dissi-pation or erosion around a patch in a 2DH plane under the condition of a wide directional wave spectrum, which is the case in realistic wave conditions. Addi-tionally waves also have many characteristic features such as breaking, shoaling, diffraction and refraction which have to be modeled at the same time.

Still, even though the modeling is undertaken, the most challenging task in the estimation of wave dissipation is how to quantify the bulk drag coefficient in an array of cylinders without any calibration. For example, the case of the most simple condition, namely the case of an array of rigid cylinders, still needs to be calibrated by field measurements. However, it might be possible to esti-mate the bulk drag coefficient. Looking into practice, in most of the cases the bulk drag coefficient of rigid cylinders is supposed to be 1.0 (Iimura et al., 2007; Narayan, 2009; de Oude et al., 2010; Das et al., 2010) for estimations when it is a simple cylindrical array (e.g. mangrove forest) and the distance of each cylinder is far enough in the subcritical flow regime. This value is decided based on flow conditions and being applied to wave conditions. This choice can be practical, but it lacks background theories and evidence. For instance, the drag coefficient of a single cylinder in planar oscillations varies from 0.5-2.5 according to Sarp-kaya and Isaacson (1981) and is quite sensitive to hydraulic parameters such as Reynolds number, Keulegan-Carpenter number and beta (frequency parameter). Not only this, the value can change in an array of cylinders. According to exper-imental studies by Heideman and Sarpkaya (1985), the bulk drag coefficient in an array of cylinders is smaller than the drag coefficient for a single cylinder in an oscillatory flow. And Nepf (1999) showed that the bulk drag coefficient in a

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flow changes drastically with different cylinder density. Massel et al. (1999) have already shown the effect of a difference in density but the density variations are limited. Considering these facts, the bulk drag coefficient in an array of cylinders under wave condition should be smaller than the one for a single cylinder and should be decided in a more reliable way.

Wave propagation over a strongly varying topography

Salt marshes often have a strongly varying topography, namely a salt marsh cliff, and its height is from a few centimeters to over 1 m (Callaghan et al., 2010). At the cliff, many processes come together: here the wave attack and wave attenua-tion are strong, and it is often the case that the cliff is the border of a mud-flat and vegetation. Also, it is the place where the salt marsh erodes. It can be assumed that structural salt marsh erosion has a negative effect on coastal defence. How-ever, it is difficult to know how effective the cliff is in attenuating waves or how dangerous it is if it erodes a few meters. Answering these questions would be im-portant for maintaining sustainable coastal management using a vegetation field but little is known about hydraulic characteristics around the salt marsh cliff due to the special nature of the topography, namely a stepped bottom and vegetation.

1.3 Objectives of this study

This study mainly focuses on wave dissipation in a field of multiple cylinders on gently sloping and stepped bottoms. An important aspect investigated is how to incorporate the wave dissipation effect into wave models and how to trans-late the shadowing and turbulence effects into the bulk drag coefficient in a field of multiple cylinders. The objectives of this study are: (i) to develop numeri-cal models capable of estimating wave dissipation over vegetation fields, (ii) to study the physical relationship between bulk drag coefficient and density of the multiple cylinders to obtain a reliable estimation for wave dissipation, (iii) to evaluate wave dissipation over a vegetation field including the effect of strongly varying topography.

1.4 Research methodology and outline

The aforementioned objectives are reached by the following steps (Figure 1.1). Before going into the main body of this thesis, a literature study is carried out in Chapter 2. It provides an overview of existing drag and wave dissipation mod-els. The existing information reveals that there are not many studies conducted deriving the bulk drag coefficient in a field of rigid multiple cylinders which is crucial for the estimation of the wave dissipation over vegetation fields.

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1.4. Research methodology and outline 5

Figure 1.1: Graphical presentation of the research methodology and thesis layout.

After the literature review, experimental work is presented. The obtained data are used for a discussion of the drag coefficient and the development of a 2DV model and 2DH model. A detailed description of the physical flume experiment conducted in Delft University of Technology is provided and the major results are shown in Chapter 3. In Chapter 4, a 2DV model, which is useful to evaluate the effect of strongly varying topography, is developed based on a 2DV Navier-Stokes equation model. Here, the concept of porosity and permeability is used considering the effect of inertia, which is not used in an energy balance equation model. To choose a practical bulk drag coefficient in a wave dissipation model, a state-of-the-art numerical model based on 3D Navier-Stokes equation model is conducted. The Immersed Boundary Method for the calculation of arbitrary shape in a Cartesian grid and a Large Eddy Simulation model for turbulence are developed and incorporated into an existing model in Chapter 5. Subsequently the output obtained in Chapter 5 is applied to engineering simulations such as a 2DH wave model, SWAN. In this thesis the SWAN Vegetation module is de-veloped based on M´endez and Losada (2004) incorporating a layer schematiza-tion in Chapter 6. In Chapter 7, two practical cases are introduced. These are based on the developed SWAN vegetation model and the bulk drag coefficient discussed in this thesis. Finally, some conclusions and some recommendations are discussed in Chapter 8.

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Chapter 2 Theoretical background and

Literature review

This chapter introduces background theories for the study of wave dissipation over vegetation fields. Firstly, basic theories and major research efforts on the topic of drag forces acting on a cylinder in a steady current are introduced in Section 2.1. Similarly, Section 2.2 provides this for an oscillatory flow indicating the importance of obtaining the bulk drag coefficient under different conditions. Lastly, formulations for wave dissipation over multiple-cylinder are introduced in Section 2.3.

2.1 Drag force and flow around a smooth cylinder in

a steady current

A flow around a cylinder and the drag force acting on a cylinder have long been of special interest among hydraulic and mechanical engineers. A number of physical experiments (e.g. Roshko, 1961; Schewe, 1983; Williamson, 1996) and numerical simulations (e.g. Jordan and Fromm, 1972; Braza et al., 1986, 1990) on this topic have been carried out. They are basic investigations but not very sim-ple due to the flow separation. To understand the wave energy dissipation by vegetation, which is represented as an assembly of cylinders in this study, it is important to review the previous studies regarding a flow around a cylinder. In this section, theories and literature reviews of a flow around a cylinder and the drag force acting on a cylinder in a steady current are introduced.

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2.1.1 Flow around a cylinder

Reynolds number and a steady current

The flow pattern around a cylinder changes drastically by the change of the Reynolds number. The Reynolds number is written as:

Re= ul

ν (2.1)

where u is the flow velocity, l is a characteristic length (in the case of a circu-lar cylinder l = D, D is the diameter of a circular cylinder) and ν (= 1.01×

10−6m2/s) is the kinematic viscosity.

The Reynolds number was originally introduced by Stokes (1851). The phys-ical meaning of this dimensionless number is the ratio of inertia force to viscous force. According to Sumer and Fredsoe (2006), when the Reynolds number is less than 5, there is no separation at the surface of a cylinder. The flow is called creep-ing flow. When the Reynolds number is between 5 and 40, separation occurs at the surface of a cylinder and a fixed pair of symmetric vortices appears behind a cylinder. When it becomes over 40, the vortex shedding starts, which gener-ates a vortex street behind a cylinder. When it is 40<Re<200, the vortex street stays laminar and there is no 3D effect in the flow. The range of 200<Re<300 is the transition range from the laminar wake to the turbulence wake. When the Reynolds number is over 300, the wake becomes fully turbulent and the 3D ef-fect can be seen (Williamson, 1996). Reynolds numbers between 300 and 300,000 indicate subcritical flow regime. The narrow Re band from 300,000 to 350,000 is known as the critical flow regime where the boundary layer on one side of the cylinder becomes turbulent at the separation point. The boundary layer on both sides becomes turbulent when the Reynolds number is between 350,000 and 1,500,000.

Vortex shedding

Vortex shedding, an unsteady flow, is the most important feature of all the flow regimes for Re>40 in which the boundary layer of a circular cylinder separates due to the adverse pressure gradient imposed by the divergent geometry of the flow environment on the side of the cylinder (Sumer and Fredsoe, 2006). In this flow, vortices are generated behind a cylinder due to vorticity generation in the shear layer and separated periodically. The Strouhal number is the representative parameter for vortex shedding and indicates the ratio of the conversion from kinematic energy of flow to oscillating energy of flow. The Strouhal number is defined as follows:

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2.1. Drag force and flow around a smooth cylinder in a steady current 9

Figure 2.1: Strouhal number for a smooth circular cylinder as a function of a Reynolds number. (Sumer and Fredsoe, 2006, p.10)

St= f D

u (2.2)

in which St is the Strouhal Number, f the normalized vortex shedding frequency, D the diameter of a circular cylinder and u the uniform flow velocity. The Strouhal number is often used as an index to evaluate numerical simulations. The relation-ship between the Strouhal number and the Reynolds number is shown in Figure 2.1.

2.1.2 Force acting on a cylinder

A flow around a circular cylinder results in a force on a cylinder due to the pres-sure differences on its surface. In general, the in-line force is known as the mean drag defined as a flow direction force component acting on a cylinder in a steady current. The cross-flow force is known as the lift force. The in-line force is shown in a summation of form drag and friction drag as follows:

FD = FDp+FD f (2.3)

where FDp and FD f are form drag and friction drag respectively; they are defined

as follows:

FDp =

Z 2π

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Figure 2.2: Drag coefficient for a smooth circular cylinder as a function of a Reynolds number. (Sumer and Fredsoe, 2006, p.43)

FD f =

Z 2π

0 τ¯0sinθr0dθ (2.5)

¯p is the time-averaged pressure, and ¯τ0 is the time-averaged wall shear stress on

the cylinder surface.

These values change with the flow pattern around a cylinder caused by vari-ation of the Reynolds number, surface roughness, cross-sectional shape and in-coming turbulence.

Drag and Lift coefficient

The drag coefficient and the lift coefficient of a single cylinder in a steady current are calculated as follows:

CD = ₁ FD 2ρDu2 (2.6) CL = ₁ FL 2ρDu2 (2.7) CD and CL are the drag coefficient and the lift coefficient respectively.

As shown in Figure 2.2, the drag coefficient is a function of the Re number. When wave dissipation over vegetated fields is considered, most cases are in the

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2.2. Drag force and flow around a smooth cylinder in an oscillatory flow 11

range of the subcritical regime where the drag coefficient is almost 1.0. However, some cases of vegetation, such as mangroves or willows, which have a large di-ameter under extreme storm conditions can be in the critical and supercritical regime, where the drag coefficients decrease drastically by drag crisis.

Drag crisis

In Figure 2.2, the drag coefficient drastically decreases around Re=300,000. This phenomenon is called drag crisis. This can be explained by the behavior of the separation point. In the case of the subcritical regime, the separation point is located around 80 degrees according to Achenbach (1968). In this case, the sep-aration is called laminar sepsep-aration. On the other hand, in the case of the super-critical regime, the separation point is located around 140 degrees, and it is called turbulence separation. Not only the separation point but also the wake pattern is changed to extremely narrow when the flow regime shifts from subcritical to supercritical. In this case, the negative pressure becomes very small resulting in a small drag coefficient.

Bulk Drag coefficient in a constant flow

In an array of cylinders, cylinder interference affects the drag force acting on a cylinder. A downstream cylinder located in the wake of the upstream cylinders may experience wake interference, sheltering and turbulence effects resulting in a different bulk drag coefficient. Thus, determination of the bulk drag coefficient in a flow is an important subject to evaluate the flow pattern in the vegetation, namely an assembly of cylinders in this thesis. Nepf (1999) shows the relation-ship between the bulk drag coefficient and a spatial parameter in a flow condition as shown in Figure 2.3.

From Nepf(1999)’s results, it can be concluded that the bulk drag coefficient is a function of the spatial parameter ad = D_S22, where D is a diameter of a cylinder,

S is distance between each cylinder.

2.2 Drag force and flow around a smooth cylinder in

an oscillatory flow

The oscillatory flow around a cylinder and the drag force acting on a cylinder have also been an important subject for ocean engineering. A number of physi-cal experiments (e.g. Sarpkaya, 1976; Williamson, 1985; Obasaju et al., 1988) and numerical simulations (e.g. Stansby et al., 1983; Justesen, 1991) have been con-ducted. In this section, theories and literature reviews of an oscillating flow around a circular cylinder and the force acting on the cylinder are introduced.

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Figure 2.3: Bulk drag coefficient versus ad, a spatial parameter in a flow condition. (Nepf, 1999)

2.2.1 Flow around a cylinder in an oscillatory flow

Keulegan-Carpenter number and an oscillatory flow

Flow regimes in an oscillatory flow around a smooth circular cylinder depend not only on the Reynolds number but also on the Keulegan-Carpenter number. The Keulegan-Carpenter (KC) number is defined as below:

KC= UmT

D (2.8)

in which Um is the maximum velocity, T the period of the oscillatory flow and D

the diameter of a cylinder.

According to Sumer and Fredsoe (2006), the physical meaning of the KC num-ber can be explained by observing that it is the ratio of UmT and D. UmT can be

also expressed as 2πa, in which a is the amplitude of the motion. Thus KC is proportional to the ratio of the stroke of the motion and diameter. With very small KC, the separation behind a cylinder may not even occur because the or-bital motion of water particle is small relative to diameter of a cylinder. On the other hand, when KC is large, separation and vortex shedding occur. With very large KC, the flow becomes like a steady flow. The detailed explanation of flow regimes for different KC numbers is as follows.

When the KC number is less than 1.1, there is no separation. When the KC number is between 1.1 and 1.6 separation takes place, the Honji instability Sumer and Fredsoe (2006) occurs and mushroom-shaped vortices are generated at the surface of the cylinder. In the range 1.6<KC<4, the separation is observed in

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the form of a pair of symmetric vortices. When KC is over 4, the pair of vor-tices becomes asymmetric. With a further increase of KC to 7 which is called the vortex-shedding regime, vortex shedding occurs during the course of each half period of oscillatory motion. According to Williamson (1985), the flow pat-terns in the vortex-shedding regime changes with KC and they are divided into regimes, viz. 7<KC<15, 15<KC<24, 24<KC<32, 32<KC<40, 40<KC<48 and so on. Each of them is called a single pair regime, double pair regime, three pairs regime, four pairs regime and five pairs regime, and so on. Thus flow patterns around a smooth cylinder are strongly related to the KC number.

2.2.2 Force acting on a cylinder in an oscillating flow

According to Morison et al. (1950), the wave force can be expressed as the sum-mation of the drag force and the inertia force as follows:

F= 1

2ρCDDu

2₊

ρCMA˙u (2.9)

in which CM is an inertia coefficient and ˙u is the acceleration of the flow. This

equation is called the Morison equation. This equation can be also expressed as follows using the hydrodynamic mass force (the second term) and the Froude-Krylov force (the third term).

F = 1

2ρCDDu

2₊

ρCmA˙u+ρA ˙u (2.10)

where Cm is shown as below.

Cm =CM−1. (2.11)

Determination of drag and inertia coefficients

To determine the drag and inertia coefficients from measured forces acting on a cylinder in an oscillatory flow, a least square method (e.g. Dean and Aagaard, 1970; Sumer and Fredsoe, 2006) is used in this thesis. In this method, the mean squared differences between measured forces and predicted forces by the Mori-son equation become minimal. The description of the equations are follows:

ε2=Σ[Fp(t) −Fm(t)]2 (2.12)

where ε2is the summation of the difference, Fp(t)is the predicted force and Fm(t)

is the measured force. To make ε2minimum,

∂ε2 ∂ fd

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∂ε2 ∂ fi

=0 (2.14)

where fd = 12ρCDD and fi =ρCMA.

These equations lead to: fdΣu4(t)

+ fi(Σu(t)|u(t)|˙u(t)) = Σu(t)|u(t)|Fm(t) (2.15)

fd(Σu(t)|u(t)|˙u(t)) + fiΣ ˙u2(t)

+ = Σ ˙u(t)Fm(t) (2.16)

where the summation is taken over the total record length. By solving Equation 2.15 and Equation 2.16, CD and CM are obtained.

Variation of the drag and inertia coefficients in an oscillatory flow

In an oscillatory flow, the drag coefficient and the inertia coefficient are depen-dent not only on the Re number but also the KC number. Sarpkaya and Isaacson (1981) conducted a physical experiment about the drag and inertia coefficient in a U tube with a wide range of Re, KC and β (frequency parameter). The results are shown in Figure 2.4 and Figure 2.5. According to these results, the varia-tion of the drag coefficient is around 0.5-2.5 in the range and is quite sensitive to hydraulic parameters such as the Reynolds number, the Keulegan-Carpenter number and β.

Figure 2.4: Drag coefficient versus KC number for various of the frequency parameter. (Sarpkaya and Isaacson, 1981, p.96)

Effect of flexibility

The wave force acting on a flexible vegetation can be expressed by velocity dif-ferences between fluid and a plant as follows:

F = 1

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Figure 2.5: Inertia coefficient versus KC number for various of the frequency parameter. (Sarpkaya and Isaacson, 1981, p.96)

where ub is the velocity of the plant and ˙ubis the acceleration of the plant.

Thus, a flexible plant has to be modeled with the equation above in a strict manner. In practice, however, this effect is included into the bulk drag coefficient in many works (e.g. M´endez and Losada, 2004) which is a practical solution in an engineering application.

2.2.3 Bulk Drag coefficient in waves

As described earlier, wave dissipation by vegetation is supposed to be a function of wave conditions and vegetation parameters. However, it is often difficult to choose an appropriate bulk drag coefficient to estimate vegetation induced wave attenuation. This is partly due to the complexity of the turbulence structure over the vegetated field. To understand the wave dissipation, it would be important to understand the bulk drag coefficient appropriately, as this is strongly related to the turbulence structure in a multiple cylinder field in waves. It is not a triv-ial task to obtain bulk drag coefficients under different hydraulic and vegetation conditions without calibration but it is assumed to be possible for a case of a sim-ple array of rigid cylinders. In practice, many authors (e.g. Iimura et al., 2007; Narayan, 2009; de Oude et al., 2010) assume the bulk drag coefficient of vertical rigid cylinders to be 1.0 in the case of a simple cylindrical array (e.g. mangrove forest) for subcritical Reynolds numbers. This value, CD=1.0, is decided based

on flow conditions shown in Figure 2.2 and is applied for wave conditions. This choice, though practical, lacks background theories which support this value. For instance, the drag coefficient of a single cylinder in planar oscillations varies from 0.5 to 2.5 according to Sarpkaya and Isaacson (1981) and is quite sensitive to hydraulic parameters such as Reynolds number, Keulegan-Carpenter number and β (frequency parameter). Not only that, the value can be different in the case of multiple cylinders. For example, according to experimental studies by Heideman and Sarpkaya (1985), the bulk drag coefficient in an array of cylinders is smaller than the drag coefficient for a single cylinder in an oscillatory flow. Nepf (1999) also shows that the bulk drag coefficient in a flow changes drasti-cally with different cylinder density. Massel et al. (1999) propose an estimation

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method to calculate the bulk drag coefficient depending on mangrove density by using a modification parameter based on the drag coefficient presented in SPM (1984). Considering these results, it is assumed that the bulk drag coefficient in an array of cylinders under waves is smaller than for a single cylinder. Mangrove forests and salt marshes are often densely vegetated, so it would be important to understand the bulk drag coefficient in dense vegetation conditions under wave conditions, which may not be the same as the drag coefficient for a single cylin-der. In Chapter 5, the relationship between the bulk drag coefficient and cylinder density based on hydrodynamics in a multiple cylinder field is to be investigated.

2.3 Formulations for wave dissipation by vegetation

2.3.1 Comparison of different approaches to wave dissipation

by vegetation

There are two main approaches to describe wave energy dissipation by vege-tation in the literature. One is the bottom friction approach and the other the cylinder approach. In this section these are described and compared and it is dis-cussed which model is most suitable to provide a physical description of wave dissipation by vegetation.

Bottom friction approach

Different numerical and analytical models have also been proposed in the last three decades that attempt to reproduce the hydrodynamics within a vegetation field with regard to wave energy dissipation. One frequently used approach is the bottom friction or bed roughness approach (Van Rijn, 1989; Hasselmann and Collins, 1968) that accounts for the effect of vegetation in terms of a bottom fric-tion parameter. The amount of energy dissipated is calculated using this param-eter to estimate the work done by the resulting friction force. Reliable measured data are a necessity for this approach to be able to calibrate and validate the fric-tion parameter for each type of vegetafric-tion. Quartel et al. (2007), from their field experiments in Vietnam, found that the across-shore wave attenuation per meter due to the bed roughness of the mangrove vegetation was four times higher than that due to a sandy bed.

Cylinder approach

Another approach is to consider the vegetation as structural elements - usually cylinders - and estimate the dissipation due to the resulting force (Dalrymple et al., 1984; Kobayashi et al., 1993; Vo-Luong and Massel, 2008). All such models for wave attenuation in vegetation assume that linear wave theory is valid within

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2.3. Formulations for wave dissipation by vegetation 17

the vegetated zone. Vo-Luong and Massel (2008) propose a theoretical predictive model for wave propagation through a non-uniform forest of arbitrary water depth, validated using experimental data from Southern Vietnam. Their study finds that wave-breaking and wave interaction with vegetation are the dominant energy dissipation processes in such a forest. Mazda et al. (2006) with their field work, also from Vietnam find that thick mangrove leaves are capable of dissipat-ing huge amounts of wave energy durdissipat-ing storms and typhoons and recommend a quantitative formulation of the relationship between vegetation characteristics, water depth and incident wave conditions in order to protect coastal areas from severe events. Dalrymple et al. (1984) proposed a formula for wave damping by vegetation that considers the vertical extent of the cylinders over the water col-umn for normally incident waves and a constant, arbitrary water depth. They suggest the use of a bulk drag coefficient to account for all the approximations and factors not considered in the formula. The wave damping formula was ob-tained by integrating Morison’s equation for the drag force due to waves over the height of the cylinder. M´endez and Losada (2004) in their paper, present an expansion of the Dalrymple formulation that includes the possibility for vege-tation schematization and can handle sloping bottom conditions and breaking waves as well. They assume the drag force to be the dominant force and use a drag coefficient parameterized with respect to the Keulegan - Carpenter number to represent wave transformation in a vegetation field.

Conclusions

The latter approach, the cylinder approach, more closely represents the physical processes within the vegetation since it takes into account the diameter, density and height of the vegetation in the calculation of the bulk drag coefficient. More-over, this formulation can be implemented in standard numerical wave propaga-tion models with only calibrapropaga-tion of the bulk drag coefficient required for a given plant type. Though this coefficient accounts for many processes not yet fully un-derstood, it seems that the M´endez and Losada (2004) formulation based on the cylinder approach of Dalrymple et al. (1984) is most suitable in terms of physical representation of processes. The model can be applied easily to a specific vege-tation type under certain wave conditions and estimates the energy dissipation. Based on a non-linear transformation of the drag force, the model depends on a single parameter related to the drag coefficient calibrated for a specific type of plant.

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2.3.2 Wave dissipation model

The energy of waves propagating through a vegetation field (e.g., salt marshes, mangrove forests) is dissipated due to the work done by the waves on the vege-tation. In all cases the bed is assumed to be rigid and impermeable. The general form of the energy conservation equation is as follows:

∂Ecg

∂x =εv (2.18)

where, E is wave energy, Cg is wave group velocity, εv is time-averaged rate of

energy dissipation per unit horizontal area induced by vegetation. A popular method of expressing the wave dissipation due to vegetation is suggested by several authors such as Dalrymple et al. (1984), and Kobayashi et al. (1993) where energy losses are calculated as actual work carried out by the vegetation due to plant induced forces acting on the fluid, expressed in terms of a Morison et al. (1950) type equation. In this method, vegetation motion such as vibration due to vortices and swaying is neglected. For relatively stiff plants the drag force is considered dominant and inertial forces are neglected. Moreover, since the drag due to friction is much smaller than the drag due to pressure differences, only the latter is considered in the modeling. Based on this approach, the definition for the time-averaged rate of energy dissipation per unit area over the entire height of the vegetation, εvis given by

εv =

Z −h+αh

−h Fu dz (2.19)

where, αh is vegetation height, the over-bar represents the time-averaging of the energy dissipation term and F is the horizontal component of the force acting on the vegetation per unit volume. From the Morison equation and neglecting swaying motion and inertial forces Dalrymple et al. (1984), F the horizontal force per unit volume can be described as

F = 1

2ρCDbvNvu|u| (2.20)

where ρ is the water density, CD is the drag coefficient, bvis the stem diameter of

cylinder (plant), Nv is the number of plants per square meter and u is the

hori-zontal velocity due to wave motion. Dalrymple’s formula for energy dissipation as presented by M´endez and Losada (2004) is

εv= 2 3πρCDbvNv gk 2σ 3 sinh3kαh+3sinhkαh 3kcosh3_kh H 3 _(2.21)

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2.3. Formulations for wave dissipation by vegetation 19

This formula was modified by M´endez and Losada (2004) to enable estima-tion of wave dissipaestima-tion by vegetaestima-tion in narrow-banded random waves. The wave height, H was converted to a root mean square wave height Hrms, yielding

an averaged vegetation dissipationhεvigiven by,

hεvi = 1 2√πρ ˜CDbvNv gk 2σ 3 sinh3kαh+3sinhkαh 3kcosh3_kh H 3 rms (2.22)

with ˜CD being a bulk drag coefficient that may be dependent on the Keulegan

-Carpenter (KC) number applied.

According to M´endez and Losada (2004), for wave height evolution for monochro-matic waves in the case of a horizontal bottom without breaking, it can be derived that: H = Ho 1+βx (2.23) β= 4 9πC˜DbvNvHok sinh3kαh+3sinhkαh (sinh2kh+2kh)sinhkh (2.24) For wave height evolution for random waves in the case of a horizontal bottom without breaking, it can be derived that:

Hrms = Hrms,o 1+ ˜βx (2.25) ˜β= 1 3sqrtπC˜DbvNvHrms,ok sinh3kαh+3sinhkαh (sinh2kh+2kh)sinhkh (2.26) These equations are used for a calibration of drag coefficients in case of a flat bottom in this study.

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Chapter 3 Physical model tests

3.1 Introduction

Salt marshes, characterized by cliffs with halophytic plants, increasingly attract attention from hydraulic engineers and coastal managers as an effective feature to reduce impacts to the sea-defense. It is known that salt marshes have an abil-ity to attenuate wave energy (Brampton, 1992; M ¨oller et al., 1999; M ¨oller, 2006) and can be a resistance for flow. Not only is such a protection functional, a salt marsh itself is also valuable to the ecological system. In spite of their signifi-cance, a number of salt marshes are endangered by environmental change such as sea level rise and human activities such as land reclamation and dredging. Especially, salt marsh cliffs, which are a common and important feature of most salt marshes, are being eroded. For instance, cliff erosion was observed in the Westerschelde estuary in the southwest of the Netherlands between 1982 and 1998 (van de Koppel et al., 2005) and is still ongoing as shown in Figure 3.1. The cliff erosion might be related to higher tides and increased wave heights (Wolters et al., 2005). However, the limited knowledge of the hydraulic mecha-nisms around salt marsh cliffs requires further study to clarify hydro- and mor-phodynamics on vegetated salt marshes. To this end, physical flume tests using artificial and natural vegetation were conducted. This offers a good approach to extend this study to phenomena around the cliff in detail, including the ve-locity field and impact pressure on the cliff. Additionally the data are used to validate several numerical modeling approaches described in Chapter 4 and for the analyses in Chapter 5.

In this chapter1, the experimental arrangement and data processing methods employed are described. In Section 3.2 the experimental configurations are de-scribed in addition to the instrumentation, including Particle Tracking Velocime-try (PTV). Next, the test program is given in Section 3.3. It is followed by a data processing method in Section 3.4 and finally in Section 3.5 the obtained data and

1_{This chapter is based on Suzuki et al. (2008) and Suzuki and Klaassen (2011).}

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Cliff erosion

Figure 3.1: An example of the cliff erosion of a salt marsh in the Westerschelde estuary in the southwest of the Netherlands. The length of the arrow (about 1.0 m) shows regression of the position of the cliff during about one year.

results are addressed.

3.2 Experimental configuration

3.2.1 Geometry

The physical model experiment both for a cliff and a flat bottom have been con-ducted at the Environmental Fluid Mechanics Laboratory of Delft University of Technology. The wave flume used for the experiments was 40 m long, 0.80 m wide and 1.0 m high. A piston type wave generator, which has a functionality to compensate reflected waves, was installed at one side.

For cliff cases, the model structures shown in Figure 3.3 were placed at 19.3 m from the central position of the wave paddle. At the end of the flume, a mild slope consisting of crushed stones was installed to alleviate the influence of re-flection. Three types of model structures (a bare cliff, a cliff with artificial veg-etation and a cliff with natural vegveg-etation) were tested as shown in Figure 3.3. Behind a gentle slope and flat bottom, which represents a mud flat in the field, an impermeable cliff with a height of 15 cm was installed resembling a salt marsh cliff. Rigid artificial vegetation made of smooth plywood cylinders with diame-ter D=0.6 cm, cylinder height hveg=10 cm and their densities of 0 units/m2(Case

C0), 242 units/m2 (Case C2) and 962 units/m2 (Case C9), were set on the cliff vertically in a staggered grid. Furthermore, natural vegetation, Spartina anglica, which is commonly seen in salt marshes in the Netherlands and UK, was also used with a density of approximately 1550 units/m2 and a height of 30-50 cm (Case CV). It is noted that Spartina anglica is a gramineous perennial character-ized by stiff stems and leaves.

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3.2. Experimental configuration 23

962 units/m2 (Case F9)were placed at 16.3 m from the central position of the wave paddle.

Density terms

The parameters of the density terms are defined as follows: N = √2

3S2 (3.1)

ad= D

2

S2 (3.2)

n= longitudinal row spacing

lateral row spacing (3.3)

in which D is a diameter of a plant, S is a distance between each plant, N is the number of cylinders in a unit area, ad is a definition of density by Nepf (1999) and n is the ratio of longitudinal row spacing and lateral row spacing, which defines the array atructure.

3.2.2 Instrumentation

This section describes the instruments used in the flume experiment to measure the wave height distribution throughout the vegetation field, the velocity field around the salt marsh cliff and the pressure to the cliff. Also the measurement overviews are described here.

For the measurement of the wave height distribution, 6 capacitance type wave gauges were used for 11 measurement points as shown in Figure 3.4 by repeating the experiment after repositioning of the devices. The wave gauge was connected to an A/D converter and branch boxes and finally the obtained data were stored on a PC. The capacitance type wave gauges were calibrated daily at the begin-ning of each experiment and the relationship between voltage and water level was used for the analysis. Each time series lasted 5-20 minutes with a sampling frequency of 100 Hz. As for the measurement of the velocity fields around the cliff, 2 Electro Magnetic velocity Flow (EMF) were used for 5 measurement points also by repeating the experiment. EMFs can measure two components, the hor-izontal velocity u and the transverse velocity v. The vertical velocity w was not measured in this experiment. EMFs were also connected to a PC through an A/D converter and branch boxes. EMFs were not calibrated in this experiment since they already had calibrated values. The sampling time and frequency was the same as that of the wave gauges since the branch boxes were shared. The mea-surement points are also shown in Figure 3.4.

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Figure 3.2: Experimental set-up. Three types of model structures for cliff cases (C0: with-out cylinder, C2 and C9: with cylinders, CV: with natural vegetation, Spartina anglica) and one type of model structure for flat botton case were tested.

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Figure 3.3: Definitions of density terms.

Figure 3.4: Positions of wave gauges and EMF in the flume experiment in a case with h=25 cm.

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Figure 3.5: Positions of pressure sensors on the cliff.

Figure 3.6: Positions of wave gauges and EMF in the flume experiment in a case with h=10 cm.

For the measurement of the pressure on the cliff, a pressure sensor was used to determine the pressure for 3 points as shown in Figure 3.5. The pressure sen-sors were also connected to A/D converters and branch boxes, and finally the obtained data were stored on a PC. The calibration for the pressure sensor was not conducted and calibrated data were used to calculate the pressure on the cliff. For the measurement of the pressure, it is necessary to use a high frequency in order to catch the shock waves with very small duration. Therefore the sampling frequency was set at 1,000 Hz and measured for 3 minutes.

For the flat bottom cases, only the wave height distribution and velocity field for irregular waves were obtained for the 6 measurement points shown in Figure 3.6. The measuring methods were the same as for the cliff case above.

3.2.3 PTV measurement

To understand the emergence of seedlings of the salt marsh plants is important for their ability to restore the salt marsh. The salt marsh patches can expand their area mainly through the seedlings. However it is often the case that the offshore edge of the salt marsh fields consists of a cliff, which makes it more difficult to understand the velocity field and the mechanism of expansion or recession of the salt marsh. The studies of hydrodynamics around a salt marsh cliff, which would be one of the determining factors for the seedlings, are scarce and therefore far

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from being understood until now. One of the difficulties is the strong varying topography. For example, theoretical approaches to the flow around a step-type topography has limitations due to the flow separation, which may occur in the vicinity of the cliff. The most promising methods to examine the entire flow would be a flume experiment. However, the measurement points are limited in general when single measurement devices such as EMFs are used. To fulfill the purpose of understanding the flow around the cliff, the PTV technique was em-ployed in the present study. The other possible approach consists of numerical simulations, which will be described in Chapter 4. PTV results are also used for the validation of the numerical simulations.

Particle Image Velocimetry and Particle Tracking Velocimetry (PIV and PTV) have their roots in flow visualization techniques (Van Dyke, 1982) and these methods have been popular for analyzing flow around a structure for decades. The difference between PIV and PTV is the number of tracer particles. In case of PTV, a sparse seeding is used and each tracer particle can be analyzed indi-vidually. In this analysis, the PTV technique is applied for flow analysis around a cliff under wave condition because flow separation is observed at each step. By analyzing the consecutive pictures of the particle positions, the instantaneous velocities are obtained step by step. Figure 3.7 shows an example of the captured consecutive pictures from a video camera used to analyze the motion of the wa-ter. The upper part shows the first picture and the lower the second, and the velocity is calculated based on the different spatial positions, analyzed based on a correlation technique and divided by the time difference of two pictures. The time interval is 1/25 sec here.

The selection of the particle is one of the most challenging tasks. If the size of one particle is smaller than one pixel cell of a video camera, it is not suitable for PTV analysis. In this study, an off-the-shelf home video camera with a resolution of 576×720 is used. The area of interest is about 50 cm in the vertical and 70 cm in the horizontal, thus the size of the particle will have to be, at least, more than 1 mm. The selected material is Ball Bullets for an airsoft gun, whose density (1061 kg/m3) is almost the same as water (1000 kg/m3). The diameter of the Ball Bullet is 6 mm. To fill the density gap between the Ball Bullets and water, candle wax which has a low density was used. Firstly candle wax was melted in a cup and a Ball Bullet was soaked in it to cover the Ball Bullet with wax. Thus the density of the Ball Bullet becomes less due to the wax’s lower density. The waxed Ball Bullet still maintained its isotropy for direction since the wax was almost uniform. After the waxing, the density of the Ball Bullets was checked by putting them in water one by one. Only those waxed Ball Bullets, which could float for more than 5 seconds in virtually the same position in the water were selected and this procedure was repeated until enough particles were available for use in this experiment, 250. Figure 3.8 shows the particle and a set of processed particles. Figure 3.9 shows the recording area of the video camera.

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Figure 3.7: Captured consecutive pictures used to analyze the motion of the water by PTV technique.

(a) A Ball Bullet. (b) The processed particles.

Wave dissipation over vegetation fields

Wave Dissipation Over

Vegetation Fields

Wave Dissipation Over

Vegetation Fields

Contents

Summary

Samenvatting

Chapter 1

Introduction

1.1

Background

1.2

Problem description

Vegetation model and bulk drag coefficient

Wave propagation over a strongly varying topography

1.3

Objectives of this study

1.4

Research methodology and outline

Chapter 2

Theoretical background and

Literature review

2.1

Drag force and flow around a smooth cylinder in

a steady current

2.1.1

Flow around a cylinder

Reynolds number and a steady current

Vortex shedding

2.1.2

Force acting on a cylinder

Drag and Lift coefficient

Drag crisis

Bulk Drag coefficient in a constant flow

2.2

Drag force and flow around a smooth cylinder in

an oscillatory flow

2.2.1

Flow around a cylinder in an oscillatory flow

Keulegan-Carpenter number and an oscillatory flow

2.2.2

Force acting on a cylinder in an oscillating flow

Determination of drag and inertia coefficients

Variation of the drag and inertia coefficients in an oscillatory flow

Effect of flexibility

2.2.3

Bulk Drag coefficient in waves

2.3

Formulations for wave dissipation by vegetation

2.3.1

Comparison of different approaches to wave dissipation

by vegetation

Bottom friction approach

Cylinder approach

Conclusions

2.3.2

Wave dissipation model

Chapter 3

Physical model tests

3.1

Introduction

3.2

Experimental configuration

3.2.1

Geometry

Density terms

3.2.2

Instrumentation

3.2.3

PTV measurement