P r e p a r e d fo r:

Rijkswaterstaat, RIKZ

Tidal asymmetry and sediment transport in the Westerschelde estuary

a d e s k s t u d y

N o v e m b e r 2 0 0 0

WL I delft hydraulics

¿EL 2.8 6 4 -

R 0 0 0 8 2 1 9

Tidal asymmetry and sediment transport in the Westerschelde estuary

a d e s k s t u d y

C . J e u k e n

Z . B . W a n g

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WL I delft hydraulics

WL I d e l f t h y d ra u l i c s

R i j k s w a t e r s t a a t

C L I E N T : R I K Z

T IT L E : T i d a l a s y m m e t r y a n d s e d i m e n t t r a n s p o r t in t h e W e s t e r s c h e l d e

A B S T R A C T :

B a s e d o n f i e ld o b s e r v a t i o n s a s w e l l a s r e s u l t s o f h y d r o d y n a m i c a n d s e d i m e n t t r a n s p o r t m o d e l s , t h e r e l a t i o n b e t w e e n th e

a s y m m e t r y o f t h e h o r i z o n t a l t i d e a n d t h a t o f t h e v e r t i c a l t i d e a n d t h e r e l a t i o n b e t w e e n t h e a s y m m e t r y o f t h e h o r i z o n t a l t i d e a n d

t h e r e s i d u a l s e d i m e n t t r a n s p o r t in t h e W e s t e r s c h e l d e h a v e b e e n a n a l y s e d . T h i s a n a l y s i s h a s t h e o b j e c t i v e t o i d e n t i f y t h e

s i g n i f i c a n c e o f t h e t i d a l a s y m m e t r y f o r t h e m o r p h o l o g i c a l d e v e l o p m e n t in t h e e s t u a r y .

F o r t h e l o c a l r e s i d u a l s e d i m e n t t r a n s p o r t , t h e r e s i d u a l c u r r e n t , i .e . t h e MO c o m p o n e n t o f t h e f l o w v e l o c i t y , is th e d o m i n a t i n g

f a c t o r o f t h e a s y m m e t r y o f t h e h o r i z o n t a l t i d e . T h e r e s i d u a l c u r r e n t is d e t e r m i n e d b y t h e b a t h y m e t r i c c h a r a c t e r i s t i c s a n d th e p h a s e d i f f e r e n c e b e t w e e n t h e h o r i z o n t a l t i d e a n d t h e v e r t i c a l t i d e , r a t h e r t h a n t h e o v e r t i d e s . F o r t h e i n t e g r a t e d r e s i d u a l

s e d i m e n t t r a n s p o r t t h r o u g h t h e e s t u a r y , b o t h t h e r e s i d u a l c u r r e n t a n d t h e o v e r t i d e s a r e i m p o r t a n t . F u r t h e r it is c o n c l u d e d t h a t

f o r t h e r e s i d u a l s e d i m e n t t r a n s p o r t t h e s i x t h - d i u r n a l t i d e is a s i m p o r t a n t a s t h e q u a r t e r - d i u r n a l t id e .

R E F E R E N C E S :

V ER . O R I G I N A T O R V D A T E R E M A R K S R E V IE W / A P P R O V E D BY

1 C. Je uken% ■

17 O c to b e r 20 0 0 Z.B . W an g2 C. Je uken m 8 N o v e m b e r 2 0 0 0 H.J. D e V r iend - 1 ? / t . S c h i lpe roo r t

P R O J E C T I D E N T I F I C A T I O N : Z 2 8 6 4

K E Y W O R D S : T ida l a s y m m e try , R e s id u a l se d im e n t t ranspor t , res idual f low , W e s te rs ch e ld e

C O N T E N T S : T E X T P A G E S 21 T A B L E S F IG U R E S 12 A P P E N D I C E S 1

S T A T U S : □ P R E L IM IN A R Y □ D R A F T 3 F IN A L

T idal a sy m m e try an d se d im e n t tra n s p o r tin t h e W e s te rs c h e ld e Z 2 8 6 4 N o v e m b e r, 2000

C onten ts

In trod u ction ....................................................................................................................................1-1

1.1 B ack g ro u n d ...................................................................................................................... 1-1

1.2 O bjec tive o f the s tu d y ....................................................................................................1-2

1.3 Set up o f the s t u d y ..........................................................................................................1-2

1.4 A c k n o w le d g e m e n t ..........................................................................................................1-3

C onsiderations on residual sed im en t transport in the W estersch eld e ............... 2 -1

2.1 D e f in i t io n s ........................................................................................................................ 2-1

2.2 Significance for morphological d eve lopm en t .......................................................2 -2

2.3 Relation to tidal a sy m m etry ........................................................................................ 2 -3

2.4 Sum m ary w ork ing h y p o th eses ................................................................................... 2 -4

E laboration o f the hypotheses on the basis o f observ a tion s.................................... 3 -1

3.1 In troduction .......................................................................................................................3-1

3.2 Large scale residual sediment transport in the e s tu a ry .......................................3-1

3.2.1 Field D a ta ...........................................................................................................3-13.2.2 Relation to the asym m etry o f vertical t id e ............................................. 3 -2

3.3 Results o f a one-dimensional m o d e l ........................................................................3 -3

3.4 Tidal and residual transport within ch a n n e ls ........................................................3 -4

3.4.1 Velocity observations from the f ie ld ........................................................ 3 -43.4.2 Results from 2DH-transport m o d e l l in g .................................................. 3 -5

3.5 Residual flow and b a th y m e try ...................................................................................3 -6

3.5.1 Single branch considera tion ....................................... 3 -63.5.2 Tw o-branches c o n s id e ra t io n .......................................................................3 -7

D iscu ssion , con clu sion s and recom m en d ation s............................................................. 4 -1

4.1 Discussion and c o n c lu s io n s ........................................................................................4-1

4.2 R eco m m en d a t io n s .......................................................................................................... 4 -3

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Tidal a sy m m e try and se d im e n t tra n s p o r tin th e W e s te rs c h e ld e Z 2 8 6 4 N o v e m b e r, 2000

Appendices

A R eferen ces...................................................................................................................................... A - l

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T ida l asy m m etry and se d im e n t t ra n s p o r tin th e W e ste rsc h e ld e Z2864 N o v e m b e r, 200 0

Introduction

1. i Background

The W esterschelde is one o f the rem aining open estuaries in The Netherlands that is s trongly influenced by man. Land reclamation has reduced the size o f the estuary by 40 % in less than 300 years. In this century the dredging and dum ping activities have increased from less than 0.5 Mm'Vyear in 1950 to over 15 M m V year in 1975 (Vroon et al, 1997, Van den Berg et ah , 1996). In recent years, a large dredging and dum ping program has been executed to enlarge and maintain the navigation route to Antwerp. Since 1997 a deepening program is in progress and a new dredging and dum ping program is initiated. For the various w ater m anagem ent aspects, e.g. flood control and ecological functioning o f the estuary, it is important to understand the impacts o f hum an interference on the m orphological deve lopm ent o f the estuary in com bination with the ever changing natural forcing, e.g. via tide, sea level rise etc.

The natural morphological developm ent is the result o f interactions between w ater motion, sedim ent transport and bed topography. In an estuary like the W esterschelde w here tidal action is an im portant forcing factor, it is the residual sedim ent transport that determines the morphological developm ent. Therefore insight into the processes and mechanisms influencing the residual sedim ent transport plays a key role in the understanding o f the morphological developm ent o f the estuary under the influence o f changing natural conditions and human interference.

An important factor causing residual sedim ent transport in estuaries is tidal asymmetry. In the W esterschelde it is possibly a principal factor influencing the sedim ent exchange between the ebb tidal delta and the estuary, as well as between the various parts o f the estuary. A nalyses o f the historical data on tide and morphological developm ent in the W esterschelde (Gerritsen et al., 1999) indicate that there is a clear relation between the change o f asym m etry o f the vertical tide and the morphological developm ent in the estuary. T hey also show that there is p robably a relation betw een the asym m etry o f the vertical tide and the net sedim ent flux. Insight into the generation o f tidal asym m etry and its influence on the residual sedim ent transport is required for answ ering questions like:

° will the estuary drown under the influence o f sea level rise o r will it silt up fast enough to keep up with the sea level?

© will there be a return f low o f sedim ent between the dum ping locations in the western part o f the estuary and the dredging sites in the eastern part and w hat are the involved time-scales?

© can sand m in ing be continued w ithout affecting the system to an unacceptable extent?

In the last few decades a large num ber o f publications have appeared on tidal asymmetry and its effects on the sedim ent transport and m orphological developm ent in estuaries. A literature survey and desk study has been carried out by W ang et al (1999), w ho sum m arise

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the knowledge related to tidal asymmetry, sedim ent transport and morphological developm ent in estuaries, as published in the last several decades. In the desk study the concepts / theories found in the literature haven been investigated for the particular s ituation o f the W esterschelde. The present report describes the continuation o f the desk study as described in W ang et al (1999).

1.2 Objective of th e study

T he objective o f the present study is• to evaluate the sign if icance o f the tidal asym m etry for the morphological system o f

the W esterschelde estuary;© to make recom m endations for further s tudies w hich will lead to a better

understanding o f the tidal motion and the morphological developm ent in the W esterschelde estuary.

S .3 S e t up of th e study

T he approach applied in the present study is schematically depicted below. Four different aspects have to be considered in o rder to evaluate the im portance o f the tidal asym m etry for the estuarine morphology. All fou r aspects w ere discussed by W ang et al. (1999) on the basis o f a literature rev iew and som e data analyses. However, the re la tionship between the asym m etry o f the horizontal t ide and the sand transport w as only briefly addressed. This issue that is the key elem ent for evaluating the significance o f the tidal asym m etry for the morphological system o f the W esterschelde, is subject o f this study. Based on the study o f W ang et al. (1999) the fo llow ing hypothesis was used as first guideline in the present study: The tidal asym m etry that is related to the generation o f residual currents, the so-called subharm onics, determ ine the residual sand transport at the spatial scale o f the estuarine section (see also Ch. 2). T he velocity asym m etry related to the generation o f the higher harm onics control the sed im ent exchange between estuarine sections.

asym m etry horizontal tide

morphology

residual sand transport

asym m etry vertical tide

First a conceptual model concern ing the residual sedim ent transport in the W esterschelde is presented in C hapter 2. It results in a fram ew ork for the a forem entioned hypothesis and the formulation o f underly ing hypotheses. These basic hypotheses in this conceptual model are checked with field data and / o r model results in C hapter 3. T he conclusions from the study and recom m endations fo r further research are given in C hap ter 4.

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1.4 A cknow ledgem ent

The present study is carried out by Mrs. C. Jeuken, and Dr. Z.B. W ang from Delft Hydraulics in close co-operation with Mr. B.A. K om m an from RIKZ-RW S.

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T idal asy m m etry an d se d im e n t tra n s p o r tin th e W e ste rsc h e ld e 2 2 8 6 4 N o v e m b e r, 2000

2 Considerations on residual sed im en t t r a n s p o r t in th e W esterschelde

2. ¡ Definitions

Sedim ent transport in a estuary can be considered on various time- and space scales. On different time scales distinction can be m ade between the instantaneous transport, the ebb- transport, the flood-transport, and the residual transport. The ebb- and flood-transport are the integral o f the instantaneous transport over the ebb and flood period respectively. The residual transport is the integral o f the instantaneous transport over the w hole tidal period and is thus equal to the difference between the ebb- and flood-transport.

sc — f Isldt (2.1)k J 1

s f = [ , |s |dt (2.2)/ Io n , I

s r = j \s 'dt = s f - se (2.3)

In these equations

s = instantaneous sedim ent transport (positive in flood direction)se = ebb-transports f = flood-transportsr = residual transport (positive in flood direction)Tebh = flood periodTflood = ebb periodT = tidal periodt = time

On the different spatial scales, the pattern o f circulation cells in the residual transport field is interesting. The m ost important c irculation cells are those in the various macro-scale ebb- and f lood-channel systems. Such a ebb and flood-channel system consists o f two large, parallel-aligned channels, divided by a tidal flat o r a tidal flat com plex. The Westerschelde estuary consists o f a chain o f such ebb- and flood-channel systems, also referred to as estuarine sections (see e.g. Jeuken, 2000 and W interwerp et al., 2000). From the head tow ards the mouth o f the W esterschelde six sections can be identified (EC =ebb channel, FC=flood channel, see Jeuken 2000 for an overv iew o f the m orphologic evolutions within each section, Fig. 2.1):

1. Het vaarwater boven Bath (EC) - A ppelzak (FC).

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Tidal asy m m etry an d sed im en t tra n s p o r tin th e W e ste rsc h e ld e Z 2864 N o v e m b e r, 200 0

2. Het N au w van Bath (E C ) - Schaar van N oord (FC).

3. Het Z uidergat / O verloop van Valkenisse (E C ) - Schaar van Valkenisse (FC).

4. Het Gat van O ssenisse (EC) - M iddelgat (FC)

5. De Pas van Terneuzen (EC) - Everingen (FC)

6. De Honte (E C ) - Schaar van Spijkerplaat (FC).

By integrating the residual sedim ent transport over the channels, the total residual transport through the individual ebb- and f lood-channels can be obtained. Integrating the residual transport over the w ho le cross-section o f the estuary gives the total residual transport through the estuary. Similarly, one can obtain the ebb- and flood-transport through the channels and through the whole estuary.

The dem arcation o f ebb and flood channels within a certain cross channel can be based on bathymetric considerations, i.e. the location o f the h ighest point in the profile. Though it should be noted that the dem arcation o f ebb and flood channels is not always unambiguous. The residual transport in an ebb-flood channel system can thus be considered as consisting o f a c irculating com ponen t and a net residual com ponent through the estuary,

2.2 Significance for morphological developm ent

Sediment transport in the W esterschelde is m ainly driven by the tidal flow. This has the consequence that the ebb- and flood transport are a lm ost equal to each other, which means

chb-channel

(2.4)

flood-channel

(2.5)

( 2 .6 )

Herein

y

residual transport trough the ebb channel residual transport trough the flood channel residual transport t rough the estuary lateral co-ordinate

$ r,circulation rehh + ^ r )hoi, ) ̂2 (2.7)

( 2 .8 )

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T idal a sy m m e try an d se d im e n t t ra n s p o r tin th e W e s te rsc h e ld e Z2864 N o v e m b e r, 2 000

that the m agnitude o f the residual transport is an o rder o f smaller than that o f the ebb- or flood-transport. This applies to all spatial scales.

se » Url s f » 15/*I (2.9)

Within an ebb- and f lood-channel system in the W esterschelde the c irculating com ponent o f the residual transport is m uch larger than the net th roughflow s.

I $ r circulation | > > \ $ r ,ncl | ( 2 . 1 0 )

The various transports as d iscussed above each have their own influence on themorphological deve lopm ent in the estuary. It can be stated that the com ponent o f theresidual transport through the estuary Srne, is responsible for the morphologicaldevelopm ent on the m ega-scale, w hereas the c irculation com ponen t Sr,circulation is responsible for the m acro-scale morphological development.

O bviously the m orphological developm ent is de term ined by the residual sediment transport. However, also the ebb- and flood-transports are im portant for studying the morphological development, especially under the influence o f hum an interference. The change o f the residual transport induced by hum an interference (a deepened area by dredging) is related to the m agnitude o f the ebb- and flood-transports under non-disturbed condition. So the time scale o f the morphological developm ent induced by the interference is related to the ebb- and flood-transports.

2.3 Relation to tidal asym m etry

Local residual sed im ent transport is directly related to the asym m etry o f the horizontal tide. As shown by Van de Kreeke and R obaczew ska (1993) the long-term mean bed-load transport is determ ined by the flow velocities associated with M 0, M 2 and its overtides. The d imensionless expression for the tidally averaged bed-load transport reads as

^ - - f i b M 2, M oi f f 2

3+ — ̂ 4 cos/? M 2> M 4

3+ — £4e6 c o s ( ß - y ) M 2,M 4,M 6

(2 . 1 1 )

withq = volum etric rate o f sand transport per unit widthu = am plitude o f the M 2 tidal current£,k s4 e6 - am plitude ratio o f the residual, M 0, M 4, M 6 and the M 2 tidal current

respectively

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Tidal a sy m m e try and se d im e n t tra n sp o rtin th e W e ste rsc h e ld e Z 2864 N o v e m b e r, 200 0

ƒ = function o f sedim ent and fluid characteristicsy = phase o f tidal current M 6 relative to the M 2 tidal currentß = phase o f tidal current M 4 relative to the M 2 tidal current

An approxim ate analysis o f the tidal and residual suspended sedim ent transport, based on cross-sectionally averaged velocities com puted with a ID -m odel, indicates that for the residual suspended transport o f coarse sedim ent m ore or less the sam e applies as for the bed-load transport (not shown).

The residual transport in the ebb- and flood-channels, S,,ebb and Sr tioocl, and thus the circulation in the m orphological cells, is mainly determ ined by the residual flow velocity or the tidal rectification, i.e. the M 0 constituent o f the horizontal tide. T he residual transport through the estuary Sr is closely related to the overtides o f M 2.

T he overtide o f M 2 in terms o f f low velocity is related to the asym m etry o f the vertical tide w hereas the M 0 com ponen t is m ainly geom etry and bathym etry induced.

Thus the circulation com ponen t o f the residual sed im ent transport is mainly induced by the bathymetry difference betw een the ebb- and f lood-channel. The residual transport through the estuary is closely related to the asym m etry o f the vertical tide in the estuary. This means that the asym m etry o f the vertical tide is important for the morphological developm ent on the mega-scale w hereas the residual currents (=tidal rectification) induced by bathymetry is important for the morphological developm ent on the macro-scale, i.e. the estuarine sections.

2.4 Sum m ary working hypotheses

In sum m ary the fo llow ing hypotheses have been proposed in the previous sections (see also Fig 2.2):

1. The residual sedim ent transport, local, through a channel or through the whole estuary, is m uch sm aller in m agnitude than the corresponding ebb- or flood transport.

2. The residual sed im ent transport through an ebb- and/or a flood channel is much larger than the residual transport through the estuary. In o ther words, the c irculating com ponent o f the residual transport is much larger than the com ponen t through the estuary.

3. The circulating com ponen t o f the residual transport is m ainly related to the residual flow field and m uch less to the overtides.

4. The com ponent through the estuary o f the residual transport is c losely related to the overtides o f the flow velocity.

5. The circulating com ponen t o f the residual transport is responsible for the macro-scale morphological developm ent, i.e. the m orphologic evolution o f a system o f two parallel main channels. For the m acro-scale m orphological developm ent the residual flow (M 0) is therefore m uch m ore im portant than the overtides (M 4, M 6, etc.) o f the f low velocity.

6. T he net throughput o f sedim ent over the entire estuarine cross-section is responsible for the mega-scale m orphological developm ent, i.e. the sedim ent exchange between estuarine sections and larger stretches o f the estuary. The overtides o f the flow velocity therefore play a significant role in the mega-scale morphological development.

W L I D elft H ydraulics 2 - 4

Tidal asy m m etry an d se d im e n t tra n s p o r tin th e W e ste rsc h e ld e Z2864 N o v e m b e r, 2000

3 Elaboration of th e hypotheses on th e basisof observations

3.1 Introduction

Basically, the fo llow ing information is available to evaluate the hypotheses as formulated in the previous chapter:

• Sand transport measurem ents.• Results o f large-scale sedim ent budget analyses® Sedim ent transports from the D elft3D -M O R runs carried out within the long-term vision

W esterschelde pro jec t (W interw erp et ah, 2000).• Results from ID tidal model (Schoem an, 2000)• Flow velocity data in individual main channels near Terneuzen (Jeuken, 2000)

These observations are addressed below, focusing on the hypotheses.

3.2 Large scale residual sedim ent t r a n sp o r t in th e estuary

3.2.1 Field D ata

Field data on large scale sedim ent transport in the W esterschelde are scarce. Allersma (1992) and Storm (1996) present some data for a num ber o f cross sections in the estuary based on direct m easurem ent o f (suspended) sedim ent transport. These all concern 13 hour (one tide) m easurem ents at a limited num ber o f verticals for each cross-section. These data give a good indication o f the m agnitude o f the total (ebb + flood) transport through the cross-sections but cannot be considered to be accurate for the determination o f the residual transport through the cross sections. This is p robably the reason w hy Storm (1996) only presented the total transport through the cross sections but not the residual transport. Moreover, the tidal conditions during the m easurem ents are seldom cyclic, resulting in a bias o f the transports.

The m ost com plete data on the long-term large-scale residual sedim ent transport are those based on the sedim ent-balance studies. Uit den Bogaard (1995) constructed a sediment- balance for the six parts o f the estuary based on the da ta o f the morphological development and dredging / dum ping records. The results for the residual sedim ent transport are shown in Fig.3.1. The upper panel o f the figure show s the residual transport at the mouth into the estuary, from the w estern part to the central part (vak4-vak3) and from the central part to the eastern part. In the lower panel the 5-year m oving average o f the transports at the same cross sections is show n. The averaging w as done to sm ooth out errors in the data. Furthermore, it should be noted that the sed im ent balance is based on the assumption that the sedim ent exchange at the border between T he N etherlands and Belgium can be ignored.

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Tidal a sy m m e try an d se d im e n t tra n s p o r tin th e W e ste rsc h e ld e Z2864 N o v e m b e r, 2000

It also emphasised that the observations relate to both sand and mud. It reveals the following features:

® The positive transport at the mouth (positive = import) decreases until 1985, especially in the period 1978-1983, after 1985, more or less constant around 0.

• In the period 1975-1980 there is a net sediment transport from the western part tothe central o f the es tuary part that increases with time. T he sedim ent exchange reduces in 1982-1986. Since then it is more or less constant.

• A qualitatively sim ilar temporal variation in sedim ent exchange can be observedbetween the budget sections 3 and 2 ( ‘vak3-vak2’ in Fig. 3.5), the central and landward part o f the estuary.

Huijs (1996) has analysed the data o f the morphological deve lopm ent and the dredging / dum ping records on a m ore detailed scale by dividing the es tuary into morphological units o f channels and tidal flats. However, from this analysis it is not possib le to determine the sedim ent exchange between the units. Moreover, the applied schém atisa tion o f the channels and shoals is not sam e for subsequent years. This is a com plicating fac tor in interpretation o f the results.

3.2.2 Relation to th e asym m etry of vertical tide

The tidal asym m etry param eters are presented in W ang et al (1999). T he M 4 related to the M2 tide is shown in Fig.3.2 together with the large-scale sedim ent transport. Com parison o f the tw o figures show s that there is not an unam biguous re la tionship betw een the asymmetry o f the vertical tide and the large-scale sedim ent transport in the es tuary (this contrasts with the observations o f G erritsen et al., 1998). This indicates that, if present, the relation between the direction o f large-scale sedim ent transport and asym m etry o f the vertical tide is a com plicated one. Possible reasons for this com plexity are:

® The direction o f change in the tidal asym m etry at different sta tions is different. At H answ eert it becom es less ebb-dom inant w hereas at Bath it becom es less flood- dominant.

• The relation between the asym m etry o f the horizontal tide and that o f the vertical tide is com plicated . T he discharge at a cross-section is related to the w ater level variation in the w hole estuary upstream o f the cross-section, including the Zeeschelde.

• The residual sedim ent transport through the estuary is an integral o f the local residual transport through individual ebb and flood channe ls (see Eq.1.6). This local residual transport s trongly depends on the residual ve locity (Van de Kreeke and Robacewska, 1993). In other words, the sedim ent exchange between estuarine sections m ay be influenced by 2D (or even 3D) channel processes. For instance, the study o f Jeuken (in press) show s that the sedim ent exchange betw een the estuarine sections 4 and 3 is effectively influenced/determ ined by the behaviour o f connecting channels in the bar area o f the main flood channel Everingen. This implies that relatively small-scale processes, i.e. m edium -scale channel behaviour, can be involved in the large-scale sedim ent transport in the estuary.

W L I D elft H ydraulics 3 - 2

Tidal a sy m m e try an d se d im e n t tra n s p o r tin th e W e s te rs c h e ld e Z2864 N o v e m b e r, 2000

3.3 Results of a one-dimensional model

Schoem an (2000) set up a one-dimensional model to study the relation between the tidalasym m etry and the m orphology in the Western Scheldt. The results o f one o f the simulations o f this model, with the realistic bathym etry o f 1996, is used here to analyse the relation between the asym m etry o f the horizontal tide and tha t o f the vertical tide, and the relation between the residual sed im ent transport and the asym m etry o f horizontal tide.

T he am plitude ratio between the M4 tide and the M2 tide as well as the phase lag between M4 and M2 for w ater level, discharge and flow velocity (cross-section averaged) are shown in Fig.3.3.

® The am plitude ratio between M4 and M 2 for the cross-sectionally integrated discharge is larger than 2 times that for the w ater level, w hereas the amplitude ratio for the velocity is sm aller than 2 times that for the w ater level. This agrees with the analysis on the non-linear effects due to the hypsom etry (W ang et al, 1999).

• The difference o f the phase o f M2 relative to that o f M 4 between the horizontal tideand the vertical tide is about 80°. There is also a difference between the phase lag for the flow velocity and that for the discharge. This difference varies from about - 10° at the mouth to about 10° at the upstream end o f the Westerschelde.

T he amplitude ratio between the M6 tide and the M2 tide as well as the phase lag between M 6 and M2 for w ater level, d ischarge and flow velocity (cross-section averaged) are shown in Fig.3.4.

• The am plitude ratios between M6 and M2 for the d ischarge as well as for the flow velocity are about 3 tim es that for the w ater level. Also this is in agreem ent with the results o f the analysis carried out by Wang et al. (1999).

• The phase lag betw een M6 and M2 for the vertical tide decreases from about 70° at the mouth to about 0° at the upstream end, w hereas the phase lag for the horizontal tide, for the d ischarge as well as the flow velocity, is almost constant through the whole estuary: about 160°.

The three terms in the long-term averaged sedim ent transport (eq. 2.11) derived from the results o f the flow velocity are show n in Fig.3.5.

• It is rem arkable that even the results o f such a ID single-branch model show a M0 com ponent for the f low velocity. The term related to this com ponen t is the largest one o f the three. The ebb-dom inant current even without upstream river discharge is due to the fact that ebb-flow occurs at a lower w a te r level than the flood-flow. This confirm s the concept o f Bakker and De Vriend (1995).

• The contribution due to the M4 com ponent is in the same order o f magnitude as that o f the M 6 com ponent. The contribution o f M 4 is negative (export) in the western part and positive in the eastern part. T he contribution o f the M6 com ponent is the other w ay around.

• If all three te rm s are taken into account the calculated residual transport is negative. I f only the overtides are taken into account it is slightly positive (flood-dominant) in a lm ost the w ho le estuary.

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Tidal asy m m etry an d se d im e n t t ra n s p o r tin th e W e ste rsc h e ld e Z 2864 N o v e m b e r. 2000

® N o te that for the calculation o f the transport the variation o f the (transport) width, which will m ake the transport som ew hat (5-10% ) more positive because the water level during flood is higher than during ebb, is not taken into account.

It is a lso noted that for all the cross sections the ebb and flood transport are o f the same order o f m agnitude, and both much larger than the residual transport (not shown).

3.4 Tidal and residual t ra n sp o r t within channels

3 .4 .1 Velocity observations from th e field

The results o f a d ischarge m easurem ent and some long-term current observations in the system o f main channels near Terneuzen (Jeuken, 2000) were harm onically analysed (for locations see Figure 3.6). The relative contribution o f the depth-averaged residual current and the quarter and sixth-diurnal ve locity com ponents to the sand transport were determ ined fo llow ing Van de Kreeke and R obaczew ska (1993, see equation 2.11).

Point observations

The results o f the long-term current m eter observations are depicted in Figure 3.7. For both the main ebb channel and the main flood channel three locations are indicated, viz.: the entrance o f the channel (E), the central part (C ) and the bar area (B, see figure 3.6).

The m ain ebb channel is characterised by strongly ebb-dom inant residual currents. In the central part o f the channel the am plitude o f M 4 relative to M 2 am ounts 0.15. T he amplitude ratio o f M 6 is considerab ly smaller. T he relative phases approxim ate 100 and 140 degrees respectively. T he contribution to the residual sand transport ( lower panel) show s that the residual currents determ ine the ebb-dom inant direction o f the net transport in the central part o f the channel. R em arkable is the ebb-dom inan t direction o f the interaction between M 2 and M 4. T he triple-interaction betw een IVE M 4 and M 6 is associated with a flood- dom inant direction. In the bar area (B) and the entrance (E) where the channel exhibits a curved-channel a lignment, the ellipses o f the overtides M 4 and M 6 are strongly inclined with respect to the M 2-ellips. As a result it is not meaningful to consider the interaction between M 2 and its overtides in the main f low direction. P resum ably this phenom enon o f s trong inclination o f the ellipses is due to transverse secondary flows.

At the three locations (E, C ,B) in the straight main flood channel Everingen this phenomenon! o f inclined current ellipses is absent, which seem s to confirm the above interpretation. Figure 3.7 reveals a large spatial variation in the relative m agnitude o f the residual currents and the overtides. In the deep central part a small ebb-dom inant residual current exists, w hereas clearly f lood-dom inant residuals occur in the entrance and bar area o f the channel. Except for the entrance o f the channel, w here M 4 is relatively large, M 4 and M 6 are o f similar relative m agnitude. The phase differences relative to M 2 range between some 100 and 160 degrees respectively (m iddle panel). T he direction o f residual sand transport is determ ined by the effect o f the residual currents. Rem arkable is the negative

W L I D elft H ydraulics 3 - 4

Tidal a sy m m e try and se d im e n t t ra n s p o r tin th e W e ste rsc h e ld e Z 2864 N o v e m b e r, 200 0

contribution o f the interaction M 2M 4 and the f lood-dom inance o f the triple interactionm 2m 4m 6.

D ischarge m e asu rem en t

In 1996 a d ischarge m easurem ent has been carried ou t with an Acoustic D oppler Current m eter in the central part o f Terneuzen section during strong spring tidal conditions (with practically cyclic tides, transect 7 in Fig. 3.6).

The results o f the harm onic analysis show a small ebb-dom inant residual current, s imilar to the ID -m odel. This current is probably due to the phase differences between the horizontal and vertical tide. Because o f this phase differences the m axim um ebb currents occur at lower w ater level and smaller cross-sectional area than the m axim um ebb flow. This favours an ebb-dom inant residual current. Furthermore, an approxim ate ly equal contribution o f the M 4 and M 6 overtides in the horizontal tide can be observed (Fig. 3.8). The m agnitude o f the asym m etry in the horizontal tide, indicated by the am plitude ratio (upper panel), is larger than that o f the vertical tide: the asym m etry in the d ischarges and velocities is two to three times larger than in the water levels. This m ore or less confirm s the previous analyses o f Wang et al. (1999) and the ID model results described in section 3.2. Similar to the 1D- model results (for m ean tidal conditions), the asym m etry related to the quarter-diurnal com ponent is slightly larger than that o f the sixth-diurnal one. Also the relative phase difference between M 2 and the overtides M 4 and M 6 are similar, i.e. some 90 and 140 degrees respectively.

The relative contribution o f the various com ponen ts to the residual transport o f coarse sedim ent ( low er panel) show s again a strong influence o f the residual currents, both for the entire estuarine cross-section and for the individual main ebb and flood channels. The relatively small residual current (see upper panel) largely determ ines the direction o f the net transports. The contribu tion o f the overtides to the residual transport is several times smaller. Averaged over the entire cross-section the interaction between M 2 and M 4 is a ttended with a small flood-dom inant transport, w hereas the triple interaction (M 2M 4M 6) induces a small ebb-dom inant transport. The contribution o f the overtides in the individual main channels is opposite: in the flood channel the interaction between M 2 and M 4 yields a flood-dom inant t ransport w hereas it induces an ebb-dom inan t transport in the ebb channel. The triple interaction between M 2 M 4 and M 6 is attended with a small ebb-dom inant transport in the flood channel and an flood-dom inant transport in the flood channel. This em phasises the large spatial variation as pointed out in the previous section.

3.4.2 Results from 2 D H -tran sp o rt m odelling

The sedim ent transport through some cross-sections in the estuary has been determined from com puted sed im ent transport fields that w ere carried out within the fram ew ork Long­term Vision project (W interwerp, 2000). T he results o f some transects w ere analysed to obtain an impression o f the tidal and residual transports within and through a system o f two parallel ebb and flood channels. For each o f the th ree seaw ard located estuarine sections (num bers 3-6, see section 2.1) tw o representative cross-sections w ere selected which clearly separate the main ebb channel from the main flood channel. The results in term s o f ebb,

W L I D elft H ydraulics 3 - 5

T idal a sy m m e try an d se d im e n t tra n s p o r tin th e W e ste rsc h e ld e Z 2864 N o v e m b e r, 200 0

flood and residual transport, in individual channels and in the system o f channels as a whole, are show n in Figure 3.9. It is em phasised that the distinction between ebb and flood channels in Figure 3 .9 is based on m orphologic arguments: the ebb channel has a bar at its seaward end, w hereas the flood channel has a bar at its landward end. The lateral demarcation between the channels follows the ‘w a te rshed ’ across the elongate shoals between the two channels. This implies that when ebb and flood-dom inant transports occur within the same channel (e.g. in the flood channel G at van Ossenisse), the sum o f these transports is presented. Furtherm ore, the m agnitude o f the transport depends on the transport formulation chosen (Engelund-H ansen) and on the sedim ent param eter settings (grainsize o f 240 pm ). H ence the results give an indication o f the o rder o f magnitude o f the various transport constituents and their relative magnitude.

Figure 3.9 gives rise to the following observations:• T he main ebb channe ls (EC) exhibit an ebb-dom inant transport, w hereas the main flood

channels (FC) are clearly flood-dominant.• The tidal and residual transport in the main flood channels (FC) tend to exceed those in

the main ebb channel, resulting in a net flood-dom inant residual transport through the system o f two parallel main channels . This net com ponen t is sm aller than the individual ebb and flood transport rates, though in five o f the six cross-sections it is o f same order o f magnitude.

® A similar observation applies to the sand transport in the individual channels. The m agnitude o f the net transport through a channel resem bles the magnitude o f the subordinate, i.e. sm allest tidal (ebb or flood), transport.

Similar observations are m ade by Jeuken (2000). She further concludes that the direction o f the ebb-dominated transport in the (main) ebb channel is due to the ebb-dom inant residual currents. The generally large, flood-dom inant transport in the flood channel coincides with flood-dominant residual currents and an overall, i.e. in both main channels, f lood-dominant asym m etry o f the m ax im um velocity.

3.5 Residual flow and bathym etry

In the previous sections it has been show n that the residual velocity plays an essential role in the residual sedim ent transport. Therefore an analysis will be carried out in order to identify the factors de term in ing the residual current.

3.5.1 Single b ranch consideration

The results o f the one-dim ensional model, as well as the field measurem ents, show that there is a residual current in the ebb-direction, even when there is no upstream discharge (so no residual d ischarge in the ID -m odel) . This is due to the fact that the ebb flow occurs at a lower w ater level than the flood flow. This can be dem onstrated as follows. In case that there is no residual discharge, the ebb-volum e must be equal to the flood volume:

f “|ep = f “ |ep (3.1)

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T idal a sy m m e try an d se d im e n t tra n s p o r tin th e W e s te rsc h e ld e Z 2 8 6 4 N o v e m b e r. 2 000

T he residual current in the ebb-direction is equal to

02)* ebb + 1 flo o d V A cbb A flood

Since Aflood>Aebb the residual current vr is always negative, i.e. in the ebb-direction, independent o f the ebb- and flood duration and hence independent o f the m axim um ebb- and flood discharge. The factor de term ining the cross-sectional averaged residual current is thus the phase lag between the horizontal tide and the vertical tide.

3.5.2 Tw o-branches consideration

In an ebb- and f lood-channel system, the residual flow through the channels can be explained by s im plify ing the tidal flow to two steady-flow periods, one in the flood direction and one in the ebb direction, both with the same discharge Qm. Furthermore, it is assum ed that the w idths o f the tw o channels are equal. If the w ater level during flood is 8 above the reference level and the w ater level during ebb is 8 under the reference level, the d ischarge through the flood channel during flood follows from

a .■. < ; r f -..a. o.»(/?, + Ô) + (fh + 8)

During ebb it is

a.-, j g-(hx - S ) +(h2 - S )

In these two equationsh, = depth o f the flood channel with respect to the reference levelh 2 = depth o f the ebb channel with respect to the reference levela = pow er depend ing on formulation for bed shear stress, fo r M anning it is 5/3

T he residual discharge through the flood channel then becomes

AO 1 1

ai +

/'hL 8_

81

h)

1 +h, h,

(3.3)

1 -h,

So there are two param eters de term ining the residual discharge through the system o f channels: h2/h¡, characteris ing the bathym etry o f the system, and 8/h¡, where 8 is determ ined by the phase lag betw een the horizontal tide and the vertical tide. I f the flood channel is shallower than the ebb channel and the w ater level during flood is higher than during ebb the residual d ischarge in the flood channel is in the flood direction.

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Tidal asy m m etry an d se d im e n t t ra n s p o r tin th e W e ste rsc h e ld e Z2864 N o v e m b e r, 2 000

The expression (3.3) is depicted in the upper panel o f Figure 3.10. T he residual discharge norm alised w ith the total d ischarge through the system is m ore o r less proportional to 5/h¡. It is rem arkable that the relative residual discharge increases with h2/h¡ but the increase becom es sm aller w hen its value approaches 2. This is m ade better visible in the lower panel o f Figure 3.10, in which the derivative o f the expression to ó/h¡ is depicted as function o f hi/hj. Th is derivative has a m axim um value when h2/h¡ is about 2.

Finally, it is noted that there are also o ther geom etric parameters, i.e. the length o f the channels , influencing the discharge distribution through the channels and thereby the c irculation d ischarge in the ebb and flood channel system. A nother m echanism generating such a circulation is due to the width variation o f the channels (the width o f the flood channel increases in the upstream direction) as dem onstrated by Van Kerckhoven (1995). However, in general it can be concluded that the residual circulation is determ ined by the geometric and bathym etric characteristics o f the estuary' and by the phase lag between the horizontal tide and the vertical tide.

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4 Discussion, conclusions andrecom m enda tions

4.1 Discussion and conclusions

First the hypotheses as sum m arised in 2.4 are evaluated based on the findings in C hapter 3.

Hypothesis 1 : The residual sedim ent transport, local, through a channel or through the whole estuary; is much sm aller in magnitude than the corresponding ebb- or

f lo o d transport.

This hypothesis is supported by the ID model results, but not fully supported by the results from the 2D H model. A ccord ing to the 2DH model, the residual transport through a cross section can be o f the sam e order o f m agnitude as the sm allest o f the ebb- and the flood- transport, depending on the location o f the cross-section. The hypothesis is thus confirmed when the w hole estuary is considered, and rejected when the individual channels are

considered.

Hypothesis 2: The residual sedim ent transport through an ebb- and/or a f lo o d channel is m uch larger than the residual transport through the estuary. In other words, the circulating component o f the residual transport is much larger than the com ponent through the estuary.

This hypothesis has been proven false. The circulating com ponen t and the com ponent through the estuary o f the residual transport can be o f the sam e order o f magnitude.

Hypothesis 3: The circulating component o f the residual transport is m ainly related to the residual f lo w f ie ld and much less to the overtides.

This hypothesis is fully supported by all data available and can therefore be considered as proven true.

Hypothesis 4: The com ponent through the estuary o f the residual transport is closely related to the overtides o f the f lo w velocity’.

N o conclusion about this hypothesis can be draw n yet. It is show n that there is a relation between the (vertical) overtides and the residual sedim ent transport through the estuary, but it is also show n that the residual f low plays an im portant role in the residual transport. Even according to the s ingle-branch ID model, the residual current gives a predom inant contribution to the residual transport. This raises doub t about w hether it is justif ied to relate the cross-sectional averaged sedim ent transport to the cross-sectional averaged flow velocity. I f this is done, the ID model will a lw ays give a residual transport in the ebb- direction, even i f all the characteristics o f the tidal asym m etry are reproduced. This is

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Tidal a sy m m e try and se d im e n t t ra n s p o r tin th e W e s te rsc h e ld e Z2864 N o v e m b e r, 2 000

clearly not in agreem ent with the reality. At this m oment, on ly the fo llowing conclusion can be drawn: The residual transport through the estuary is the integral o f the local residual transport over a cross-section o f the estuary. The local transport is dom inated by the circulating residual flow, but the integral can be influenced by the residual flo w as well as the overtides.

Hypothesis 5: The circulating component o f the residual transport is responsible fo r the macro-scale m orphological development, i.e. the morphologic evolution o f a system o f two para lle l main channels. F or the macro-scale morphological developm ent the residual flo w (M0) is therefore much more important than the overtides (M4, M 6, etc.) o f the flo w velocity.

This hypothesis can be considered as proven true.

Hypothesis 6: The net throughput o f sediment over the entire estuarine cross-section is responsible fo r the mega-scale m orphological development, i.e. the sediment exchange between estuarine sections and larger stretches o f the estuary. The overtides o f the f lo w velocity therefore p la y a significant role in the mega- scale m orphological development.

This hypothesis should be modified as (see the evaluation o f hypothesis 4): The net throughput o f sedim ent over the entire estuarine cross-section is responsible fo r the megci- scale m orphological development. The overtides o f the f lo w velocity therefore p la y a significant role in the mega-sccile m orphological development, in addition to the residu a l flo w .

Further the fo llow ing conclusions have been drawn:• In the residual sed im ent t ransport and hence also in the morphological development

o f the W esterschelde estuary, the residual current plays a very important role.• For the residual sedim ent transport the quarter-diurnal and sixth-diurnal com ponent

o f the tide are equally important.• The residual current is determ ined by the geom etric and bathymetric characteristics

o f the estuary, and by the differences in w ater level during flood and during ebb. The latter is determ ined by the phase difference between the horizontal tide and the vertical t ide in the estuary.

In the analysis by W ang et al. (1999) it has been dem onstrated that the mega-scale morphological deve lopm ent influences the asym m etry o f the vertical tide. The present study shows that the m ost im portant characteristic o f the asym m etry o f the horizontal tide is the residual current (the MO com ponent). It is noted that the bathym etric characteristic influencing the residual current, the depth difference between the flood channels and the ebb channels, is also strongly influenced by the hum an interference, such as dredging and dum ping activities. Therefore, m ore insight into the residual current and the residual sedim ent transport m echanism s under the influence o f the bathymetric characteristics is necessary for s tudying the impact o f hum an interference.

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Tidal a sy m m e try an d se d im e n t tra n sp o rtin th e W e ste rsc h e ld e Z 2 8 6 4 N o v e m b e r, 2000

4.2 Recom m endations

Based on the findings o f the present study, the fo llowing recom m endations are made for further studies:

• Study the relation between the residual current and the bathym etry in more detail with 2D h and 3D models. Use ID netw ork m odels to explore the influence o f bathymetric changes on the asym m etry o f the vertical tide.

• Pay m ore attention to the M 6 com ponent in the studies. Up to now only the M4 com ponent has been analysed in relation to the morphology.

© Use 2D H sedim ent transport models to analyse the relative importance o f theovertides (as com pared with the residual current) to the residual sedim ent transport, especially the net throughput o f sedim ent over the entire es tuarine cross-section.

• A nalyse the m orphologic evolution o f the individual channels within the estuarine sections (Jeuken, 2000).

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Tidal asy m m etry and se d im e n t t ra n s p o r tin th e W e ste rsc h e ld e Z 2 8 6 4 N o v e m b e r, 2000

A References

A lle rsm a , E ., 1992. S tu d ie in ric h tin g o o stc lijk d ee l W es te rsc h e ld e , A n a ly se van het F y sisch e sy s teem , N o ta voor d e w e rk g ro e p O O S T W E S T , R a p p o rt Z 3 6 8 . W ate r lo o p k u n d ig L ab o ra to riu m .

B o g aard , L .A . U it den . 1995, R e su lta ten Z a n d b a la n s W e s te rsc h e ld e 19 5 5 -1 9 9 3 . IM A U rep o rt. R 95-08 .

G erittsen , H ., W ang , Z .B . an d A . V an d e r W eck , 1999, M o rfo lo g isc h e in te rp re ta tie v an d e v e ra n d e rin g e n in het ge tij in d e W este rsch e ld e , W L | D e lft H y d ra u lic s , R e p o rt Z 2 6 7 1 .

H u ijs , S .W .E ., 1996, D e o n tw ik k e lin g v an d e m o rfo lo g ie in d e W este rsch e ld e in re la tie to t m en se lijk e ing repen , R ap p o rt R 9 6 - 17, IM A U .

Je u k en , M .C .J .L .. 2 0 0 0 . O n th e m o rp h o lo g ic b e h a v io u r o f tida l c h a n n e ls in th e W este rsch e ld e e s tu ary . P hd- th es is , U trech t U n iv ersity . 378 p p .

K erck h o v en , J .D .M . van , 1995. M o rp h o lo g ic a l m o d e llin g o f eb b a n d flood c h a n n e lsy s te m s in e s tu aries . M a ste r th es is . D e lf t U n iv e rs ity o f T e c h n o lo g y , F acu lty o f c iv il E n g in eerin g .

S ch o em an , P .K . (2 0 0 0 ). G e tij-a sy m m etrie in de W este rsch e ld e . M a s te r th es is . D e lft U n iv e rs ity o f T ech n o lo g y , F a c u lty o f c iv il E ng in eerin g .

S to rm , C ., 1996, R e sid u e le za n d tra n sp o r te n in d e W este rsch e ld e , RIK.Z W e rk d o cu m en t O S -9 6 .8 3 7 X , RIK.Z, R ijk sw a te rstaa t.

V an d en B erg . J .H .. M . C . J.L . Jeu k en and A .J .F . v an d e r Spek (1 9 9 6 ). H y d rau lic p ro cesses a ffe c tin g the m o rp h o lo g y an d e v o lu tio n o f th e W e s te rsc h e ld e e s tu ary . In: E stu a rin e sho res : E v o lu tio n .E n v iro n m e n ts an d H u m an A lte ra tio n s , N o rd s tro m a n d R om an (ed s). W iley , pp. 157-184.

V ro o n J. C . S to rm . J C o o sse n (1 9 9 7 ). W es te rsch e ld e , s tram o f s tru is? E in d ra p p o rt v an het p ro jec t O o s tw est. een stu d ie n a a r d e b e ïn v lo e d in g v an fy sisch e en v e rw an te b io lo g isc h e p a tro n e n in een e s tu ariu m . R ijk sw a te rs taa t rep o rt R IK .Z -97.023 (in D u tch ).

W ang , Z .B .. Je u k en . C . an d II.J . D e V rien d . 1999, T id a l a sy m m e try and re s id u a l se d im e n t tra n sp o r t in es tuaries . A lite ra tu re s tu d y a n d ap p lic a tio n to th e W es te rsc h e ld e , W L | D e lft H y d rau lics . R e p o rt Z 2 7 4 9 .

W in te rw erp . J.C .. M .C .J .L . Je u k en , M .A .G. v an H e lv ert. C . K u ijp er. A . v an d e r S pek . M .J.F . S tiv e . P .M .C .T h o o le n and Z .B . W 'ang (2 0 0 0 ). L a n g e -te rm ijn V is ie S c h e ld e -e s tu a riu m c lu s te r m o rfo lo g ie . W L |D elft H y d rau lic s , re p o rt Z 2 8 7 8 .

W L I D elft H ydraulics A - I

I c h a n n e l b a r o f B a thII c h a n n e l b a r o f V a l k e n i s s eIII c h a n n e l b a r o f H a n s w e e r tIV c h a n n e l b a r o f B o r s s e l ek m

Saeftinghe.

N A P -2 m N A P -1 0 md r e d g i n g s i t e X'Y d u m p i n g s i t e e m b a n k e d s i n c e 1 8 0 0

/ u d i v a n8 S c h a a r va n V alkeñiSse9 Z u id e rg a t

3 E oschaar van d e S p i/ke rp la a t 10 O v er lo o p van V a lken isse4 E v erm g en 11 N a u w va n B ath5 Pas van T e m e u ze n 12 S c h a a r v a n N o o rd6 M id d e lg a t 13 A p p e lz a k

1 W ie lingen2 H on te

Location of various main ebb and flood channels in the W este rsche lde in 1992 (from Van den Berg et al., 1996)

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W L I D E L F T H Y D R A U L I C S Fig.2.1

— S r . f

- ►F C

► s fs e

► S r = S r , f + S r ,

E Cs e

s e = e b b t r a n s p o r t t h r o u g h c h a n n e ls f = f lo o d t r a n s p o r t t h r o u g h c h a n n e lS r , f = r e s i d u a l t r a n s p o r t t h r o u g h f lo o d c h a n n e l F C

S r , e = r e s i d u a l t r a n s p o r t t h r o u g h e b b c h a n n e l E CS r = r e s i d u a l t r a n s p o r t t h r o u g h e n t i r e c r o s s - s e c t i o n , i .e . S r , f + S r , e .E C = m a i n e b b c h a n n e lF C = m a i n f lo o d c h a n n e l

S chem atic representation of the residual sed im ent transport at the spatial sca le of an es tuarine section.

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11/2000

W L I D E L F T H Y D R A U L I C S Fig.2.2

Residual sediment transport

4 -

3 ■■

o.

197: 1980 1995

-2

y e a r

5 year averaged transport

4

roa>coE2

1975 1980 1985 1990 1995

y e a r

N e t sed im ent tran spo rt inferred from a large-scale sed im ent budget study (U itd en Bogaard, 1995). + = landward directed transport, -= se a w a rd directed transport.

Z2864

o k t o b e r 2 0

00

WL I D E L F T H Y D R A U L I C S Fig-3.

faseverschil

20 - -

10 - -

1980 1985 1990 1995 2000

-10

-20 - -

-30

j a a r

vliss ingen

X — te rn eu zen

—Xi— h a n s w e e r t

■O— bath

5 year averaged transport

co

197! 1980 1985 ‘1990 1995 2000

y e a r

Asym metry of the vertical tide related to the generation o f M4 and the large-scale sed im ent transport in th e estuary.

Z2864

I/2000

WL I D E L F T H Y D R A U L I C S Fig.3.2

am p litu d e ratio M4/M2

Phase difference between M4 and M2

0.18

0.16

0.14

0.12

ár

0.08 --

0.06 -

0.04

0.02 - -

0 20000 30000 4000010000 50000 60000

010000 20000 30000 40000 50000

-20 - -

-40CM

-60 --

-80

-100

X

Asym metry o f the vertical and horizontal tide related to generation of M4 inferred from I D m odel results. w l= w a te r level, q = discharge and cross- sectionally averaged velocity.

Z2864

II/2000

WL I D E L F T H Y D R A U L I C S Fig-3.3

am p litu d e ratio M6/M2

0.25

0.2

0.15 --

0.05

0 10000 20000 30000 40000 50000 60000

phase difference between M6 and M2

100

50 -■

10000 20000 30000 5000040000 60000

CD5CN2CO

-100

-150 --

-200X

Asym metry o f the vertical and horizontal tide related to generation of M6 inferred from I D model results. wl = w a te r level, q = discharge and cross- sectionally averaged velocity.

Z2864

I I/2000

WL I D E L F T H Y D R A U L I C S Fig-3.4

contribution various tidal constituents to residual transport

0.04

0.02 -

10000 20000 30000 40000 50000 00- 0.02

-0.04 --n£<n

-0.06 -

-0.08

- 0.1 - -

M0-M2

M2-M4- 0 .1 2 - -

M2-M4-M6

-0.14

X

residual transport

0.04

0.02

2000010000 30000 40000 50000 60000

- 0.02 - -

-0.04</>

-0.06

-0.08 --

- 0.1 M0-M2-M4-M6M2-M4-M6

- 0.12 -

X

I D model resultsContribution o f various com ponen ts to the residual sed im ent transport according to equation 2.9.

Z2864

ok tober2000

W L I D E L F T H Y D R A U L I C S F ig -3 .5

2 >

■o

o

CT)

Location of long-term current m eters (9, 102,100, 10,101 and 8) and d ischarge transec t 7(a+b). (From Jeuken , 2000).FC1=flood channel, EC 1=ebb channel.

Z2864

11/2000

WL I D E L F T H Y D R A U L I C S Fig.3.6

Main ebb channel - Pas v. Terneuzen

0.3

0.2

.2 0.1 13

Q .

I -0.1

- 0.2

-0.3

L

B , C E □ M4/M2-- □ M6/M2

——

Main ebb channel - Pas v. Terneuzen

o

© '300 c01© -60 c t5 ©« -90ro.cQ.a>£ 12013©

“ -150

-180

B— i--------------------

E

□ 2M2-M4

□ 3M2-M6

Main ebb channel - Pas v. Terneuzen

0.3

0.2 - -

□ M0M2□ M2M4

□ M2M4M6□ M0M2M4M6

C/5

- 0.2 - -

-0.3

-0.4

Main flood channel - Everingen

s 0.4

0.1 -

f c . i i

□ M0/M2□ M4/M2

□ M6/M2

Main flood channel - Everingen

CU -150

□ 2M2-M4

□ 3M2-M6

Main flood channel - Everingen

0.5

0.3

0.2 - -CO¿I</)

- 0.2

□ M0M2

□ M2M4□ M2M4M6

□ M0M2M4M6

Results o f long-term cu rren t m easurem ents in the T erneuzen section.E = entrance, C = c e n tra l part, B = bar area of main channel. For locations see Fig. 3.6.

Z2864

I/2000

WL I D E L F T H Y D R A U L I C S Fig-3.7

Discharge transect 7

o2a>T¡3o.E<

M0/M2 M4/M2 M 6/M 2

- 0.1

Discharge transect 7

100

50

o- -50

® -100

-150

Discharge transect 7

□ WL□ Q-TOT□ U-TOT

□ WL

□ Q-TOT□ U-TOT

0.05 -

U-TOT U-FC5 -0.05 -

- 0.1 -

-0.15 --

- 0.2

□ M0M2

□ M2M4□ M2M4M6

□ M0M2M4M6

Results o f discarge m easurem ent near T erneuzen . W L = w a te r level, Q- to t and U -to t= d ischarge and velocity through en tire estuarine cross- section. U-EC=velocity in ebb channel, U-FC=velocity in flood channel

Z2864

o k to b e r2000

WL I D E L F T H Y D R A U L I C S Fig. 3.8

Vlissingen section (6) - transect 1 Vlissingen section (6) - transect 2

□ flood

□ ebb

□ difference

Terneuzen section (5) - transect 1 Terneuzen section (5) - transect 2

6 - -

□ flood

□ ebb

□ differenceoQ .incro

EC FC FC+EC

Hansweert section (4) - transect 1 Hansweert section (4) - transect 2

□ flood

□ ebb

□ difference

Results o f 2DH sedim ent tran spo rt model. E C = e b b channel, FC =flood channel

Z2864

o k to b e r2000

W L I D E L F T H Y D R A U L I C S F ig .3 .9

0.18

0.16

0.14

0.12

¿ 2 0 1 o

§ 0 .0 8

0.06

0.04

0.02

00 0.05 0.1 0.15 0.2 0.25 0.3 0.35 0.4 0.45 0.5

delta/h1

df/dx

0.35

0.3

0.25

g 0.2a>

335I 0.15 33"O

0.1

0.05

0

Residual flow circulating in a flood- and ebb Z2864channel system and the role o f the channel depth.

ok to b e r2000

W L I D E L F T H Y D R A U L I C S F ig .:Î . I 0

31 2.50.5

h2/h1

h2/h1= 1.2 h2/h1= 1.4 h2/h1= 1.6

h2/h1= 1.8 h2/h1= 2

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