The M.Sc. Thesis: Cross-sectional Stability of a Two-inlet Bay System

Cross-sectional Stability of a Two Inlet Bay System

C.S Borsje

March 2003

Delft University of Technology Section of Hydraulic Engineering

Two Inlet Bay System

Master Thesis

his Borsle

Profi MAF Siue (Tu Dela)Drlr A van Mazik (Tu Den)Ie HJ Verhagen (Tu Der)

Profit v-van de Kreeke (University of Mam)

TU Delt, Facul of Cul Engineering and Geosciences, Section of Hydrauic Engineering Det, March 2005

‘This master thesis deals witha study on cross-sectional stably of estuaries with wo inlets This hao

been caried out within the framework of the Faculty of Cill Engineering at Daft Unversity of

‘Special thanks go to the examination committee, for heir supervision during my work: prot Site, lr

Verhagen, dr van Mazik and prot van de Kreeke for heir devotion and much valuable Information

{and assistance, Also, | would Ike to thank i Tghiem Tien Lam for helping me out with his report his Borsje

‘Tidal inlets are connections between smal, shallow bays and the sea In a tde-dominates

environment, the status c ths inlet isa balance between local given condtions such ag channel ‘geometry and the hydraulic environment According to Escoffet, when the equilorium is disrupted Ít Should generally retur to is orginal state

In tidal lagoon systems with more ines, t's more uncertain to predict a stable canston foreach inlet

‘There are cases where some channels wil close and others stay open, while other systems remain

overall stable, Le each inlet has an equllum state, An analytical method to determine this tabi I Yet no avaliable Therefore, the focus attends to researeh a model bay system with two ocean inlets, were there could be an unconditional stale environment For this, th fllowing important

‘assumptions and starting angles are set up

+ Thewalerlewelinthe bay area moves uniformly:

+ Vardalone in ocean tide and phase levels may give new insights

+ A hirởinlet imaginary or real, wih esuting small wate level differences inthe bay, s added,

For his case, a double inlet lagoon system is modelled ths consists ofa bay area with no significant

shape, two channels wit relevant ficton and inertia parameters and an idealized ocean tde wath a

tial range and phase at each niet troat Further, a variaton of tis done by (vifualy) spliting up

the bay On each model a series of tats has been done wih calculation and graphic sofware, Every

inlet has an equllorum flow curve, ie a ctass-sectonal area where the maximum curents ate just

enough to fush sediment and Keeping the channel open If this is the case fr both cross-sections, the

hole lagoon system i refered to a8 stable (E-type flow condition) In the graphic images, tis is

‘Shown by the inlersections ofthe equilbrum flow curves,

‘The normal medel bay system showed that thera is ø stable condton when the túa range atthe

seaside s diferent at each inlet provided tha his isnot oo large In adaton, the channels should be

Suffcienlly short with icon not lo high This is also vald fr higher tidal ranges, where the

iferences are even smaller

‘The bay system withthe parifon had the same stablty conditions Higher ie levels at both inlets

could also ensure stability, a9 the thd niet becomes relatively smal Next, the E-ype flow condtton Is

‘more key if the thi inlet is smaller or longer Further, the rato in bay area on either sie ofthe

partiton channel has some negative influence on tis, but in combination with tie đfferenee, a

Balanced system can remain.

“The models are futher implemented on a present-day situation, a lagoon inlet system located inthe

Huệ province In Vietnam Here, there are two inlets, located far apar, eting the system be relatively

stable In his patcular case, repeated flooding and breaching of the sand barrer resulted into

‘another init next tothe main inet inthe northern part of he lagoon, The appearance ofthis tied

‘channel has raised the question whether the two close inlats could be stable, although the authoriies

would rather have tis channel closed The pattion made! indicated that his can be the case.

Although the lagoon is also largely influenced by wave acton, frequent storm surges and river runo,

the tidal inlet models 9 useful ool in order fo understand the basie behaviour ofthis lagoon beter should be understood thatthe models that were used could never fly represent real hydraulic

environments, as there are aways other influencing factors present For tde-dominated estuaries,

they can however be a valuable stating point Nevertheless, the resulls show by both models are

salstactory A deeper investigation could be made on pars of this subject.

22 One- het bay system 3

2.3 Twain bay system 4

24 Goalofthssudy 8

CHAPTER3 MODEL FOR CROSS-SECTIONAL STABILITY

3.4 Principles of stably analysis 9

32. Classification of equilrium flow curves „

331 Two inlet bay system hệ

332 Two inlet bay system with partion 18

vụ

42 Onesiniet bay system 1943 Twosnlet bay system 2

444 Twornlet bay system with partion, 23

45 Veriication ofthe solutons 24

CHAPTERS CALCULATIONS

54 Introduction 7

5.2. Reference situations a

52.1 Two inlet bay syst 27

522 Two inlet bay system with partion 28

823 Discussion 2

S3 Symmetical ocean tide conditions lo both inlets 30

53.1 "Variations with one parameter 20

53.2 Variations with two parameters, 31

55. Phase ferences inside the bay, 40

‘551 Variations with one parameter 40

55.2 Variations wth two parameters, 48

8.3.1 Simulation excluding the Hoa Duan inet 54

83.2 Simulaton exclusing the Thuan An inlet sẽ

633 Simulations excluding the Tu Hien inet sĩ

CHAPTER7 CONCLUSIONS AND RECOMMENDATIONS

vụ

APPENDIXG CALCULATIONS ON THE Two INLET BAY SYSTEM.

CÓ Reference situation 10

€2 Variations in tidal wave "

C21 Tidal Period "

622, Tidal amplitude 2

623 Short lengths combined with tal amplitude 18

C24 Tidal amplitude dierence 14

C25 Shor lengins combined with an amplitude diference 16

C26 Tide mbalance at higher dal anges 6

D21 Shor lengths combined with ampltude dference 28

D25 Stability condiuonslorinefeasing taldifeence 29

126 Stability conaitons for increasing Soa diference (big parton) 30

27 Shor inets %

Ø3 _ Vaisiens with pariton inet 2

D31 Large cross-sectional area 32

D32 Larger cross-sectional area 33

03.3 Small cross-sectional area 4

D34 Longlenath 38

D35 - Sealiiyofparilon inet 3

D4 Variations with bay ratio 4t

Dat Bay Ratio 4t

D42 Bay Ratio with smal partion inlets +“

D43 Bay Ratio with tdal ampltude difference 49

APPENDIXE — INLET AND BAY PARAMETERS OF THE TAM GIANG - CAU HAI LAGOON, VietNam

F2 Thuan An nit closed, with partion 61F4 TuHienhletoosed 64

F.4, Tubien inlet closed wit patton 6

(Closure curve ofa stable ta inet 4

Closure surface of init 1 potted against init 2 5

Equlirium flow curve of niet 1, potted against inet 2 5

Closure surface of Inlet 2 potted against net 1 6

Equilorium fow curve of niet 2, potted against inet 1 6

Possible configurations of equliolum flow areas 7

(Cross-sectional area ~ Tidal Prism Relationship for nets in the USA 1m

Type A fow cure H

‘Type 8 flow curve 2

Type C flow curve 3

Type D flow curve 8

Examples of instability in type D „

Type E flow curve 6

Examples of stayin Type E 1

Two = niet bay system 7

Two inlet bay system with partion 18

Triangular cross section 20

Closure scenario, 20

Top view of Matagorda Bay, In the cenre below is Pass Cavallo; aie to the north,

splting the barr, is Matagorda Inlet 24

EEquilorum flow curves for Pass Cavalo and Matagorda Inet (van de Kreeke 1980) 25

Equilorium flow curves for Pass Cavalo and Matagorda inlet, calculated by the wo

inlet bay system model 26

Equitorlum flow curve forthe two nit bay system 28

Equlorium flow curve or the two init ba system with te partion 29

(Changes inthe equim fow curves around lọ, = 0.59 m, %

Equllrium fow curves at higher tide diferences 35

Closure surfaces of Inlats 1 and 2 at increasing de diferences, 36

Equlorium flow curves at increasing phase differences 38

ype flow curve as a result of tae aference 40

ctype flow curve, caused by a smaler partion init ái

Limit E-type condition aLA3 = 2000 m2 and a main tide of 0.50 m 4

Limit E-type condition at A3 = 6500 m2 and a man de of 1 00 m 48

Limit E-type condition at AS = 10400 mỡ and a main ide of 1.50 m 4ã

Limit E-type condition at A3 = 14000 m2 and a main te of2 00 m 4

Limit E-type condition at AS = 18500 mỡ and a main tde of 2 60m 4

‘Water evel amplitude differences inside the bay ata bay ratio of 1 (a), 2 (0) and 10 (2)

Phase level differences inside the bay at abay rao of 1 (a), 2 (b) and 10 (6) -47

Equitorium flow cura at ho) = 0.56 m 48

‘Map of the Tam Giang ~ Cau Hal lagoon system 51

(Overview of lagoon areas and inlets with cross-sectional profs s

Model of the lagoon system 53

3D image of the closure cuve of Thuan An inlet (ross section A), ploted against Tu

Hien init (cross section A) 54

3D image of the closure curve of Tu Hien inlet (cross section A), plotted against Thuan

‘An inlet (cross section A) sẻ

EEquilorium flow curves for Thuan An inlet and Tu Hien inlet, at Ao = 0.18: ra 88

xị

Figure 6.10, Cloture surfaces for Thuan An inlet (ef) and Hoa Duan iit (ght) 58

Figure D.1 Flow curves for amplitudes at inlet 1 of 6,60 m (green, 0.58 m (ole), 0.56 m (ed) and0.59 m (magenta) 29Figure 2, Flow curves for amplitudes at Inlet 1 of 0 50 m (green), 053m (bue) 0.56 m (ed) ana

0.59 m (magenta) 30 Figure 0.3, Equlbum Row curves for AlAs valves of 0 1 (red), 1 (green) and 10 (blue) a1

Figure 0.4 Equilibrium flow curves for bay area ratios of 0.10 (a), 1 (b) and 10 () 43

Figure D5 Equilbium flow curves for bay area ratios of 0 10 (a), 1 (0) and 10) 50

Figure D6 Equllbvum flow curves for bay area ratios of 0.10 (2), 1 (b) and 10 () sỉ

Figure D7 Equilbum flow curves for bay area ratios of 0 103) 1 (0) and 10 (e) 52

Figure E.1 Map of te lagoon system wih dept profes 56

Figure F 1 Simulation wth @: = 18x rad sẽFigure E2 Simuabonwihi@,=00 5sFigure E3 Simulalonwiho, 60Figure F.4 — Simulaton with @: 61Figure FS Simulabon with gs s2Figure E6 Simulalonwiho, 63Figure F 7 Simulaton with 9: 64Figure E8 Simulabon with gs 85Figure E8 Simulalonviho, g6Figure F 10 Simulaton with @: 67Figure F 11 Simulabon with gs 88Figure F.12 Simulation wth @,=-002: rad 68

xi

‘Summary of simuiation results wih symmetical de condiiona

(Observed variations ine, mit flow areas and fow types,

type conditions at diferent ide evel.

Instabity at higher phase ferences

‘Summary of simulaton reeute,

‘Summaton of fow types at aferen pation cross sectons on a tde of 0.50 m.

‘Summaton of fow types a diferent partion cross sectons on a tde of 1.00 m.

‘Summaton offow types at diferent patton cross sectons on a tde of 1.60 m

Ratio between tidal ampitudes and parilen cross-sectons,

‘Summary of flow types at different simulations.

EEquilorum cross-sectional values for diferent tidal amplitudes at init.

Equilrium cross-sectional values for diferent dal amplitudes at inlet 1.

Equiltrium cos>-seclonal values for different bay area ratios

Equllorium cross-sectional values for different bay area ratios,

Equiirlum erose-sactonal values for different bay area ratios

Equilorium cross-sectional values for different bay area ratios

Equilrlum rose seclonal values for different bay area ratios,

Equllorum cross-sectional values for different bay area ratios

Equilrlum cos>-seclonal values for different bay area ratios

Equllorium cross-sectional values for different bay area ratios

‘Average inlet characteristic ofthe Tam Giang-Cau Hal lagoon system (Lam, 2002)Inet parameters of the Tam Giang-Cau Hai lagoon system

Chapter 1 Introduction

‘Over the years, alot of study has been done on coastal inlets and tal basins Estuaries or lagoons,

connected by the outer ocean by one or more chanel, re generally subjected o s varous dynamic

forces such as tides, wind waves, storm surges and rverrunot Next long-shofe and eross-shore

currents continuously influence the state of his coastal environment by the tediment balance Inthe

tase of strong long shore transpor, the accretion of barrier spits and sand bar migration results into

changing postions cf tese inlets As fara locaton is concerned, these systems are unstable Other

inlets remain in relative positon because of equllonum in sediment bypassing, and have a more or

lose balanced cross section After a disruption of this eauilvlum, some ofthese estuaries can restore

to hef onginal stuaton over a course of me, while others require constant attention to avord

intolerable damage There can be 2 number of reasons forthe naed to have stable tidal areas: safety

forthe hinterand, navigational demands for shipping through inlets, environmental and economical

‘epecte are examples ofthis

In estuaries wth more inlets in some cases an overall stable environment can exist Previous studies

were undertaken fo explain hs condition analytical Wh the approximations that were made, 2

workable solution to inieate this has net yet Been found.

This study wil put further research inthis problem by widening the approach The scope wil be on a

tide-dominated bay system, with two ocean inlets

Inthe folowing chapter, a problem analysis is gven, witha status ofthe stuation as its right now.

CChapter 3 sets some boundaries and staring points on this project Next possible diferent

Configurations are defined folowed by to main models that willbe used In Chapter 4 he

hydrodynamics ofthe tidal inet systems modelled lo a series of systems of differential equations,

‘These i folowed by analytical solutions and fnaly verified The next chapter deals wih simulations

com both modes These are run ina caleviation program and further graphically explaineo with

MATLAB From this, some conclusions với be drawn, In Chapter 6, the two basin models are used to

find an explanation on the stably ofa lagoon system in Vietnam that is frequently exposed to

|yphoons and floods It hus might serve as a bass fo understand this coastal area better

Final, some conclusions are drawn, followed by a few recommendations for further study.

2.1 Introduction

Tidal inlets are connections between a bay or shallow water environment andthe ocean Each tal

period, water enters and leaves the bay During food, sediment is carried into the inlet The ebb

utren flushes this sediment out again In the inlet channel, large ebb and flood veleclLes can aceur

{due fo water level cferences on each side of the channel This results ín 8 maximum value of Bottom

shear stess through the channel

ree pe @

\When dealing with inlet stabilty, a main cisincton can be made between location stability and

cross-sectional stably The ioral material ransported toa tal let can cause constriction ofthe niet.

throat The decrease in cross-sectonal area wll result n greater scouring capacties, which wil cause

efoslonof the downdrit beaches: the inlet tends to migrate, depending onthe rate of sediment supply,

‘wave energy and tial currents A severe storm can open a new inlet, which makes the old one

‘obsolete, and repeats the process of downdht migration Ths isan example ofan unstable inlet as far

9 location in combination wih ross secton is concerned,

Tidal inlets with a stable throat position have @ nor-migrating ebb channel, Sand bypassing a these

inlets occur trough the fotmaton of bars which migrate and attach to the downait coast New bars

wil constantly develop dus to a more of less continuous sand delvery by the ebb tdal channel Thus,

sediment bypassing in ths case depends on sand deliveries through the channel system.

Subsequently, a stable cross secton is largely the result of large ebb currents, which ae capable of

carrying enough sediment outof the inet

From here on, the location of an nit considered stable; the focus wil leon cross-sectional stably 2.2 One - inlet bay system

‘Stabity or more precisely the cross sectional stability, deals with the equllrlum between the init’

cross-seclonal area and net hydrodynamics The pertinent parameters are the actual dal maximum

ofthe bottom shear stess + andthe equilrium shear stess ray, The equiibrium shear tress is

Gefined as the bottom shear stress induced by the tidal current thats required to lush the sediments

tarred into the inlet bythe long shore currents, The corresponding tidal maximum inthe vertically

‘averaged veloc isthe equilbrium velocity Among other things, the value of the equiixium shear

‘ress sa function of the itora dt the larger te itral ait, the lager the equilibrium shear stress,

coffer (1840) showed thal when the actual curent velocity equa the eauilodum velocty the inet|S in equilbsium with the hydraulle envionment When the actual shear sess is larger than theeaullorum shear stress, the inet isin scouring mode; when the actual shear stress is smaller than the

‘equiliium shear stress, the inlets in shoaling mode This relatonship is shown in figure 2.1

=5 =¬ A

Figure 2.1 Closure curve ofa stable til inlet

Here, the curve represents the inlets current velocity as a function ofits cross-sectional area A An

inlets efered to as stabie when the closure curve has two points of intersection withthe equilibrium

Velecfy curve The fst intersecion (SP) isan unstable equlpnum: If Ac is located lf of this poi,

the maximum currents to small to fush sediment trough the channel, soit wil eventual close

When Ais located right of SP, the maamum veloc wil increase, the inlet wil scour unt treache,

the stabe intersection point SP, If A is lager than SP,, the tidal currents are too small Then the inlet

wil gradually shoal unl SP; is reached The equllbrum is therefore caled stable if after a small

change, for example a severe storm, when the value of Ais moved, the ilet's cross section returns to

is orginal equllerum value

\When the closure curv ies entirely below the equirium veloc there are no intersections, and

therefore no eqUllblum cross-sectional areas The inet wil lose

2.3 Two inlet bay system

Fort inlets connected tothe same bay, iis iferesting to study the closure cuve of one inkt in

comparison tothe other When the cross section of inlet 2 (A,) is, Inlet t will show a closure curve as

Shown in igure 2.1 increases, more flow transported through inlet 2, so the maximum

veloctes in Inet 1 will decrease, causing the closute curve to len out more and more Eventually,

there willbe a value of A, where Inlet 7 cannet reach ts equiirlum velocity making ikely to close,

This process i illustrated in igure 2.2 Ay ison the -axs, A, on the y-axis and ô, (the maximum

currentin Inlet 1) on the 2-25 For every value ofA; 3 closure cuve for A, can be drawn Together

they form the elosure surface for dy (Âu A)

‘The physically interesting pat of each closure cuve isthe stabilly interval, stating at SP Further, to

‘obtain a possiba stable cross section foreach nat, the maximum current should be larger than the

'equllĐrum current In Figure 1, this isthe interval of 9, = 9, For increasing values of A,, this

Interval wil narow Its therefore convenient to portray this interval for al value of Inlet 1 where 0 =

ạ, This shown in Figure 2.3 In other words, this sa cantour pt fom figure 2 2øf all combinations

(ofA, and Ay where; = ny projected i the (8, A) plane, This curves further referred lo as the

equilorum fow curve The thick part ofthe curve i the stable section this Uns fom (Amn Am) 8

‘The same procedure can be cari out for Inlet 2 Again, the influence of larger crass section of Inlet

† can be observed in smaller closure curvas of lat 2 se figure 2.4 Only now, the maximum

currents of niet 2 (0) are potted on he 2-28 Next, he stabity Interval SP, ~ SP, can be led in

the (A, A) plane (igure 25)

‘The curves in figures 2.9 and 2 6 can be potted together, showing thi relaive poston inthe (As, A)

plane Examples ofthe general shape ofthese equilibrium fow curves are presented in Figure 26.

Figure 26a suggests the exstence of two equilbrim flow areas, noted by the two intersectionsFigure 260 imples the existence of fur sets of values for which both inlets have cross-sectional

ateas that are in equlorum wit the hydraulic environment The enhanced pars ofthe equlibrium

‘low curves in figure 26 represent stable equim flow areas For example, when assuming the

‘cross-sectional area for niet 1 to remain constant the intersection of A, = constant and the enhances

part of the equilerium flow curve fr Inlet 2 corresponds to he stable equilorium cross-sectional area

for Inlet 2 The intersecton of Ay = constant and he part ofthe equibrium flow curve tat not

enhanced, coresponds fo the unstable equilrium cross-sectional area for Inlet 2.

`Van de Kreeke (1990) stated that fora simultaneous existence of stable equilrum flaw areas fr two

inlets, the enhanced parts of the two equilbxium flow curves should intersect Furthermore, applying

the goneral principle ofthe stably hypothesis that inlets shoal when 0 = Oa, and scour when 0> 0x,ItTolws that only the configuration of the equilibrium fow curves in Figure 2.6b allows a set ofUnconditional stable rose sections In this casa, the stablity intervals the cross-hatched afea, Le,

after a storm (Ay, A) remains in this cross-hatched region the inet cross-sections wil return to thelr

Stable equilbvium values

a a

Figure 2.6 Possible configurations of aquirium flow areas.

‘Several sues have been done with Escofierstheory onthe stability of one-inlt bay ystems An

extension lo multiple (N) inlets is presented in van de Kreeke (1990) When taking N= 2, a set of two

‘qulliorum fow areas are found, See gute 2 Ga As stated before, in that case fortwo unconditionally

‘table equllvium flow areas to exist, the enhanced pats ofthe equilbsur flow curves have toInlersect Le the configuration of the equlibrum fow curves has to be as indicated in igure 2.6 b.However, inthe same publication wae concluded that such a contguraton can net exist In amving

at this conclusion, use was made ofa simpfhed lumped parameter model to calculate the closure

Surfaces inthis model, a linearized fiebon was Used and local inertia was neglected Furthermore, the

bay level was assumed to fuctuate uniformly and the same simple harmonic de was used for both

inlets

2.4 Goal of this study

‘This study deals withthe cross-sectional stabilty of wo inlet bay system

In view of the foregoing the folowing goals forthe study are defined

+ Toinvestigate the dependence ofthe equim flow curves on inlet, bay and ocean tide

+ Todetermine whether diferent ocean tides at each inlet can lead to a set of two tuncondlonaly stable inlets

+ Todetermine whether a non-unformly fluctuating bay level can lea toa set of twotuncondiionaly stable ints

In audio, the method descrive in section 2.3 wil be applied to the Tam Giang ~ Cau Hai lagoon in

Vietnam to determine the equilrium flow areas and stably of the inet, Ths Isa multiple inlet,

system connected by two and sometimes thre inlets to the Gulf of Tonkin

Chapter 3 Model for cross-sectional stability

Predicting the adjustment of the inlet morphology after for instance, a storm event and, in gariculs,wether ane ofboth inlets wil cose o wil remain open requires a detaled knowledge ofthe

Sedimentary processes inthe vicity ofthe it These processes are governed by complex

Interactions of tial currents, waves and sediment In spite of recent advances in the description ofthe

flow Feld near the inet and understanding of sediment transport by waves and currents, stil not

possible to accurately predict the adjustment of inlets Unt sufcant detaled knowledge ofthese processes becomes avaiable recourse has tobe taken into a more pragmatic approach refered to 45

stabil analysis, already discussed in Chapter. 3.1 Principles of stability analysis

According to Escolfef (1840), isthe literal deft hat attempts to close the inlet and the ebb tidal

Current that keeps it open ARer entering the inlet region, part of the tora dit is carried ito the inlet

channel and pat oft continues it pat via the ebb tidal deta tothe down drift sie of the inlet The

‘and thats carried ino the inlet channels) is ansported ina landward irection by the food currents

and is eposled at high water slack For nets tha are in equlibrum the sand that fs deposited inthe

inlet channel is carned seaward by the ebb tidal currents

Restricting attention to a set of inlets that have similar hydrodynamic and morphological characteristics

‘and for which te Iitoral drifts the same, itseems reasonable lo assume thal fr those net the

fraction ofthe ioral drt carried ino the inlet channels clase tothe same, Furthermore, fill be

assumed tat in etuming these sediment đeposls, the transport capaci ofthe ebb currents is

proportional some pawer ofthe amplitude of the dal current 0 Therefore, when assuming the ints

to be in equllvium withthe hydrodynamic envizonment, the amplitudes ofthe tidal curenk the inlet

channels should be the same for those inlets As mentioned before, this veloc is referred to à the equilibrium velocty du The equllvlum velocity can be related to Tal prism P The tidal prism equals the ebb oF flood tidal discharge integrated over half a tidal cycle

Ïopa=ð [ãneoar

Inwhich _@= ebb o food tal discharge

(02 angular equency ofthe tie

P )

inwhien se= đi7 )

Conversely, the valve of 0, for that set of inlets can be determined when the value ofc known form

(Brien (1993, 1969) orginally determined a similar relationship between minimum throat

cross-sectional area of an inlet below mean tie level an the tidal prism The abave relation implies that a

larger tidal prism means a larger cross-sectional area As an example, fonts in the U.S.A the

relationship between cross-secional area and tidal prism is presented in Figure 3 1

eT: mou eames se

Figure 31 Cross-seclonal area ~ Tidal Prism Relationship for ints inthe U.S.A,

‘A small ioral eri will resultin relatively small equiibtium velocity of about 0.8 ms, whereas a large

litora deft can cause values of 1.2 to 1.3 ms Correspondingly, on aluual coass, equlibcum values lof shear stress are roughly Between 35 and 5.5 Nim’ (Bruun, 1978) This is afar narrow range

From here on, an equlbsum flow velocity value of 1.0 mfs wil be used to determine equilibrium fow

10

3.2 Classification of equilibrium flow curves.

In section 22, iwas already pointed out that cross-sectional stability can be ilustrated by poting the

two equilibrium flow curves inthe (As A.) plane Depending on input parameters and local conditions,

this plt can have a set of equilbrum fow areas for nits and 2 The two equim flow curves,

can have vaPous configurations, but a general cassifiation can be made, in order to establish a

Detter understanding af @ possible stably condition As described in the next paragraphs, five

aitferent configurations ae distinguished 3.24 Type A

‘The Type A flow curve has a shape, shown in figure 3 2 This plot has no stable intersections, Le at

‘any paint where Inlet 1 is within the stable domain, Inlet 2's unstable and vee versa The enhanced part at each flow curve represents the stable domain ofeach nit

Figure 3.2 Type A Now curve

‘The explanation of the small eters inthe figure i 9s followed:

' | Both nits are nthe unslable area and wil shoal and cose,

| Inlet Ts in the stable domain and wal scour unit reaches t equilbsum value at‘A= Inet 2 với close

| Oniy one inlet stays open, whe the ater closes This depends on the current value of (Ay, A)

in the pane For mstance, i his i located at the black dot Inlet 1s too large and Inet 21 ao

‘small When Ay taken constant Inlet 1 wil shoal unl itreaches its stable section From here

fon condition b applies

@ [Inlet 2 sn the stable domain and wil scour uni reaches 1S equilbsum value at

A 6, Inet t wil close

4

3.22 TypeB

‘The Type B flow cuve is shown in igure 3.3 This plot has two equllbrum flow areas However, these points are not atthe stable branches of the equilbrium fow curves The condition within the overap is thus set atc, so one inet stays open The remainder of the figure isthe same as figure 3.2

Figure 3.3 TypeBilowcuve 323 Typec

‘The Type C flow curve is shown in gure 34 This plot has two equliium flow areas, where one point lies onthe stable branch of the equilorium flow curve of nit 2 Stil this does not give stability, ae the lable part of Inlet has no intersecton Again, the overtap& a e-condtion, although In ths particular picture probably Init 2 stays open Finally, considering the shape ofthe figure, itis very like that Int 1 remains the sole inlet, because its stably interval fs much broader than Inet 2

12

Figure 3.4 Type flow curve 3.24 TypeD

“The type D flow curve is shown in figure 3.8 There are two equlibrum flow areas, bu contrary to type ‘A,B and C, one ofthese flow areas bes on the stable part of bath nlet 1 and 2 Nevertheless, tis ‘ably condition s condilonal turns out that when after a storm evento such, the flow areas Geviat fom the equirum position, hey do not necessarily retum to that postDon, This s explained in figure 36.

Figure 3.5 Type D flow curve

Consider a severe storm, after which the cross-sectional areas of Inlet and 2 have increased, and the cross-seciongl areas are at pont A The folowing will occur

+1

‘Both channe's are outside their equilbrium flow curve, For Inlet 2 to retun, assume A;

constant Inlet 2 il shoal

Now niet 2 isn equlibdum wth the hydraulic envionment, while Inet 1's not Consider A:

Constant, inlet | should now scour to ls equilonum value

Inthe new point, the cross-sectional area of Inlet 2s too irge, so it should shoal (Ay =

‘The result of tis wil be that Inet 1 stays open atts equllorium value s

‘Silay, ater the storm the cross-sectional areas can be in point 8 The same procedure yields

‘Both cross-sectional areas are inside thelr equlbum flow curve For Inlet 2 to return, assume

‘Av constant Inlet 2 wil gradual scour.

Now Init 2 is in equilrium with the hydraulic envionment, while Inlet 1 isnot Consider Ay

constant inlet 1 should now shaal os equlium valve.

Inthe new point, the cross-sectional area of Inlet 2s foo smal, so should scour (A,

3.28 TypeE

‘This configuration is unconditionally stable: when the cross-sectional areas le inthe hatched pat of the (As, Aa) plane (area e), the two inlets wil gradually return tothe stable equlltrium poston Indicated by the black dot (igure 3.7) Inet 1 a8 well s niet 2 now stays open This is ustated in

‘igure 37 The other intersections are unstable equilsium fw areas The stably condition s further

explained with gure 3.8 on he next page

Figure 3.7 Type Now curve.

+6

Consider again the poston of te inlets at point A The following steps are taken

‘Both cross-sectional areas are outside ther equilibrium fow curve Fr inlet 2 to return, take

‘Ay constant Inlet 2 wil shoal

[Now init 2 s In equilrium withthe hydraulic environment, while Inlet 1 isnot Consider A;

‘constant Inle wil shoal tts equilibrium value

Inthe new point, the cross-sectional area of Inlet 2s too small so should scour (Ay =

‘The result of tis wil be that both inlets gradually move towards the stable equllrium position

(black dot

‘Similarly, the fw area can be in point 8 The same procedure yields

ot cone eoioral areas te tước egos how crv, Fort 21 ret ke Ay

conv t2 wil goal soa

Now int Bìm equine wife hyớnufc enviroment i i 1s not Cone A

constant’ shoud row eo ta equ rae

intve nv pont he cursor aren (t2 oợiage so shoul shoal (A,coma

‘ren fis wilbe ht aan, both 1111111111111. 42

Figure 3.8 Examples of stabilty in Type E

Note: these processes can only occur when the curent set of cross sectional areas le IN the stable

‘domain, marked by the enhanced ines,

16

3.3 Inlet-bay schematization

To attain the frst three goals ofthis study, two schematizations ofthe tuo-nlet bay system are used

‘one mode! wth ang the other without a partion In te bay The partion has an opening that allows

ater to fow between the two bay compartments The purpose ofthe patton isto remove the

Condition of a uniformly fluctuating bay level 3.3.4 Two inlet bay system The bay

Reterting to gure 39, the bay is connected tothe sea by two channels The bay is considered small and deep As a resUl, volume changes of the bay only cause uniform vertical water level variations

(to) The entre bay area is expected to react uniformly, even ifthe rat inlet has water flowing into thebay and the other inlet outa the bay.

The inlets

Each nets characterized by length, with, depth, hydraulic radius and fiction coefficient (bd R

-ang ) In the present application the inlets are assumed to be triangular After a change, the cross-Sections remain geometcaly similar

The ocean tide

‘The ocean tide forces water in and out ofthe bay A sem-diunal ide Is assumed, but one can also Use one dal period a day Ampliudes and phases ofthe ocean tide canbe atferent for the two nets ‘Suppose that he dal wave arives ft at Inlet 1, thee wil be a phase ference between the inlets

Ifthe tae is represented by a simple smusoidal equation, tis wil result inthe folowing

a(0)= hu c0s(o-1 +9) © Inet ocean Inet 2

hel) nal

Figure 2.9 Two inlet bay systom.

Note:The value of y and is supposed tobe very small If for instance a tidal wave travels along the

‘coast through water deptns of about 10 m, ithas a propagation velocity of roughly c= gd = 10 mis I the inlets are 12 km apart the wave arrives after 1200'seconds at the 2” inlet (ne tid ofan Hout).

Fora semi-durnaltde, this means a phase difference tự - of roughly 3607"(1/3/T2= 10 is not

likely thatthe two inlets ae completely out of phase (eg 6 M9)

+

3.8.2, Two inlet bay system with partition

Relerence is made to igure 3 10 Except forthe pation opening, this models the same as the

previous one described in 3 3 1 The pation can be classified in diferent forms: ítcan ether ave

Similar charactersies as the main inlets witha finte crose-secbanal value or can be seen a a very

wide separation, as wide as the bay sel In tis way, the influence of phase differences inthe basin

can be examined

Inlet 1 Ocean Inet 2

igure 3.10 Two inlet bay system with parton

16

Chapter 4 _ Inlet hydrodynamics 4.1 Introdu

In this chapter, a deserition ofthe model schematzation ofthe bay system i given together wit the

‘mast important equations.

A brief outline is given ofthe hydrodynamies of a one — inlet bay system, folowed by the

‘schematization and equations for the two-ilet bay system and the two-inlet bay system with the partiton The model forthe tưo.nletbay system 1s validated using information on Matagorda Bay in Texas, USA

4.2 One-inlet bay system

‘Assume thatthe water level inside the bay fluctuates uniformly, the folowing balance equation holds

o- 4,7 ø were Q =the channel discharge: flood is postive

‘Ac the bay's surface area,

Fora single bay, connected to the ocean by a channel, the equation of motion is

# H3

In which m = summation term of entrance and ext losses

Hygraulicraaus ofthe channel cross-secton,

bed ticlon factor

From equation (3) ifolows that Is dependent on the nits hydraule radius When the cross

Sectional area changes, so does R Subsequentely, R can be defined asa functon of A Therefore,

the inlet cross section is heve schematsed to a tnangle the depth is zero al the shore and inearly

inereases fo a maximum depth inthe middle ofthe cross section, This model s preferable to a

fectangular cross section, because is more realistic, An mage ofthe cross section f given in gure

+6

Figure 4.1 Triangular cross section,

Here itis assumed that when A changes, both the width B and depth ở change at an equal ate In

this way, the inlet always becomes wider and deeper, or smaler and shallower the ross section is geometrically the same ITA gets smaller and smale: and ở wil simultaneously decrease to Utimately clase the Inlet (ee figure 42).

Figure 42 Closure sconaro

with a=} Jsinarcosar đi

\When the slope angle is known, for each value of A the valve offR can be calculated

To facia the leugtons n equation (2) te ficlon tems ineanze, Assuming Qt be a smple

Ramone unelon oft

00 0ò °

20

Making use of equation (8), equation (2) can be written as

+WØ=h, ~

where 1 the tnearleed fron term,

‘Substituting equation (3) n equation (1), the folouing wellknown relaton between bay and ocean is

This deserbes a Inear system, e.g, the damped spring-mass system, where xis @ damping factor and

(MU) related tothe system's natural frequency:

Given A, to and fi, the velocty amplitude can be calculated a8 a function ofA fram equation (18)

This resus in the closure curve presented in igure 2.4

a

4.3 Two-inlet bay system

‘The bay is connected by two inlets wih the cozan Assuming a uniformly fluctuating bay level

continuly yields:

0,0) +0,()= 4, "6

06)+0/0=4 5 (6) where Q, = the discharge through the frelinle

, =the discarge through the second ke,

the bay surface area

the bay's water level ‘The equation of each inlet channels

anh, (8)

ana 2:

2, ‘=, a friction factor for’eA

ang Af, = 2, an neta term for and2

‘The ampltude of is yet unknown and has to be estimated frst.

‘The solution of the system of three equations (16), (17) and( 18) wth three unknown parameters Q, ,, and h le resented in Appendix A From Appendix A becomes clear that iteration Is necessary in order obtain these parameters To start the calculation, the primary values of Q, and Q; have to be postive (eg >0), Itdoes not mater how high these values have to be taken This can be

itusrated by the moton equations (17) and (18) The afference in water level between ocean and bay 's pally caused by the ricton term Even I the factor Wis low as a result of ow chosen input

Values of Q, and Q,, i already produces bay water levels lower than outside During the folowing

iteration step this number Is again adjusted toa smaller value Aer each sep, a new averaged set of

values is taken, and the process is repeated unt the calculation is stablized

For each simulation, total number of S0 x 50 points (ie 2500 combinations of low areas A, and A, wh the corresponding maximum currents 0, and 0;) are calculated, which can be plotted as a 3D

‘sure surface, shown in Chapter 2 and contour mages, as clsssfied in Chapter 3 Unless

‘mentioned diferent, these contour images are all drawn at an expected equlibrum flow velocity of 1.0

me 89 eater stated in Chapter 3

2

4.4 Two-inlet bay system with partition

Here the bay is divided in two paris, separated by a partion with an opening inthe form ofa channel

“The two bays have the folowing continuity equations

0,-2.0) = 4, ST = yh, (9)

2.) + 0.0) Ags (20)

winere Q, = the discharge through the stint,

= the iecharge through the second init,

{= the discharge through the inietn the parttin, flow is postive from bay 1 to bay 2,

‘Avi and A,z= the bays surface areas,

hy and hy = the bay's water levels, ‘The equations of mation ae:

+0, = hy he en

47,0, =hị =h, (2)

“4 -afdelon factor for i= 1,2 and 3

and M, = 2, an nei term for

“The ampltude of is yet unknown and has to be estimated frst

‘This system of fv equations with fve unknown parameters Q,, Qz, Qs hy and hz has @ general

solution, A complete algebrae calculation ofthis is ven in Appendix B In Appendix, ine values of

di, Q, and @) are presented Further, the same computational methods yield, as earlier shown in

section 4 3: posve staring values forthe discharges are Used, the new Values are averaged with the

‘ld ones, the caleulation i repeated unl ts stabilzed Again, a total of B0 x50 flow areas are

Computed to determine 3D closure surfaces and equllrium flow areas Also, both the main inlets and

the parition channel are modell wit trangular cross-sections.

Ey

4.5 Verification of the solutions

‘The general solutions ofthe bay systems, given in sections 4.3 and 44, form the basis ofthe futher

stably research It's important to see whether the solutons are actualy abd, Fortis, a comparison

Is made with stability calculations for a two inlet bay system in Texas (van de Kreeke, 1985) This tidal

system wil be inuoduced bret folowed by the resuts ofthe stably calculation of van de Kreeke

(18860) His resuts are compared with simulations obtained by applying the solon presented in

Section 43.

Pass Cavallo one a he inets ofthe barrier island chain off the southwest coast of Texas The inet

has ©ssled fr atleast 200 years, Unt 1963, kwas the sole inlet connecting the Gulf of Mesieo and Matagorda Bay (igure 4.3), arelatvely large and shallow bay with a surface area of 317 km and an ‘average depth of 3m.

Figure 4.3 Top viow of Matagorda Bay In the centre below is Pass Cavallo; lite fo the north, “plfing the barre, Is Matagorda init.

n 1953, a companion inlet, futher referred to as Matagorda let was dredged 5 km to the northeast

of Pass Cavallo, Matagorda Inlet serves as the entrance tothe Matagorda shipping channel After the

‘redging of Matagorda Inet, the cross-sectional area of Pass Cavallo has gradualy decreased

whereas, during the decades pro: to the dredging, the inlet confguralon remained relatively constant.

Van de Kreeke (1989) calculates the stably ofthe two inlets using a model similar to that presented

In section 43 The daa, used in tis study area are presented in Table 4.1 In this table, Wand VN,

fate the width of Both inlets and shovld not be mixed with the fịchon term Wi nthe previous secons,

Ey

| Parameter Value Parameter Value |

Table 4.1 Values of parameters used in Matagorda Bay.

`Van de Kreeke implemented both a rectangular and tiangular eoss-sectional schematisation ofthe

inlets na linearized luznpsé parameter model In this model the inertia term i left out A uniform bay

ater levels assumed The ocean tidal ampitude at each inlet is set at 0m Exit and entrance

losses are neglected under assumptions of mainly a ficton-dominated tow.

12000 —¬

Figure 4.4 Equilbrium fw curves for Pass Cavalo and Matagorda niet (van de Kreeke, 1990).

For the triangular cross-section, the resulting equibrum flow curves of Inlet (Pass Cavallo) and Inet 2 (Matagorda Bay) are presented in Figure 4.4 Iniet 1 has an equllorlum flow curve from 1500 m to

11000 mand Inlet 2 has an equilbrium Fow curve fom about0 m to 11500 m The configuration of

the equilstum flow curves Isa Type C The values ofthe equilibrium cross-sectional areas are (A, Ad] = (10800, 420)

Taal = (1400, 58)

\When the values ofthe cross-sectional areas (A, As] ae located in he cross-hatched area net 1

remains open and Inet 2 closes When located inthe diagonally-hatched area, Inlet 1 closes and Inlet

2 remanne open And wien located inthe white area, one Inst closes and one remains open; however

inthis case which one closes depends on the relative case of scouring and fr shoalng The black dot

in the fgure represents the situation of inlet 1 and 2 in 1870 From this pont Inlet 1 wil close and Inet 2 wil enlarge unt allan a value of 17500 m (onthe A,-axls)

Ey

Using the two inlet bay system madel from section 42, and the parameter values in Table 4,1, the

fequtvum fow curves for Pass Cavallo and Matagorda inlet are calEulated

The equilbrium flow curves are shown in fgure 4.5, As before, the configuration is a C-type There are

two equilbrum fw areas:

‘oad ooo MU 8000 THỤ TU THNU

Figure 4.5 Equilbrium fw curves for Pass Cavalo and Matagorda inet, caleuated by the vo

Inlet bay system model

‘The shape ofthe equilrium flow curves largely corresponds with these in figure 44 Also, the

coordinates ofthe equilbrum flow areas show close agreement According to present day conditions,

‘marked by the black dot Matagorda Inet val become the soe Inlet.

2