Hydro-morphological study Douro

ADMINISTRACAO DOS PORTOS DO DOURO E LEIXÓES

Hydro-morphological study

Douro Estuary

Part 1

Wave penetration calculations

november 1982 / P613

PORT AND WATERWAY ENGINEERS

hyÖRondmiG-TABLE OF CONTENTS

1. INTRODUCTION 1 2 . MATHEMATICAL BACKGROUND OF THE MODEL 3

3 . DETERMINATION OF INPUT-DATA 5

k, CALCULATIONS WITH THE OVERALL MODEL 8

5 . CALCULATIONS WITH THE DETAILED MODEL 9

6 . WAVE EXCEEDANCE DIAGRAMS 10

1. INTRODUCTION

The

Administracao dos Portos

do

Douro

e Leixoes is confronted with

the fact that

futu~e ~xp~"5ion

of

the po~t a~ea

of

Leixoes is

limited by the surrounding hills

and· urbanisation. One of the

al-ternatives for future expansion might be the creation of port

facil ities in the Douro estuary, where a relatively large, flat area

i

s Bva

i

1

ab 1 e.

Howev~r.

the river entrance is rather unstable from a morphological

point of view, so that regular dredging is required to maintain an

access channe 1 •

In

order to el iminate the risk of unexpected morphological changes

in the Douro estuary, due to harbour works in de Douro estuary, APDL

has decided

to study the morphology of the Douro bar thouroughly,

and to make a design for a mathematical model to investigate the

in-fl

uence of harbour works in the area.

This study has been offered to APDL by the Sociedade Portuguesa de

Dragagens in January 1982.

After receipt of the letter of

adjudica-tion from

APDL, dated July 29th, 1982,

Hydronamic bv was asked by

S. P. D •. to start the study.

The study is subdivided into six phases, viz:

a1. wave penetration calculation

a2. calculation of longshore tran!port

a3. calculation of the tidal prism

aA. s e d i m e n t t r a n s p o r t m e a s u r e m e n t s b m o r p h o l o g i c a l e v a l u a t i o n c s e t - u p o f t h e m a t h e m a t i c a l model As d e s c r i b e d in our p r o p o s a l o f J a n u a r y 1 9 8 2 , a r e p o r t f o r e a c h p h a s e w i l l be p r e s e n t e d to APDL. T h i s r e p o r t g i v e s t h e r e s u l t s o f phase a l , wave p e n e t r a t i o n c a i c u i a t i o n s . 2

2 . MATHEMATICAL BACKGROUND OF THE MODEL

The t r a n s f o r m a t i o n o f waves coming from t h e deep s e a and a p p r o a c h i n g t h e s h o r e depends on t h e l o c a l b a t h y m e t r y , t h e t y p e o f bottom and t h e t y p e o f w a v e s . The Hydronamic Wave P e n e t r a t i o n Model c o n s i s t s o f a nunber o f programs in o r d e r to c a l c u l a t e t h e s e t r a n s f o r m a t i o n s . The main p r o g r a n o f t h e model i s t h e program R E F D I F . The input f o r t h i s p r o g r a n i s t h e bottom topography o f t h e n e a r s h o r e a r e a and t h e wave c h a r a c t e r i s t i c s o f one component o f t h e wave c l i m a t e . The b o t -tom topography i s e n t e r e d a s a depth m a t r i x . The program i s run f o r e a c h component o f t h e wave c l i m a t e and c a l c u l a t e s a l o n g w a v e - r a y s tJie v a r i o u s w a v e - h e i g h t d e t e r m i n i n g p a r a m e t e r s .

T h e s e a r e p a r a m e t e r s f o r r e f r a c t i o n , s h o a l i n g , f r i c t i o n , p e r c o l a t i o n and b r e a k i n g . The r e s u l t s o f t h e s e c a l c u l a t i o n s a r e p r i n t e d out and s t o r e d on computer d i s c f o r f u r t h e r p r o c e s s i n g .

S e p e r a t e programs c a n p l o t t h e s e d a t a a s r a y - d i a g r a m s .

In o r d e r to t a c k l e t h e c a u s t i c problem two o p t i o n s a r e a v a i l a b l e , v i z . t h e method o f Bouws S B a t t j e s ( u n p u b l i s h e d m a n u s c r i p t , I 9 8 I ) or t h e method of a v e r a g i n g e n e r g y in e a c h s q u a r e . Bouws' S B a t t j e s , method i s v e r y a c c u r a t e , but r e q u i r e s much c o m p u t a t i o n a l e f f o r t making I t e x p e n s i v e . T h e r e f o r e t h e method of a v e r a g i n g e n e r g y in e a c h s q u a r e has been u s e d .

The r e s u l t o f t h i s o p e r a t i o n c a n be p l o t t e d as a w a v e - h e i g h t c h a r t .

The m a t h e m a t i c s o f r e f r a c t i o n a r e not d i s c u s s e d in t h i s r e p o r t . L N E C - p u b l i c a t i o n n o . 5 5 1 , Modelos m a t e m a t i c o s p a r a o e s t u d i o da propagacao e deformacao d a s ondas de g r a v i d a d e by J . M . Afonso C o v a s c a n be r e f e r r e d to f o r a v e r y d e t a i l e d d e s c u s s i o n o f t h i s s u b j e c t .

Bottom f r i c t i o n , p e r c o l a t i o n and w a v e b r e a k i n g a r e a d d i t i o n a l f e a -t u r e s o f -t h e Hydronamic Wave P e n e -t r a -t i o n model no-t d e s c r i b e d in L N E C - p u b l i c a t i o n 5 5 1 .

The d i s s i p a t i o n o f e n e r g y by bottom f r i c t i o n a n d / o r p e r c o l a t i o n c a n b r i n g about s i g n i f i c a n t l o s s o f wave e n e r g y w i t h a p o s s i b l e r e d u c -t i o n o f w a v e - h e i g h -t , p a r -t i c u l a r l y f o r h i g h waves o f long p e r i o d w h i c h a r e propagated i n t o a s h a l l o w r e g i o n o f v e r y g e n t l e bottom s l o p e . The r a p i d a t t e n u a t i o n o f e n e r g y by bottom f r i c t i o n f o r waves o f long p e r i o d can be e x p l a i n e d q u a l i t a t i v e l y a s due t o t h e f a c t t h a t t h e long waves e f f e c t i v e l y " f e e l " bottom sooner than t h e s h o r t p e r i o d waves and c o n s e q u e n t l y a r e s u b j e c t to f r i c t i o n a l d i s s i p a t i o n o v e r a g r e a t e r d i s t a n c e . In a complex wave g r o u p , t h i s s e l e c t i v e a t t e n u a t i o n c o u l d p r o d u c e , under c e r t a i n c o n d i t i o n s , a s h i f t in t h e peak o f t h e e n e r g y - s p e c t r u m t o w a r d s lower p e r i o d s a s t h e waves t r a v e l t o w a r d s s h o r e .

The method used in t h e Hydronamic Wave P e n e t r a t i o n Model i s t h e method d e s c r i b e d by B r e t s c h n e i d e r , ( t e c h n i c a l mano n o . ^5 o f t h e

Beach E r o s i o n B o a r d , 1 9 5 7 ) . a l t h o u g h some more r e c e n t c o e f f i c i e n t s f o r f r i c t i o n have been a p p l i e d ( T r e l o a r S A b e r n e t h y . D e t e r m i n a t i o n o f a bed f r i c t i o n f a c t o r , C o a s t a l E n g i n e e r i n g , v o l 2 , 1 9 7 8 ) .

W a v e - b r e a k i n g i s c a l c u l a t e d a c c . t o Goda ( w a v e s and wave a c t i o n , c o u r s e p r e s e n t e d at t h e A s i a n I n s t i t u t e o f T e c h n o l o g y , 1977) and t h e b r e a k e r i n d e x i s c a l c u l a t e d c o n t i n u o u s l y a s a f u n c t i o n o f t h e w a t e r -d e p t h , t h e w a v e - h e i g h t an-d t h e bottom s l o p e .

The above mentioned p u b l i c a t i o n s c a n be f e r e r r e d to f o r t h e d e t a i l e d d e s c r i p t i o n o f t h e m a t h e m a t i c s o f t h e s e a d d i t i o n a l f e a t u r e s .

3 . DETERMINATION OF INPUT-OATA

S e v e r a l s o u r c e s o f w a v e - d a t a o f t h e P o r t u g u e s e c o a s t a r e a v a i l a b l e . F o r L e i x o e s t h r e e s o u r c e s c a n be u s e d :

1 . R e i s de C a r v a l h o 5 B a r e e l o

A g i t a c a o m a r i t i m a na c o s t a o e s t e de P o r t u g a l M e t r o p o l i t a n o LNEC Memoria No. 2 9 0 - 1 9 6 6

2 . E s t u d o de A g i t a c a o m a r i t i m a em L e i x o e s , I n s t i t u t e H i d r o g r a f i c o , 1 9 7 ' *

3 . L e i x o e s , t r a t a m e n t o de dados de o n d u l a c a o I n s t i t u t e H i d r o g r a f i c o , 1 9 8 O

In p u b l i c a t i o n ( 1 ) s e v e n y e a r s o f v i s u a l wave o b s e r v a t i o n s from F i g u e i r a da Foz a r e p u b l i s h e d . In t o t a l 3 ^ 7 1 o b s e r v a t i o n s have been made. W a v e - h e i g h t s and p e r i o d s were measured w i t h a f l o a t i n g p o l e on a buoy and a l e v e l l i n g i n s t r u m e n t .

D i r e c t i o n s have been e s t i m a t e d v i s u a l l y .

B e c a u s e o f t h e used m e a s u r i n g method the d a t a a r e not v e r y a c c u r a t e (Nowadays b e t t e r i n s t r t m e n t s a r e a v a i l a b l e ) .

In p u b l i c a t i o n ( 2 ) f i v e y e a r s o f w a v e - m e a s u r e m e n t s w i t h a C h a t o u p r e s s u r e meter a r e p u b l i s h e d . In t o t a l 6 8 O s i m u l t a n e o u s o b s e r v a -t i o n s o f w a v e - h e i g h -t , w a v e - p e r i o d and w a v e - d i r e c -t i o n have been made. The w a v e - d i r e c t i o n was e i t h e r o b s e r v e d w i t h r a d a r o r e s t i m a t e d V i s u a l 1 y .

In p u b l i c a t i o n ( 3 ) o n l y t h r e e months o f measurements ( O c t o b e r -December 1980) a r e p r e s e n t e d . T h e s e measurements have been made w i t h a w a v e - r i d e r b u o y . In t o t a l 528 o b s e r v a t i o n s o f w a v e - h e i g h t s and wave p e r i o d s and 663 o b s e r v a t i o n s o f wave d i r e c t i o n s a r e p r e s e n t e d . An e l a b o r a t i o n o f the d a t a a c c . t o T u c k e r - D r a p e r i s g i v e n .

The r e s u l t s o f p u b l i c a t i o n s 1-3 a r e summarized in f i g . 2 , 3» k. In f i g . 2 t h e s i g n i f i c a n t w a v e - h e i g h t i s g i v e n . As c a n be seen a l l s o u r c e s a g r e e . A s i g n i f i c a n t w a v e - h e i g h t o f 2 m I s most common. C o n c e r n i n g the wave p e r i o d , t h e r e I s more v a r i a t i o n between t h e v a r i o u s s o u r c e s . The d a t a from F i g u e i r a da Foz e s p e c i a l l y show much

l o n g e r p e r i o d s t h a n t h e d a t a from L e i x o e s . T h i s I s p r o b a b l y c a u s e d by t h e m e a s u r i n g method. The d i f f e r e n c e s between t h e L e i x o e s d a t a a r e p r o b a b l y c a u s e d by s e a s o n a l i n f l u e n c e s .

In f i g u r e h t h e d i r e c t i o n s a r e shown. Here a l s o the d a t a from F i g u e i r a da Foz show a w i d e r band o f d i r e c t i o n s than t h e L e i x o e s d a t a .

One may c o n c l u d e from t h e above c o m p a r i s o n o f t h e measurements t h a t t h e d a t a from F i g u e i r a da Foz a r e not v e r y r e l i a b l e , due to an o u t -o f - d a t e m e a s u r i n g meth-od. The m-ore r e c e n t measurements p r e s e n t e d in ( 2 ) and ( 3 ) a r e more r e l i a b l e .

I t has been d e d i d e d to use the wave d a t a from ( 2 ) as Input f o r t h e w a v e - p e n e t r a t i o n m o d e l , b e c a u s e t h e s e measurements c o v e r a much

l o n g e r p e r i o d than t h e d a t a from ( 3 ) .

From t h i s t a b l e a l l e l e m e n t s have been s e l e c t e d w i t h an o c c u r a n c e o f more than 0 . 1 % . T h e r e a r e 3^ e l e m e n t s w i t h such an o c c u r a n c e . For e a c h o f t h e 3^ e l e m e n t s a w a v e - p e n e t r a t i o n c a l c u l a t i o n i s c a r r i e d o u t .

A l l e l e m e n t s a r e t a b u l a t e d in t a b l e 2 .

The model has an i n c l i n a t i o n o f - 2 0 " , b e s i d e s t h a t , in the model t h e a n g l e o f i n c i d e n c e has t o be g i v e n w i t h r e s p e c t to t h e p o s i t i v e x - a s . The a n g l e o f i n c i d e n c e o f t h e model c a n be c a l c u l a t e d a s f o l l o w s : f i ( m ) = f i ( r ) - f i ( i ) - 180 in w h i c h : f i (m) = a n g l e o f i n c i d e n c e in model f i ( r ) » a n g l e o f i n c i d e n c e in r e a l i t y f i ( i ) = i n c l i n a t i o n o f t h e model ( - 2 0 d e g r ) 7

k, CALCULATIONS WITH THE OVERALL MODEL

In f i g . 5 t h e l o c a t i o n s o f t h e w a v e - p e n e t r a t i o n g r i d s a r e i n d i c a t e d . The o v e r a l l model has a m e s h - s i z e o f 250 m and c o n s i s t s o f 60 X 30 = 1800 mesh p o i n t s . The waves a r e e n t e r e d a t t h e b o r d e r o f t h e m o d e l . At t h i s p o i n t waves a r e a l r e a d y i n f l u e n c e d somewhat by r e f r a c t i o n , but t h i s i s a l s o so f o r t h e measured w a v e s . The l o c a -t i o n f o r wave-measuremen-ts a r e f i -t -t e d w e l l f o r e n -t e r i n g d a -t a i n -t o t h e m o d e l .

The r a y - d i a g r a m s r e s u l t i n g from the o v e r a l l - c a l c u l a t i o n s a r e p r e s e n t e d in t h e annex to t h i s r e p o r t . In t h i s annex a c h a r t i s a l s o p r e s e n t e d o f t h e d e p t h - c o n t o u r s , a s used in t h e m a t h e m a t i c a l m o d e l . B e c a u s e the v a r i a t i o n s o f w a v e - h e i g h t due to r e f r a c t i o n , s h o a l i n g , e t c a r e r e l a t i v e l y s m a l l in the o v e r a l l m o d e l , no w a v e - h e i g h t c h a r t s a r e p r e s e n t e d . 8

5 . CALCULATIONS WITH THE DETAILED MODEL

The d e t a i l e d model ( f o r l o c a t i o n s e e f i g . 5 ) has a m e s h - s i z e o f 6 2 . 5 m and c o n s I s t s o f ^tO x 8 0 = 3200 mesh p o i n t s . The input o f t h e d e t a i l e d model i s g e n e r a t e d by t h e o v e r a l l m o d e l . In t a b l e 3 t h e g e n e r a t e d input d a t a f o r t h e d e t a i l e d model a r e p r e s e n t e d . The r a y - d i a g r a m s r e s u l t i n g from t h e s e c a l c u l a t i o n s a r e p r e s e n t e d in t h e annex to t h i s r e p o r t . The r a y - c h a r t s a r e pr i n t e d on a c h a r t w i t h d e p t h - c o n t o u r s , a s used in t h e m a t h e m a t i c a l m o d e l . The w a v e - h e i g h t c h a r t s a r e a l s o r e p r o d u c e d in t h e annex to t h i s r e p o r t . 9

6 . WAVE EXCEEDANCE DIAGRAMS

A w a v e - e x c e e d a n c e d i a g r a m has been c a l c u l a t e d f o r t e n d i f f e r e n t l o c a t i o n s . The l o c a t i o n s a r e g i v e n in f i q . 6. The d i a g r a m s a r e p r e s e n t e d in f i g . 7 - 1 5 . F o r l o c a t i o n 9 t h e r e i s no e x c e e d a n c e d i a g r a m , b e c a u s e no waves p e n e t r a t e d to t h i s p o i n t in our model

( t h i s i s due to the s c a l e o f t h e m o d e l ) .

In t a b l e h t h e b a s i c d a t a f o r t h e s e d i a g r a m s a r e p r e s e n t e d . In t h e f i r s t c o l u n n the wave c l i m a t e e l e m e n t i s s h o w n , t h e s e c o n d column g i v e s t h e o c c u r r e n c e o f t h e wave c l i m a t e e l e m e n t and t h e 1 a s t 10 c o l u n n s g i v e t h e o c c u r r i n g wave h e i g h t ( u p p e r f i g u r e ) and wave d i r e c t i o n ( l o w e r f i g u r e ) f o r e a c h p o i n t . A d i r e c t i o n o f - 9 0 ° means t h a t t h a t wave c l i m a t e e l e m e n t does not e x i s t a t t h a t l o c a t i o n .

7. CONCLUSIONS

From t h e w a v e - p e n e t r a t ion c a l c u l a t i o n s t h e m s e l v e s , o n i y a few c o n ¬ c l u s i o n s c a n be d r a w n . The r e s u l t s o f t h e s e c a l c u l a t i o n s w i l l be used in t h e c a l c u l a t i o n o f t h e l o n g s h o r e t r a n s p o r t and in t h e g e n e r a l m o r p h o l o g i c a l s t u d y .

A g e n e r a l o b s e r v a t i o n i s t h a t b i g waves b r e a k t w i c e , o n c e on t h e n o r t h w e s t o f t h e e n t r a n c e and once a t t h e c o a s t . A l s o , b e c a u s e t h e w a t e r i s s h a l l o w e r , t h e w a v e - h e i g h t i n c r e a s e s above the b a r due to

s h o a l i n g . The w a v e - h e i g h t c h a r t s show t h i s q u i t e c l e a r l y .

45-Significant wave height

1 9 6 6 ) F i g u e i r a da F o z 195/.-1966 1972 ) L e i x o e s June 1967 - J u l y 1972 1 9 8 0 ) L e i x o e s oct. / n o v . / d e c . 1980 F I G U R E 2: COMPARISON OF WAVE HEIGHTS.

Wave period

— ( 1 9 6 6 ) F i g u e i r a da Foz 1954-1966 ( 1 9 7 2 ) L e i x o e s j u n e 1 9 6 7 - j u i y 1972 ( 1980 ) L e i x o e s oct. / n o v . / d e c . 1980' F I G U R E 3 : COMPARISON OF WAVE PERIODS.

Direction

( 1 9 6 6 ) F i g u e i r a da F o z 1 9 5 4 - 1 9 6 6 . ( 1 9 7 2 ) L e i x o e s j u n e 1 9 6 7 - J u l y 1972 . . . ( 1 9 8 0 ) L e i x o e s oct. / nov. / d e c . 1980

1 0 0 . 0 0 _

ao.ooU

I

LL.

80.00U

40.00L_

ao.ooL

4

8

«

i n

WAVE-HEIGHT

100.00_

ao.ooU

I

>-I

L L

so.ooU

4 0 . 0 0 U

20.00L_

o.ooi

J

O J

_ir3

WAVE-HEIGHT

100,00.

ao.ooU

I

/

J

ao.ooU

4 0 . 0 0 U

/

20.00U

o.ool

i n

WAVE-HEIGHT

1 0 0 . 0 0 _

I

fe

>-I

BO.OOL

eo.ooU

40.00

/

20.00L_

o.ooL

O J

ro

i n

WAVE-HEIGHT

1 0 0 . 0 0 _

80.00

Lü

U

<

Q

LU

UJ

U

X

LU

LJ_ O

>

u LU a

LU

OC

LL

60.00

40.00

20.00

0.00

/

c5^

O

_O

O

cu

O

c n

o

o

i n

WAVE-HEIGHT

1 0 0 . 0 0 _

80.00™.

Lü

O

< • Lü LÜ U X LU

Ü_

O

>

•z. Lü ZD

a

Lü DC LL.

BO.OOU

4 0 . 0 0 _

20.00™.

0.00

/

O

O

O

O

cn

O

c c

i r

WAVE-HEIGHT

20.001

O.ool

o

O

O

CU

O

c6

O

O

WAVE-HEIGHT

1 0 0 . 0 0 _

80.00

Lü O

<

a

Lü Lü

a

X

ÜJ

l i

-O

>

C J

ÜJ

a

ÜJ

OC

Ü„

BO.OOU

4 0 . 0 0 U

20.00

0.00

_C5^

O

_O

o

O

c n

O

O

O

WAVE-HEIGHT

1 0 0 . 0 0 _

Lü

a

<

Q LÜ LÜ U X LÜ L i . O

80.00.

/

6O.OOL

•z. UJ I D

a

LÜ CE L L

4 0 . 0 0 —

20.00

O.OQ

_{c 5}

-o

o

r u

o

CQ

O

O

i n

WAVE-HEIGHT

Tab ! pe r i od > 9 9 - 1 1 11 - 13 > 13

(S)

( s e c ) w a v e - h e i g h t 0 - 2 2 - h > k 0 - 2 2 - li > 1. 0 - 2 2 - Jl > k 0 - 5 2 - l| > k l/l (m) :ribu t 3 ' . 5 ° - 3 6 0 ° 3 1 5 ° - 3 ' . 0 ° 0.00 0 . 0 2 0 . 0 0 0.00 0.00 0.00 0.00 0 . 0 2 0.00 0.01 0.00 0.00 0 . 0 0 0.01 0 . 0 0 0.01 0 . 0 0 0 . 0 0 0.00 O.Oil 0.00 0.00 0 . 0 0 0 . 0 0 0 . 0 0 0 . 0 6 o 3 0 0 ° - 3 1 5 ° 1.70 0 . 0 6 0.00 2.2k 0.69 0.00 0 . 6 3 0 . 7 6 0 . 1 2 O.OII 0 . 1 9 0 . 0 6 6.30 3 z O 2 8 5 ° - 3 0 0 ° 18.53 0.69 0.00 23.3') 7 . 5 5 0 . 0 0 6 . 8 7 8 . 2 3 1.37 0 . 0 » 2 . 0 5 0 . 6 8 6 8 . 6 5 O - h 1-_{t J} 2 7 0 ° - 2 8 5 ° 0 . 7 7 0.21 0.00 7 . 2 6 2 - 3 5 0 . 0 0 2.1') 2 . 5 6 0.1l3 0 . 0 » 0.21 2 1 . 3 6 wav e DI R 2 5 5 ° - 2 7 0 ° 0.51 0 . 0 2 0.00 0.6^1 0.21 0 . 0 0 0.19 0 . 2 3 0.0k O.OfI 0 . 0 6 0 . 0 2 1.89 wav e _{2 2 5 ° - 2 5 S °} 0 . 2 i | 0.01 0.00 0.30 0.10 0.00 0.09 0.11 0.02 o.oti 0.03 0.01 0.90 1 n l 8 0 ° - 2 2 5 ° 0.00 0.00 0.00 0.00 0 . 0 0 0 . 0 0 0 . 0 0 0.00 0.00 o.oti 0.00 0 . 0 0 0 . 0 0 imat e 27 1 0 33 11 0 10 12 2 0 3 1 0) rt- 28 'I'l 2li k 100 CD

e l e m e n t s i g n i f i c a n t w a v e - p e r i o d a n g l e o f i n c i d e n c e o c c u r a n c e , number wave h e i g l i t ( s e c ) in t h e modei %

(m) ( d e g r e e s )

1

1

8 U 7 , 5 1,70

2

1

8 1 3 2 , 5 1 8 , 5 3 3

1

8 1 1 7 , 5 0 , 7 7 k

1

8 1 0 2 , 5 0,51 1 i 5

1

8 5 0 , Ü Q ,24 2 1 , 7 5 6 3 8 1 3 2 , 5 0 , 6 9 7 3 8 1 1 7 , 5 0,21 0 , 9 0 8

1

10

1 4 7 , 5 2 , 2 5 9 1

10

1 3 2 , 5 2 3 , 3 4

10

1 10 1 1 7 , 5 7 , 2 6 11

1

10 1 0 2 , 5 0p64

12

1 10 8 0 , 0 0,30 3 3 , 7 9 ' 13 3 10 147,5 0 , 6 9

0

3

10

132,5 7 , 5 5 15 3

10

117,5 2 , 3 5 16 3 10 102,5 0,21

17

3

10

8 0 , 0 0,10 1 0 , 9 0 18

1

12

147,5 0 , 6 3 19 1

12

132,5 6 , 8 7

20

1

12

117,5 2 , 1 4

21

1

12

102,5 0,19 9 , 8 3

22

3

12

147,5 0 , 7 6 23 3

12

132,5 8 , 2 3 Zk 3

12

117,5 2 , 5 6

25

3

12

102,5 0 , 2 3 26 3

12

8 0 , 0 0,11

11

,89 27 ^ , 5

12

147,5 0 , 1 2 28

12

132,5

1

,37 29 ^ , 5

12

117,5 0 , 4 3

1

,92 30- 3 ]k 147,5 0 , 1 9 31 3 ]k 132,5 2 , 0 5 32 3 ]k 117,5 0 , 6 4 2 , 9 8 33 14 132,5 0 , 6 8 3k Vk 117,5 0,21 0 , 8 9 9 4 , 7 6 ^

HYDRONAMIC BV

PORT & WATERWAY ENGINEERS

CALCULATED BOUNDARY DATA FOR DETAILED MODEL

ELEMENT

NUMBER

01

02

03

04

05

OG

07

08

09

10

11

12

13

14

15

IG

17

!8

19

20

21

22

23

24

25

26

27

28

29

30

31

32

33

34

FREQUENCY

%

1 .700

18.530

.770

.510

.240

.690

.210

2.250

23.340

7.260

.640

.300

.690

7.550

2.350

.210

.100

.630

6.870

2.140

.190

.760

8.230

2.560

.230

.110

.120

1 .370

.430

.190

2.050

.640

.680

.210

WAVt H E i G H t

( n )

1 1 A 1 If— r\ T r i H H V C UJ-n .

/ n r r

N

MEAN ST.DEV.

MEAN ST

.DEV.

.91

.00

144.41

,58

.91

.00

130.85

,63

.91

.00

1 16.89

,80

.91

.00

102.20

.84

.91

.00

.81 .17

,80

2.74

.00

130.85

,63

2.74

.01

116.89

,80

.94

.01

141.42

,97

.94

.01

129.34

1 ,15

.94

.01

116.32

1 ,62

.94 •

.01

102.78

1 ,57

.94

.01

82.61

1 ,50

2.81

.02

141.42

,97

2.81

.02

129.34

1 ,15

2.81

.02

116.32

1 .62

2.81

.02

102.78

1 .57

2.81

.02

82.61

1 .50

.98

.01

139.55

1 .33

.99

.01

128.27

1 ,43

.99

.01

1 15.95

2.21

.99

.01

103.02

2,02

2.96

.02

139.55

1 ,33

2.96

.03

128.27

1 .43

2.96

.03

115.95

2.21

2.96

.03

103.02

2.02

2.96

.03

83.47

2.00

4.43

.04

139.55

1 .33

4.44

.04

128.27

1 .43

4.44

,04

115.95

2.21

3.12

.03

138.45

1 .51

3.13

.03

127.67

1 ,59

3.13

.03

115.79

2,50

4,69

.05

127,67

1 ,59

4.69

.05

115.79

2.50

-==^^ ,-^^;^==^^i:^0==^,=^St^^ Q =n4.%T=^rftg--=Sr.--ih;'^^ 1 0 ? - f>(i I O ' - - 01.-1 ? - 33-J.iI2^aü—102^8 3 _ j n l . 0 5 ^ 1 ^ - 4 2 - ^ 9 0 •

nn„

1 0 2 , ^ 8 6 , -19 11 9 . a n ° 9 n ^ n n - L l i L . ^ l ^ ^ - ^ ? 7 - 9 n - n n ^ V O ^ f c i O 1 4 1 , o n i 9 s - i f t i i f > , f t n 1 7 q - F ; o _ j j i L . j & ^ n i . 5 o _ ^ i n j . n j ) _ - 9 0 ^ o ^ ^ ^ Xn^.nci i n 7 . 9 7 Q n ^ . R B J L U . 4 9 i n 7 . n n _ L a 3 ^ 1 4 106.88 J (IJL»'L'<^'^"--i.0.Q---1 Q J - J ^ f e - ^ ^ — — . — ^ ^ ; s £ i= ^ ^ v ? y^ ; : H? ; = ^ t m ^ ^ ^ ^ ^ ^ aS:^ 1 ? R • r. r> 1 9 n -1 9 i n q - Q i i 1 3 . 7 J J J ^ t i j _ l _ ? g ^ 8_ J ^ l g . g 9 ^1_22.>i)i)-Taxi,.XIÜ-J-l-5^6_7— 3 . J J _ 4 . - 4 0 _ = S i K 4 Ü . 11 1 . O ü ^ - ^ 1 9 8 . 0 0 1 9 i i ^ A 2 ^ Ü L i ^ 9 1 1 1 - ^ . 7 0 j M 7 ^ j _ J ^ 9 8 ^ 8 _ J J j ^ . J > 0 _ J ^ 2 j ^ Q 0 - 9 ^ . 0 U 5 ..6-6 H l i n 7 . f t 9 8 9 ^ 4 _ _ 9 j i _ - J 7 g _ i n 9 . n o 1 Q 3 . 2 S _ _ i n 7 . 4 4 j J ^ j - ^ j J ^ j ^ O . 0 0 , J ^ ü 3 » J . 2 _ _ fl^-t^n q q - ? q 7 f t . dj 7 4 ^ . J ^ _ g j ^ « _ _ 8 6 ^ 5 9 _ ^ l _ . 4 4_ ±0) n q - n f l t 9 4 ^ n j i ^ j j t _ d ^ i 9 ^ j j > ^ q q _ j L ? J j L 4 j _ i J j ' • 7S--r-aixa)i)----aiU-0iX^-SiU-yL^42^4^^ 1 ? R ^ f U j _ j j i L; , A 2 ^ ^ i n . f i 9 117.61 1 ? 8 . 1 8 - U - a ^ J L . Z.OO ^ U - . O O 115^7-6-1 i f t . n n 115^7-6-1 115^7-6-1 4 ^ 115^7-6-1 ^ i A " _ i i L L - i g ^ ^ - _ J L g l - l L J J j - 115^7-6-1 " . ;l O - 9 0 - . A 0 - 115^7-6-1 J J - > Ü U — . _ _ ,£.,_OLO-^

3_._h 0 _ 4,1 ^4_ ? .i_^J 3. - j ) - ^ — 'iUX-r^-A^O C W