• TABLE OF CONTENTS
HIDE
 Front Cover
 Abstract
 Table of Contents
 List of Figures
 List of Tables
 1. Introduction
 2. Literature review
 3. Approach to physical movable-bed...
 4. Laboratory experiments
 5. Evaluation of scaling laws
 6. Summary and conclusion
 Appendix A. Beach profile evolution...
 Reference














Group Title: UFLCOEL-95020
Title: Laboratory mobile bed model studies on inlet sic
CITATION THUMBNAILS PAGE IMAGE ZOOMABLE
Full Citation
STANDARD VIEW MARC VIEW
Permanent Link: http://ufdc.ufl.edu/UF00085025/00001
 Material Information
Title: Laboratory mobile bed model studies on inlet sic
Series Title: UFLCOEL-95020
Alternate Title: Modeling law on profile response
Laboratory mobile bed model studies on inlets
Physical Description: ix, 144 p. : ill. ; 28 cm.
Language: English
Creator: Wang, Xu
Lin, Lihwa
Wang, Hsiang
Florida Sea Grant College
University of Florida -- Coastal and Oceanographic Engineering Dept
Publisher: Coastal & Oceanographic Engineering Dept., University of Florida
Place of Publication: Gainesville Fla
Publication Date: 1995
 Subjects
Subject: Movable bed models (Hydraulic engineering)   ( lcsh )
Inlets -- Mathematical models   ( lcsh )
Beach erosion -- Mathematical models   ( lcsh )
Genre: government publication (state, provincial, terriorial, dependent)   ( marcgt )
bibliography   ( marcgt )
non-fiction   ( marcgt )
 Notes
Bibliography: Includes bibliographical references (p. 142-144).
Funding: Sponsored by Florida Sea Grant College.
Statement of Responsibility: by Xu Wang, Lihwa Lin, and Hsiang Wang.
General Note: Cover title.
 Record Information
Bibliographic ID: UF00085025
Volume ID: VID00001
Source Institution: University of Florida
Rights Management: All rights reserved by the source institution and holding location.
Resource Identifier: oclc - 34531762

Table of Contents
    Front Cover
        Front Cover
    Abstract
        Page i
    Table of Contents
        Page ii
        Page iii
    List of Figures
        Page iv
        Page v
        Page vi
        Page vii
        Page viii
    List of Tables
        Page ix
    1. Introduction
        Page 1
        Page 2
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    2. Literature review
        Page 4
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    3. Approach to physical movable-bed modeling law
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    4. Laboratory experiments
        Page 29
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    5. Evaluation of scaling laws
        Page 68
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    6. Summary and conclusion
        Page 111
        Page 112
        Page 113
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    Appendix A. Beach profile evolution and sediment transport rate
        Page 116
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    Reference
        Page 142
        Page 143
Full Text



UFL/COEL-95/020


LABORATORY MOBILE BED MODEL STUDIES ON INLET
PART I: MODELING LAW ON PROFILE RESPONSE





by


Xu Wang
Lihwa Lin
and
Hsiang Wang



1995


Sponsored by


Florida Sea Grant College
Sea Grant Project No. R/C-S-33
Grant No. NA36RG0070




REPORT DOCUMENTATION PAGE
1. Report No. 2. 3. Recpiaent's AccessLioe o.


4. Title and Subtitle 5. Report Date
Laboratory Mobile Bed Model Studies on Inlets 1995
Part I: Modelling Law on Profile Response 6.

7. Authors) 8. Performing Orfganiation Report No.
Xu Wang, Li-Hwa Lin and Hsiang Wang UFL/COEL-95/020

9. Performing Oranizatuoo same and Address 10. Project/Task/Work Unit No.
Department of Coastal and Oceanographic Engineering
University of Florida 11. Contract or Crant No.
336 Weil Hall NA36RG0070
Gainesville, FL 32611 13. Type of Report
12. Sponsoring Organization Name and Address
Florida Sea Grant


14.

15. Supplementary ote



16. Abstract


This study was intended to accomplish two objectives, to improve upon the mobile bed
modelling law on beach profile response and to extend the modelling law to three dimensional
applications, specifically to inlet model studies. Four existing scaling laws on beach profile response
under storm wave conditions were examined based on two dimensional wave tank tests. The tests
consisted of three different geometrical scales simulating a target prototype profile evolution test
selected from the German large wave flume (GWK) experiments. Since the intent was to extend the
modelling law for offshore application, the performance of modeling laws was evaluated beyond the
nearshore profile. The beach profile was divided into two regions, the nearshore dune region and the
offshore bar-profile region. Separate evaluation criteria were developed and applied to the test results.
Based on the comparisons, a new modelling law was proposed.

Experiments were then carried out in three-dimensional wave basin to examine the proposed
modelling law and the results were reasonably successful but were rather limited.






17. Originator's Key Uords It. Availability ScatUment
Coastal engineering
Inlet
Modelling law
Moveable bed

19. U. S. Security Classif. of the Report 20. U. S. Security Classif of This Page 21. o. of Ples 22. Price
Unclassified Unclassified 144















TABLE OF CONTENTS


LIST OF FIGURES ...............................

LIST OF TABLES ................................

1 INTRODUCTION ..............................

2 LITERATURE REVIEW ..........................

3 APPROACH TO PHYSICAL MOVABLE-BED MODELING LAW .
3.1 Principles of Similarity .........................
3.1.1 Dynamic Similarity .......................
3.1.2 Similarity By Dimensional Analysis . . . . . . .
3.1.3 Similarity By non-dimensionalizing the governing Equations
3.2 Physical Modeling Laws Of Beach Response . . . . . . .


4 LABORATORY EXPERIMENTS ............
4.1 Test Facilities .....................
4.1.1 Air-Sea Wave Tank ..............
4.1.2 Wave Flume Facility .............
4.1.3 Wave Basin Facility .............
4.2 Initial Beach Profile Design .............
4.2.1 Experimental Procedures ...........
4.2.2 Test Conditions ...............
4.3 Test Results and Data Analysis . . . . . .
4.3.1 Profile Classifications of the Test Results ..
4.3.2 Volumetric Changes along the Profiles . .
4.3.3 Beach Erosion .................
4.3.4 Profile Evolution and Bar Migration . .
4.3.5 Eqilibrium Beach Profile . . . . . .

5 EVALUATION OF SCALING LAWS . . . . .
5.1 Methodology and Evaluation Criteria . . . .
5.1.1 Geometrical Scaling and Equilibrium Profile
5.1.2 Wave Height and Wave Period Scaling . .
5.1.3 Evaluation of Morphological Time Scale .
5.1.4 Summary of Two-Dimensional Test Results
5.1.5 Test Results from Three-Dimensional Basin
5.2 Test Results from Undistorted Model . . . .


..o..o...o
. . . . . .

oooooooooo
. . . . . .
. . . . . .









6 SUMMARY AND CONCLUSION ......................... 111

APPENDIX

A BEACH PROFILE EVOLUTION AND SEDIMENT TRANSPORT RATE 116

REFERENCES ...... .. .......................... 142














LIST OF FIGURES


4.1 Initial Beach Profile In Prototype . . . . . . . ... 32

4.2 Cumulative Sand Size Distribution . . . . . . . ... 33

4.3 Fall Velocity Of Spherical Grains As A Function Of Size, Rouse
(1937) . . . . . . . . . . . . .... .... . . 34

4.4 Designed Initial Beach Profile in Model with D50 = 0.20mm . .36

4.5 Example of Beach Profile with Diffused Bar, D50 = 0.09mm . 45

4.6 Definition Of Net Sediment Transport Rate Across The Beach Profile 47

4.7 Dune Erosion Evolution With Elapsed Time in ASW(1) ..... ..49

4.8 Dune Erosion Evolution With Elapsed Time in ASW(2) . . 50

4.9 Dune Erosion Evolution With Elapsed Time in WF ...... ..51

4.10 Dune Erosion Evolution With Elapsed Time in WB ...... ..52

4.11 Definition of Longshore Bar With Respect to Initial Profile . 53

4.12 Horizontal Movement Of Bar Crest With Horizontal Scale Equal
to 20 In ASW ............................ 56

4.13 Horizontal Movement Of Bar Crest With Horizontal Scale Equal
to 20 In W F ................... .. ....... 57

4.14 Horizontal Movement Of Bar Mass Center With Horizontal Scale
Equal to 20 In ASW ......................... 58

4.15 Horizontal Movement Of Bar Mass Center With Horizontal Scale
Equal to 20 In W F ................... ....... 59

4.16 Growth of Bar Volume With Horizontal Scale Equal to 20 In ASW 60

4.17 Growth of Bar Volume With Horizontal Scale Equal to 20 In WF 61

4.18 Horizontal Movement Of Bar Crest With Horizontal Scale Equal
to 30. . . . . . . . . . . . . . . ..... 62








4.19 Horizontal Movement Of Bar Mass Center With Horizontal Scale
Equal to 30. ............................ .. 62

4.20 Growth Of Bar Volume With Horizontal Scale Equal to 30. . 63

4.21 Horizontal Movement Of Bar Crest With Horizontal Scale Equal
to 40. . . . . . . . .. . . . . . . . . 63

4.22 Horizontal Movement Of Bar Mass Center With Horizontal Scale
Equal to 40. ................. ......... 64

4.23 Growth Of Bar Volume With Horizontal Scale Equal to 40. . 64

4.24 Horizontal Movement Of Bar Crest With D50 = 0.09mm . . 65

4.25 Horizontal Movement Of Bar Mass Center With D50 = 0.09mm 65

4.26 Growth Of Bar Volume With Ds0 = 0.09mm . . . . ... 66

4.27 Beach Profile Evolution And Sediment Transport Rate . . 67

5.1 Definition of The Dune and Bar Regions . . . . . ... 69

5.2 Equilibrium Profile Comparison Between Model Test Results and
M odeling Laws ................... ......... 72

5.3 ASW Model Tests and Prototype Final Profile Comparison (1) 75

5.4 ASW Model Tests and Prototype Final Profile Comparison (2) 76

5.5 ASW Model Tests and Prototype Final Profile Comparison (3) 77

5.6 WF Model Tests and Prototype Final Profile Comparison . .. 78

5.7 Dune Volume Erosion Error Criterion . . . . . . .. 79

5.8 The RMS Error of The Bar Profile Criterion . . . . ... 80

5.9 Bar Volume Error Criterion .................. ... 81

5.10 Bar Location Error Criterion . . . . . . ... . . 82

5.11 Summary of ASW Test Results Based On Dune Profile Parameter 85

5.12 Summary of ASW Test Results Based On Bar Profile Parameter 86

5.13 Summary of WF Test Results Based On Dune Profile Parameter 88

5.14 Summary of WF Test Results Based On Bar Profile Parameter .89

5.15 Dune Profile Evolution Scaling from ASW results . . ... 90








5.16 Dune Profile Evolution Scaling From WF results . . . ... 91

5.17 Morphological time scaling of Dune Profile RMS Value from ASW
Tests . . . . . . . . . . . . . . ..... 93

5.18 Morphological time scaling of Dune Profile RMS Value from WF
Tests .......... .... .................. 94

5.19 Morphological time scaling of Bar Crest Location from ASW Tests 95

5.20 Morphological time scaling of Bar Mass Center Location from
ASW Tests ...... ........... ........... 96

5.21 Morpholigical Time Scaling of Bar Profile RMS Value from ASW
Tests ................. .............. 97

5.22 Morphological time scaling of Bar Volume from ASW Tests . 98

5.23 Morpholigical Time Scalings from WF Tests . . . . ... 99

5.24 Initial Profiles Comparison Between 5 Sections for Case 3 . .. 101

5.25 Final Profile Comparison Between 5 Sections for Case 3 . . 102

5.26 Comparison of Wave Basin Model Test No.3 with Prototype . 104

5.27 Morphological Time Scaling from Wave Basin Test No.1 against
Prototype ................. .............. 105

5.28 Morphological Time Scaling from Wave Basin Test No.2 against
Prototype .. .. .. ..... .. .. .. .. ... .. .. .. .. 106

5.29 Morphological Time Scaling from Wave Basin Test No.3 against
Prototype .. . .. . .. . . . . . . . . .. . 107

5.30 Dune Erosion Volume Comparison With Prototype . . ... 108

5.31 Dune Profile RMS Comparison With Prototype . . . ... 109

5.32 Summary of The Undistorted Model Test Results (shore profile) 110

5.33 Summary of The Undistorted Model Test Results (bar profile) .110

6.1 Wave Height Scale as A function of k Value . . . . ... 114

A.1 Beach Profile Evolution and Sediment Transport Pattern of Test
No.1. ............................... 117

A.2 Beach Profile Evolution and Sediment Transport Pattern of Test
N o.2 . . . . . . . . . . . . . . . . . 118









A.3


A.4


A.5


A.6


A.7


A.8


A.9


A.10


A.11


A.12


A.13


A.14


A.15


A.16


A.17


No.18


Beach
No.3.

Beach
No.4.

Beach
No.5 .

Beach
No.6 .

Beach
No.7.

Beach
No.8 .

Beach
No.9.

Beach
No.10

Beach
No.ll

Beach
No.12

Beach
No.13

Beach
No.14

Beach
No.16

Beach
No.17

Beach


A.18 Beach Profile Evolution and Sediment
N o.19 . . . . . . . . .

A.19 Beach Profile Evolution and Sediment
N o.20 . . . . . . . . .


Profile Evolution and Sediment

Profile Evolution and Sediment

Profile Evolution and Sediment

.....Profile Evolution and Sediment

Profile Evolution and Sediment

....Profile Evolution and Sediment.......


Profile Evolution and Sediment

Profile Evolution and Sediment

Profile Evolution and Sediment

......Profile Evolution and Sediment

Profile Evolution and Sediment


Profile Evolution and Sediment

......Profile Evolution and Sediment

Profile Evolution and Sediment


Profile Evolution and Sediment
. . . . . . . . . .

Profile Evolution and Sediment
. . . . . . . . . .

Profile Evolution and Sediment
. . . . . . . . . .

Profile Evolution and Sediment
. . . . . . . . . .

Profile Evolution and Sediment


Profile Evolution and Sediment


Profile Evolution and Sediment


.... ... 135


A.20 Beach Profile Evolution and Sediment Transport Pattern of Test
N o.21 . . . . . . . . . . . . . . . . .


vii


Transport Pattern of Test

....Transport Pattern of Test

Transport Pattern of Test

Transport Pattern of Test

Transport Pattern of Test


Transport Pattern of Test

............Transport Pattern of Test

Transport Pattern of Test


Transport Pattern of Test

Transport Pattern of Test

Transport Pattern of Test

Transport Pattern of Test


Transport Pattern of Test


Transport Pattern of Test

Transport Pattern of Test

Transport Pattern of Test

.......Transport Pattern of Test
Transport Pattern of Test
. . . . . . . .

Transport Pattern of Test
. . . . . . . .

Transport Pattern of Test
. . . . . . . .

Transport Pattern of Test


Transport Pattern of Test


Transport Pattern of Test


Transport Pattern of Test


119


120


121


122


123


124


125


126


127


128


129


130


131


132


133


134









A.21


A.22


A.23


A.24


A.25


Beach
No.22

Beach
No.23

Beach
No.24

Beach
No.25

Beach
No.26


Profile Evolution and Sediment

Profile Evolution and Sediment....


Profile Evolution and Sediment

Profile Evolution and Sediment


Profile Evolution and Sediment
Profile Evolution and Sediment
. . . . . . . . . .

Profile Evolution and Sediment
. . . . . . . . . .


Transport Pattern of Test

.......Transport Pattern of Test


Transport Pattern of Test

......Transport Pattern of Test


Transport Pattern of Test
Transport Pattern of Test
. . . . . . . .

Transport Pattern of Test
. . . . . . . .












LIST OF TABLES


3.1 Summary of Fall Speed Distorted Model Laws . . . ... 22

3.2 Summary of Wave Breaking Index ('yb) ....... . . ... .27

4.1 Scale Ratios and Physical Dimensions in ASW Tests ...... ..35

4.2 Summary of Criteria Governing Beach Classification ...... ..39

4.3 Summary of Test Conditions in ASW ........ . . .. 40

4.4 Summary of Beach Profile Classification Parameter for ASW . 41

4.5 Summary of Test Conditions in the WF . . . . ..... 42

4.6 Beach Profile Classification Parameter for WF . . . ... 43

4.7 Test Conditions in Three-Dimensional Wave Basin . . ... 43

5.1 Four Fall Speed Distorted Model Laws . . . . ..... . 70

5.2 Comparison of Model Performances . . ... . . .. 83














CHAPTER 1
INTRODUCTION


Beach and dune erosion as well as the related beach profile changes that occur

under storm waves and high water levels are of basic interest in coastal engineering.

Numerous attempts using various techniques have been made to better understand

and predict beach and dune responses under storm wave attack. Numerical simulation

and laboratory experiments are two of the most commonly employed techniques.

In general, numerical models no doubt have the advantage for their quick and

neat answers and usually cost much less than physical models. However, the process

of beach and dune erosion is difficult to formulate owing to the inherently complicated

nature of sediment fluid interaction and the highly nonlinear unsteady and nonuniform

flow condition inside the surf zone. The time varying and irregular bottom changes

further complicate the problem. Therefore, current workable numerical models can

be considered as the first generation as all of them deal with simple macro-scale gross

effects such as the total erosional volume and the final shape of the profile. Even

in these terms, the predictive capability already exceeds our fundamental knowledge

employed to build these models. For instance, the swash transport mechanism, the

beach slope effect and the bar formation are already built in some of the models,

mainly based on conjectures with no credible fundamental knowledge. Further model

improvement requires better formulas based on improved fundamental understanding.

Physical models, on the other hand, can be used to reproduce the natural con-

dition without a priori knowledge on the basic mechanisms. They also offer the

opportunity of improving our understanding and provide useful data for numerical

models. One of the major difficulties in physical modeling is the problem of the scale







2
effects, particularly when sediment transport is involved. Physical models which in-

tend to simulate sediment transport and the associated morphological changes are

also known as movable-bed models. The subject of model scaling is a difficult one,

as mentioned. Numerous papers have been written proposing various similitude re-

lationships. At present there is no general solution that is also practical. Specific

modeling laws are usually only applicable to certain restricted conditions.

The beach response physical modeling has also been studied by a number of in-

vestigators. Currently, all the proposed modeling laws for beach response are for

two-dimensional application and most of them are based on the main assumption,

explicitly or implicitly, that within the surf zone suspended sediment is the dominant

mode of transport. These modeling laws can further be classified as distorted and

undistorted depending upon whether the horizontal and vertical geometrical scales

have the same ratio. The general opinion is that the undistorted model is preferred

over distorted model. However, distorted models are more flexible in accommodating

wider ranges of variables, both in physical dimensions and other physical parameters,

such as wave heights, wave lengths and sand sizes. A common weakness of the exist-

ing profile modeling laws, whether distorted or undistorted, appears to be the lack of

sufficient information to adequately verify the morphological time scale, i.e., the mod-

eling of beach evolution process as a function of time. This is an important class of

problem, particularly if one is to extend the physical modeling to three-dimensional

applications such as studying the morphological processes of shoreline changes or

nearshore shoaling phenomena.

This study is aimed at evaluating and improving the scaling laws for distorted

models guided by the modeling theory and through a series of laboratory experiments

carried out at different physical scales. The study is restricted to two-dimensional ap-

plication although experiments were also carried out in a three-dimensional in addition

to the traditional wave tank experiments.







3
Chapter 2 provides a general review on the development of physical modeling laws

concerning coastal sediment transport and that are specifically related to beach profile

response modeling. Chapter 3 reviews the basic similitude theorem and summarizes

existing beach profile modeling laws and their origins. A modified modeling law

based on the work of Wang et al. (1990) was also derived. These modeling laws are

evaluated by the results obtained in the subsequent laboratory model tests. Chapter

4 describes the various types of experiments being carried out both in 2-D wave tanks

and in the 3-D wave basin. Chapter 5 is the heart of this thesis as it deals with the

laboratory data analysis and the evaluation of various modeling laws based on the

laboratory data. Finally, summary and conclusion of the study is given in Chapter 6.













CHAPTER 2
LITERATURE REVIEW


Physical modeling is essentially a means of replacing the analytical integration of

the differential equations governing a physical process including the often complicated

initial and boundary conditions. It is, thereby, considered an important and useful

engineering tool. Since physical models are usually conducted at reduced scales,

the relationship between the model and the prototype must be clearly established

for model design and for extrapolating laboratory results to prototype scales. The

literature on the subject of scaling law is vast. This chapter is intended to provide a

brief account on the development of movable bed scaling laws for coastal engineering

applications, especially those relevant to beach profile modeling.

To the present knowledge, the first known scale-model experiments were con-

ducted by an English engineer (John Smeaton) during the period 1752-53, to deter-

mine the performance of water wheels and windmills (Hudson et al., 1979); a French

professor (Ferdinand Reech) in 1852, was the first to express what is now known as

the Froude criterion of similitude (Rouse and Ince, 1957). The earliest movable bed

model was conducted in 1875 by a Frenchman (Louis J. Fargue) and in 1885 by Os-

borne Reynolds in England. Natural sand was used as bed material and time scale

was taken into consideration.

L.P. Vernon-Harcourt, who continued the work of Reynolds, investigated scale

models using bed materials of sand as well as lighter weight sediments such as charcoal

and pumice. And the principle of movable bed model verification, which means that

the model is thought to be verified if it can reproduce all the features of bottom

evolution observed in the past, has been proven to be the basic guideline and widely







5
applied ever since, though there has been no rigorous proof of its sufficiency.

The extremely small scale (horizontal length scale up to 40,000) models with large

distortions (up to 100) were used in the early British model studies, which later on

tended to use larger scales with smaller distortions so as to reduce the scale effect for

more reliable results. Also after the work of Reynolds, movable bed model technology

was gradually employed to solving practical engineering problems.

After World War II, experience accumulated over the years through the extensive

movable bed scale model studies made by various laboratories all over the world,

especially in Europe, the United States, Japan, has advanced the state of the art.

And, movable-model studies of coastal engineering problems were routinely conducted

in connection with almost all coastal and other hydraulic engineering projects.

Meyer(1936) first conducted the laboratory model of beach profile evolution to

investigate scaling effects in movable bed experiments, and derived an empirical rela-

tionship between beach slope and wave steepness.

Water(1939) worked on the characteristic response of the beach profile to wave

action and classified profiles as ordinary or storm type and led to the conclusion that

wave steepness can be used to determine the type of beach profile that developed

under certain wave conditions. The process of sediment sorting along the profile was

demonstrated in the experiments in which the coarser material remained near the

plunge point and finer material moved offshore.

Bagnold (1940) used a wave tank to model the interaction of the waves and

beach and presented a thorough discussion of the basic physics of the phenomenon

as well as a detailed discussion on the application of using a hydraulic model study

for the analysis of the process. Rather coarse sand (0.5-7.0 mm) and waves varied

in amplitude between 30 centimeters and 5 centimeters were used to conduct the

small-scale laboratory experiments and it was found that the foreshore slope was

independent of the wave height and mainly a function of grain size.







6
By reviewing the literature, one may conclude that the earlier works in 1950s and

1960's were mostly related to beach profile classification and that this topic is well

studied and basically understood.

Up to present time, numerous work of the physical processes involved in beach

erosion by wave action (Keulegan, 1945, 1948; Bruun, 1954; Saville, 1957; Eagle-

son and Dean, 1961;; Collins, 1963; Vanoni, 1964; Eagleson, 1957, 1959, 1965 and

Galvin,1967; Sumnamura and Horikawa, 1975; Wang, Dalrymple and Shiau, 1975;

Dean, 1976, 1977; Inman and Ballard, 1982; Vellinga, 1982, 1986; Kriebel, Dally, and

Dean, 1987; etc) would lead us to some conclusions.

Wave breaking generates turbulent motion and provides the necessary mecha-

nism for suspending and keeping sediment in suspension, thus mobilizing the grains

for transport by mean currents. Although profile change is highly stochastic on a

microscale involving turbulence, movement of individual and collective grains, and

various types of organized flows, if viewed on a macroscale, changes in the profile are

surprisingly regular and consistent with respect to large features such as bars and

berms. And the existence of an equilibrium profile was proven to be a valid concept

under laboratory conditions.

For the laboratory scale modeling law for movable-bed models, a number of simil-

itude relations have been developed, each having its own practical assumptions and

constraints, and some of them are completely empirical and some completely mathe-

matical, while power laws are the most common type of function employed. But the

exact dynamic similitude of the dominant physical processes in two regimes (existing

a transition from one basic regime of boundary flow to another as sediment motion

outside the surf zone is compared to sediment motion in the surf zone) simultane-

ously i.e., using the same model fluid and the same model laws for reproducing the

waves, currents, and bottom material for both regimes) is not possible. So far, the

attempts to establish the correct scaling law are not really successful due to the lack







7
of an understanding of the basic mechanism of coastal sediment transport limited

choices of material that can be used in the laboratory resulting in the limited sediment

sizes, specific weights, viscosity, and the lack of quality prototype data for verification

purposes, etc.

Goddet and Jaffry (1960) derived the basic relations between horizontal scale,

vertical scale, sediment diameter scale and relative specific weight scale based on the

sediment motion due to combined action of wind waves and unidirectional currents.

ND = N17/20a&/5 (2.1)


N,, = N/20 -3/5 (2.2)

Q = N6/NA (2.3)

where ND is the scale of the sediment size, N8 is the geometrical vertical scale, and Q

is the distortion, the ratio of the geometrical horizontal scale (Nx) and vertical scale.

The scale relationships proposed by Goddet and Jaffry have not achieved popular

use, and were only proposed as a first step towards a reasonable solution.

Yalin (1963) examined model scale selection for sediment transport involving wind

waves and tidal currents. The phenomenon was considered to be a function of seven

characteristic parameters

p, [7, Ys, D, T, Ub, Ub (2.4)

where ub and Ub are typical wave and tide horizontal velocities, at the bottom (im-

mediately above an oscillatory boundary layer) and T is the wave period. These

parameters were combined to give a dimensionless expression for two-phase motion

in the vicinity of the bed. By assuming that the wave period T does not influence

the phenomenon of net sediment transport, and preserving the dimensionless change

in bed level and by application of small amplitude wave theory, the relationships as:


ND = N3/4 2


(2.5)







8

N,3Nj = 1 (2.6)

were obtained from the dimensional analysis.

Fan and Le Mehaute (1969) preserved the characteristics of sediment transport,

i.e., densimetric Froude Number Fr,, and Reynolds Number for initiation of sediment

motion Re. and used equilibrium beach profile concept.

N ,NN = 1 (2.7)

NY, = N6N-3/2 (2.8)

or

ND = N /2N-1

The authors reviewed most aspects of coastal mobile bed model technology and con-

cluded the following:

a. Similarity of bottom evolution is a basic requirement for a mobile bed model,

which is only possible for a flow regime where the boundary layer is turbulent.

b. A coastal mobile bed model must be geometrically distorted. Geometric

distortion should be defined by the ratio of the equilibrium beach slopes as measured

in model and prototype.

c. Similarity of wave action is only required to the extent that

NH = NL = N6 (2.10)

where L is the short wave length. This prohibits wave height distortion.

Noda (1971) listed seven similitude requirements for profile modeling under equi-

librium conditions based on the results of a number of previous investigations, in-

cluding Fan and Le Mehaute (1969) and Yalin (1963), etc. So far, this is the most

comprehensive one in beach profile scale modeling. These eight criteria are as follows:

a. Coastal fluid phenomena are generally dominated by gravitational and inertial

forces and hence the Froude number, i.e., u/(gd)1/2 is an important parameter. The








requirement that NF, = 1 yields

N = /N6 (2.11)

where N, is the velocity scale.

b. The preservation of the densimetric Froude number, u/(gy'D)1/2 based on the

grain size and bed shear velocity gives

N,,ND = N. (2.12)

where u, is the bed shear velocity, and 7' is the relative specific weight of the material


7' = (7 tf)/7f (2.13)

here y, is the specific weight of the sediment, and 7- is the specific weight of the fluid.

c. The requirement of identical grain diameter Reynolds number, i.e., u.D/v

produces

N,,ND = 1 (2.14)



d. Bed shear velocity for steady conditions in turbulent flow is proportional to

free stream velocity:

u. oc f1/2u (2.15)



f. The scale ratio for the friction factor : f related to unidirectional uniform flow.

C = (8)1/2 (2.16)

N6
N- = (2.17)
7 NA
and
S = N(2.18)
NC N6 (2.18)
Ng=








g. Kinematic Similarity:
u z
U = -(2.19)
w y


h. Fall velocity in stokes range:

o =D (2.20)
18v



These are all supposed to be pertinent to beach processes, and there are certainly

a many of combinations and Noda derived several of the possible scale-model laws

from various combinations of seven similitude conditions but failed to sort out the

proper ones only based on a limited experiment data.

Based on the assumed equilibrium conditions and limited experiments data sets,

Noda (1972) derived a completely empirical modeling law.

NDN ,84 N6055 (2.21)

N = N.32N-0386 (2.22)

Two of the four basic parameters ND, Ny, NA,N6 can be chosen freely and the

other two are automatically constrained. Also, the limiting conditions that if N, =

ND = 1, then, NA = N5 = 1 as found experimentally are also satisfied.

This set of modeling laws has been derived from two-dimensional laboratory beach

profile data and thus the extrapolation to three-dimensional models is still in question.

The wavelength is scaled according to the vertical scale to preserve the refraction

pattern, but the number of waves in the model will be smaller in proportion to

the distortion when scaled to prototype. Diffraction and reflection processes are

not preserved. Also, mass transport, sediment concentration, and material porosity

phenomena are not scaled. The region of interest was the beach profile in the breaker

zone where the boundary conditions belong to turbulent flow regime. No wind effects

have been accounted for.






11
Dean (1973) reported that the most promising parameter used for the predic-

tion of equilibrium beach slopes and the onshore or offshore sediment transport is

the dimensionless fall velocity (H/WT), as this parameter tells whether a sediment

particle thrown into suspension by the passage of a wave will settle to the bed during

the time that the water particle motion is shoreward or seaward, resulting in onshore

or offshore movement of the particle. This parameter actually is the fraction of the

drag force in vertical (gravity) and the drag force horizontal (orbital motion of the

wave), or the time taken for a sediment particle to fall a distance equal to the wave

height.

Dean (1985) reviewed previous movable-bed modeling criteria and considered the

dominant physical mechanisms involved in surf zone sediment transport. He argued

that the Shield's criterion is not necessary in the surf zone as turbulence, not bed

shear, is the dominant cause of sediment mobilization. He argued again that sediment

fall path, i.e., the fall speed parameter between the prototype and undistorted model

should be preserved. Hydrodynamics scaled according to Froude similarity and the

undistorted model are large enough to preclude significant viscous, surface tension,

and cohesive sediment effects so that the character of the wave breaking is properly

simulated. The scale relationships were proposed as


NFr =1 (2.23)



NT = Nt = (N6)1/2 (2.24)


H H
( ) = ( ) (2.25)
WT WT


Ns = (Nw)2/3(NA)2/3


(2.26)










Nx = N6 (2.27)

where Fr is the Froude number, W is the particle fall velocity, T the wave period.

Dean's empirical relation was established through synthesizing a large number of field

profiles.

Kamphuis (1974) listed four different dimensionless parameters as requirements

for complete similarity. He proposed a set of four different modeling laws preserving

one or more non-dimensional parameters but not all of them and suitable for a specific

range of environmental conditions without comparison with laboratory data. And he

also did not specify the mode of transport assuming that the sediment transport under

two dimensional wave action is related to the four dimensionless parameters and the

asymmetry of the wave motion. These criteria for dynamic similarity in modeling

movable bed can be summarized as

N,,ND
NR. =- 1 (2.28)


NpN2
N "' 1 (2.29)


Np
N = 1 (2.30)
N


N = 1 (2.31)
ND
where D is the particle size, p is the fluid density, p, is the particle density and 7, is

the underwater specific weight, i.e., (p, p)g, and as is the wave orbital amplitude

at the bottom.

The scale effects were also discussed based on the four dimensionless parameters:

a. The Reynolds number scale effect will only be felt at low flows and flow reversals

and expected to be small in the short wave models.







13
b. Incorrect scaling of the densimetric Froude number (Shields parameter) will

result in incorrect sediment transport and an undeterminate time scale.

c. The scale effect resulting from the violation of the Np,/p = 1 is not very serious

if mass movement rather than dynamics of individual particles is the interest.

d. The geometric link criterion is normally violated which means that sediment

transport is not only incorrect but varies throughout the model with depth.

Vellinga (1978) and Graaff (1977) derived a model law for dune erosion by em-

pirical correlations of tests done at different scale dimensions in the Delft Hydraulic

Laboratory in the Netherlands when compared to a single prototype condition. The

results of model tests on dune erosion with very fine sand support the validity of the

dimensionless fall velocity parameter H/TW for small scale modeling of beach pro-

cesses. If this parameter cannot be satisfied in the model, a profile distortion based

on kinematical similarity NA/N6 = N,/Nw = (Ns/Nv)"' with a = 0.5, gives good

results for the finer sands. For coarser sands values of a ranging from 0.5 to 0.3 were

found. The morphological time scale equal to the hydrodynamical time scale and

equals to square root of geometrical vertical scale. But Hughes's attempts (1983) to

verify the Delft modeling laws using the Hurricane Eloise data proved unsuccessful.

Graaff (1977) and Vellinga (1982) conducted a comprehensive laboratory study

by using different scales in attempting to duplicate the beach and dune erosion of the

Dutch's coast. The law requires that the wave steepness (Ho/Lo) and Froude number

be preserved and takes the morphological time scale into consideration.

Saville (1980) conducted a series of tests that the fall velocity of sediment was

scaled correctly and compared the results of these small-scale tests with prototype

model tests, finding that profile similarity was best in the surf zone and on the beach-

face, where setting velocity might be expected to be a major parameter affecting the

modeling.

Hughes (1983) presented a mid-scale modeling law based on consideration of the






14
inertial forces, represented by the turbulent shear stress, and the gravity force in the

nearly horizontal direction of the principal flow, which results in a dynamic scaling

relationship for a distorted model. A great number of experiments using both regular

and irregular wave trains verified the modeling law by reasonable reproduction of the

dune erosion which occurred during prototype event. The scale relationships preserve

the dimensionless fall velocity parameter (H/TW) and Froude number.

Wang (1990) derived a relationship based on different argument from the inspec-

tion of the basic governing equation instead of from dimensional analysis of physical

quantities. Based on the two-dimensional sediment conservation equation and preser-

vation of the surf zone parameter (Tanu3/JHo/Lo) with Tanf the beach slope and

the number of incoming waves per unit time, a set of modeling relationships had been

derived as:
NT = Nt = (2.32)
NT-Nt1/2

NH = N6 (2.33)

N, = NN6N/ (2.34)

N6 = (NsNw)2/5 4/5 (2.35)

In reviewing these modeling laws a number of issues appear to be unsettled.

One important question is the morphological time scale. While most of the profile
modeling laws appear to be able to reproduce the final profile between model and

the targeted prototype, the morphological time scale usually was not well established

owing largely to insufficient time-series data of both prototype and scaled models.

Another important parameter which needs attention is the scaling of wave height NH

in distorted models. So far no matter which type of transport mechanism the modeling

laws are based on i.e., bed shear-stress dominated transport or turbulence dominated

transport, although the latter was preferred by more investigators, wave height scale

is always treat as the geometric vertical scale, which might not be automatically the







15
case. Wang (1985) argued that in movable bed experiment the water depth at any

location is the original depth (which is a geometrical scale) minus (or plus) the sand

accretion (or erosion). Such erosion or accretion depth is not a simple vertical scale

and, therefore, should not be scaled as such. From this point of view, since wave

height also varies with water depth inside the surf zone but not necessarily linearly,

then wave height scale might also not be the same as the geometric vertical scale if the

model is distorted. The apparent question is why wave height should not be scaled

according to horizontal scale so the wave steepness is not distorted. The question of

wave height scaling in distorted model must be further explored in the laboratory.

Finally, a question can be raised on the criteria of modeling law verification. So far,

the performance of modeling is judged by properties in the vicinity of waterline such

as the volume of erosion and profile shape in that region. These quantities are of

obvious importance in engineering application but may or may not be sufficient for

modeling law verification purpose.

In closing this chapter it is reiterated here which has been observed by many

authors that the modeling of the coastal problems remains more of an art than a

science at this stage. There is general guideline but no general solution. Most of all

the model laws are tailored to fit certain restricted circumstances.













CHAPTER 3
APPROACH TO PHYSICAL MOVABLE-BED MODELING LAW



A number of different modelling laws for beach profile response modelling have

been proposed in the past; most of them are empirical and can only be applied with

certain restricted conditions and there is no clear indication as to which is more

preferable than the others.

The laws of hydraulic similitude, which should conform to the principles of fluid

mechanics, define the requirements necessary to ensure correspondence between flow

conditions of a scale model and its prototype. These requirements can be established

on the basis of either dynamical considerations, dimensional analysis or the equations

governing the process. However, full correspondence between the model and the

prototype is difficult, if not impossible, for most of the hydraulic problems including

coastal processes. This is because it is usually not possible to obtain a model fluid that

has the required viscosity, surface tension, elasticity and other physical properties to

meet the exact similitude requirement unless the linear scale is such that the model

is as large, or nearly as large, as the prototype. It is known that complete similitude

is not practical and in most cases not necessary. Then, it is extremely important

to select and preserve the parameters that have the dominant effects on the process

being examined.

Different investigators based on different interpretations of the coastal processes,

may choose to preserve different physical parameters, thus, arrived at different simil-

itude relationships.

In this chapter, the basic principles on similitude is briefly reviewed first. Then

follow the work by Wang, et al. (1990) but with different consideration on wave







17
height scaling based on a general wave breaking criterion, a modified beach response

modeling law is derived.


3.1 Principles of Similarity


As stated earlier the requirements for similarity between hydraulic scale model and its

prototype can be established on the bases of dynamical considerations, dimensional

analysis or the equations governing the process. These three methods are briefly

discussed here.

3.1.1 Dynamic Similarity

Similarity between the model and the prototype consists of three categories: ge-

ometric similarity, kinematic similarity and dynamic similarity. Geometric similarity

means the model and the prototype have similar geometrical and boundary shapes.

A basic geometrical scale is then defined as the ratio of linear dimension between the

model and the prototype:
L
NA = (3.1)
L,
where L is the linear dimension and the subscripts m and p refer to model and

prototype, respectively. N\ is called the length scale which dictates the size of the

model. If all the linear dimensions are preserved with the same N\ the model is known

as undistorted. The model could also be distorted if different parts of the model have

different length scales. They are known as distorted models. A common case is a

model with different horizontal and vertical length scales.

Kinematic similarity indicates a similarity of motion between model and proto-

type. Kinematic similarity of two systems is obtained if homologous particles are at

homologous points at homologous times (American Society of Civil Engineers, 1942).

The time intervals in the two systems must have a constant ratio,


NT = T (3.2)
Tm








Where NT is time scale.

In geometrically similar models, kinematic similarity is assured when there is

dynamic similarity. Following Newton's second law of motion, dynamic similarity can

be achieved when the ratio of inertial forces (Fi) between model and prototype equals
the vector sums of the ratios of active forces, which are recognized as gravitational

forces (F,), viscous forces (F,) elastic forces (Fe), surface tension forces (Ft), and

pressure forces (Fpr) in general fluid mechanics problems, i.e.,

(F) (F, + F, + F,, + F+ F)
(Fi)m (F, + F + F, + Fe + F(,)

A more restrictive requirement that guarantees Eq.(3.3) to be true is that the ratios

of each and every force be equal, or,

{Fi)p ( gp ( Wp (>,)p ()r
= _: (F) (F) (3.4)
(Fi)m (Fg) (F)m (Fst)m (Fe)m (Fp)m

The above equation can also be written as,

S(F)p/(Fi)p (F4)p/(F)p (Ft)p/(F)p (Fe),/(F)p (Fp),/(Fi),
(Fg)m/(Fi)m (F,)m (Fi)m (F.t)m/(Fi). (Fe)m/(F)m (Fp)m(Fi)m
(3.5)

The above equation consists of five non-dimensional force ratios. If both model
and prototype are under the same atmospheric pressure condition as often to be the

case, the non-dimensional pressure force ratio will be preserved if other force ratios

are preserved. Therefore, full dynamic similarity, in general, require the other four

force ratios all to be unity. Except with a one to one scale model, it is generally

not possible to achieve such full dynamic similarity. Therefore, it is important to

examine which forces are dominant in the prototype that are to be preserved in the

model. The others which contribute little to the phenomenon under consideration are

then ignored in the model simulation. Familiar examples are the Froude similitude

which preserves only the non-dimensional gravitational force ratio and the Reynolds
similitude that preserves only the non-dimensional viscous force ratio.







19

These forces can be expressed in basic physical quantities of length (L), mass (M),

gravitational accelation (g), density (p), dynamic viscosity (p), modulus of elasticity

(E), surface tension (o), and pressure (p), that is,

Fi = mass x acceleration = (pL3)(V2/L) (3.6)


Fg = mass x gravitationalacceleration = pL3g (3.7)
velocity
F, = viscosity x c area = VL (3.8)
distance

Fst = unitsurfacetension x length = oL (3.9)

Fe = modulusofelasticity x area = EL2 (3.10)

Fp = unitpressure x area = pL2 (3.11)

Based on these expressions, the ratio of gravitational force to inertial force can be

readily obtained as 4, the inverse of which is known as the Froude number. The

preservation of gravitational force is equivalent to preserve the Froude number be-

tween the model and the prototype. Similarly, the ratio of viscous force to inertial

force given by L is known as Reynolds number. The modeling law that preserves

the Reynolds number is called Reynolds similitude.

Other similitude creteria can be derived if one of the other non-dimensional force

ratios is preserved. When surface tension force predominates, the force ratio is given

by Weber's number, We = Similarly, the elastic force to inertial force ratio is

known as Mach or Cauchy number,Ma = -

Usually, for problems in coastal engineering field where gravity wave plays an

important role, Froude similitude needs to be preserved and every effort should be

made in the model design to either compensate or minimize the effects of viscous

force.







20
3.1.2 Similarity By Dimensional Analysis

The methods of dimensional analysis were developed primarily by Rayleigh (1899),

Buckingham (1914), and Bidgman (1922). The best method of analyzing fluid-flow

problems is by direct mathematical solution. However, many physical problems are

complex and direct mathematical solutions are not possible. For such cases, labora-

tory model experiments are one of a few available alternatives. Dimensional analysis

is a means to organize test parameters and scale the test results without the knowl-

edge of the governing equations. Buckingham's theorem, generally known as the ir

theorem, is used quite commonly.

Any correct mathematical equation which governs the physical process must be

dimensionally homogeneous and each term in the equation must contain identical

powers of each of the fundamental dimensions when the terms are reduced to basic

dimensions of mass, length, and time (M,L,T) or force, length, and time (F,L,T).

If n variables are connected by an unknown dimensionally homogeneous equation,

the equation can be expressed in the form of a relationship among n-k dimensionless

products, where k is the number of fundamental dimension in the problem and n-k

is the number of products in a complete set of dimensionless products (7r terms) of

the variables, and each 7r term will have k+l variables of which one must be changed

from term to term. The general function can be written in the form

A = f(A2, A3, A4, ...,A) (3.12)


which can also be written


f'(A, A2, A3, ..,A,) = 0 (3.13)

or

f"(r, 7r2, 7r3, .., rn-k)= 0 (3.14)

And the form of the function and values of the constant, for different types of flow







21
conditions, must be determined by analytical reasoning, experiment, or a combination

of reasoning and experiment.

3.1.3 Similarity By non-dimensionalizing the governing Equations

The mathematical equations that govern a phenomenon may give more insight

into the laws of similarity than the use of dimensional analysis of the variables influ-

encing or being suspected of influencing the phenomenon. If a phenomenon can be

described with sufficient accuracy by differential equations, the equations, after being

converted to dimensionless form, provide the basis of determining transfer parameters

between model and prototype. This is simply an extension of the dynamic similitude

techniques described earlier. There are several ways to convert the differential equa-

tions to dimensionless forms. For the details the reader may refer to Langhaar

(1951), Duncan (1953), Keulegan (1966), and Young (1971).


3.2 Physical Modeling Laws Of Beach Response


A number of modeling laws have been proposed for beach response modeling.

A summary can be found in Wang et.al (1990) and Hughes (1993). In both texts,

it was pointed out that the scale criteria dependent on fall velocity appeared to be

most promising. Table 3.1 summarizes some of the modeling laws given in the texts

mentioned above. Of these formulas, the Dean's criterion is gemotrically undistorted

whereas all the others permit geometrical distortions. It was pointed out by both

authors that all these criteria converge to the same undistorted condition.

Although an undistorted model is preferred, it lacks flexibility and limits the range

of tests that can be performed either due to facility limitation or material limitation.

Therefore, in this study, the main concern is the development of criteria that permit

scale distortion.

Hughes (1993) made a general assessment on the tests of distorted modeling cri-

teria and remarked that the body of experimental evidence presently supports either









Table 3.1: Summary of Fall Speed Distorted Model Laws
Geometric Hydrodynamic Morphological
Author Distortion Time Scale Time Scale

Le Mehaute (1970)) Nf = ( )1/2 NT = Nt =
N6 W ( NN NV WN


Vellinga (1982) N = ( )028 NT N= = 2


Hughes (1983)) )1/2 NT x Nt, =


Wang, et.al (1990)) A = ((N I )1/4 NT = Ntm =


Wang,et.al (1994) NT = V(NA Nt = V,,




Vellinga's relationships or Wang, et.al.'s guidance. The geometrical relationships of
these two set of criteria are very similar but the time scale is different. Vellinga's
approach is largely empirical based on dimensional analysis of physical quantities.
Wang (1990) took a slightly different approach by the inspection of the basic govern-
ing equation to deal with a restricted case, here the two dimensional beach profile
changes under the influence of wave action. Since their approach is based on the
actual sediment transport equation it offers the major advantage that the modeling
laws can be rationally modified to accommodate different hypotheses. These model-
ing laws, in turn, can be used to explain the physical process that is being modelled,
not simply producing match scales between model and prototype. Therefore, the
approach by Wang et.al is adopted here with a brief derivation of their results then
followed by a proposed variation.







23

The basic equation, which balancing the spatial change of sediment transport rate

and the temporal change of beach profile, is the two-dimensional sediment conserva-

tion equation:


O =Oq (3.15)
at 9x
where h is the bottom elevation, q is the volumetric sediment transport rate in

the direction x. Non-dimensionalize the equation:


h qt (3.16)
at 8A Ox

where the overbar refers to non-dimensional quantities and q,, t,, 6, A represent

the reference values of sediment transport rate, the morphorogical time scale, vertical

and horizontal geometrical scale respectively.

To maintain similitude between the model and prototype requires

N t = 1 (3.17)
NsN

where N refers to the ratio of prototype to model.

It is assumed that suspended load transport mode predominates the sediment

transport inside the surf zone which is approximated by the following equation,


q, = hVc (3.18)

where h is depth, V is mean transport velocity and c is mean sediment concentration.

The suspended sediemnt concentration is then assumed to be directly proportional

to the ratio of stirring power due to turbulence and the settling power due to gravity

and can be expressed as (Hattori and Karvamata, 1980):


pu' u'
c Poc (3.19)
(ps p)W SW






24
where u' is the turbulent intensity, W is the particle settling velocity and S is the

submerged specific weight.

The ratio of turbulent velocity and wave induced velocity is a function of surf

zone parameter as suggested by Thorton (1978), i.e.,


U
S= f(() (3.20)

The surf zone parameter is defined as TanP/3/Hb/Lo with Tan/ the beach slope,

Hb the breaking wave height, and Lo the deep water wave length.

Physically, this equation states that if the surf zone property is similar, the turbu-

lent intensity should be proportional to the mean velocity scale provided the surf zone

parameter is preserved. Since in a wave field u is proportional to H/T, combining

Eqs. (1.17), (1.18) and (1.19) with Eq. (1.16) gives the following scaling law,

NvNf()NtNH = 1 (3.21)
NANwNTNs
where the subscripts correspond to various physical quantities given earlier. It should

be noted here Nv is the scale ratio of the mean transport velocity which must not be

confused with the wave-induced particle velocity, u. This mean net transport velocity

is assumed to be proportional to wave celerity inside the surf zone. Therefore, Nv

is scaled as (NNs)/2.

By requiring Nf((E) = 1, i.e.,

(g/2T Tan/H 1/2)m = (g1/2T Tan3/H1/2)p (3.22)

the hydrodynamic time scale, or here the wave period scale, is obtained as,

NT = N HN/ (3.23)
NT WN(/2 g

In the modeling law proposed by Wang et.al. (1990), it was stated that the wave

height is treated as a vertical parameter which leads to the following hydrodynmaic

time scale,

NT = N1/21/2 (3.24)
g N6







25
From here after, the N, term will be dropped from all the formulas since all of

the coastal models are carried out in the same gravity field. Wang et.al further

examined two possibilities for geometric modeling. The first case was by letting the

morphological time scale to be the same as the distorted hydrodynmaic time scale

which is equivalent to preserve the number of waves in determining morpholical time

scale. The second alternative is to preserve the sediment particle fall trajectory. The

first possibility leads to the following pair of morpholical time scale and geometrical

scaling laws,

NA
NT = N, =

N6 =(N )2/3N2/3Nr2/3 (3.25)
-v"

The second case offers the following scaling equations,

NT NA
NT 1/2

Nt = Nv- N

N8 = ( )215N25N 4/5 (3.26)
-(-y
Therefore, geometric distortion is permissible by both scaling laws. Wang et.al. indi-

cated that the second pair is perferred by comparing with experimental results. The

distorted modeling law offers a major advantage over undistorted modeling laws in

that it greatly relaxes the requirement of laboratory facilities.

It has been noted that in this modeling law, the wave height is treated as a vertical

scale. This assumption is re-examined here. Clearly, in modeling beach profile change,

wave height inside the surf zone should be similar between model and prototype. By

treating wave height as a vertical geometrical scale in essence implicitly assumes that

wave height is proportional to the local water depth, i.e., H = bh with the 7b a

constant value. This relationship was originally proposed by McCowan (1984) as a

breaking criterion and has been widely used. To maintain wave height similitude for







26
the region to be simulated, here the surf zone, however, also requires that the same

criterion be true for the entire surf zone. This may or may not be case. therefore, a

more general wave height scaling law is proposed here with the following form,

NH = NNs (3.27)

with N, being the scale ratio of the breaking index, yb. This is the major difference

from the one proposed by Wang, et.al. Substituting the above equation into Eqs.

(3.21) and (3.23) give the modified modeling laws,

NT = N1/2 N (3.28)
16
and

NT NsNwN. 2/3
N, [NT NSNWN 2 (3.29)

A guideline on determining N, is proposed here by examining the functional

form of yb as developed by various investigators. A summary of different empirical

formulas for -Y is given in table 3.2 (from Wang, 1990). From this Table it can be

seen that the breaking index 7b could be affected by beach slope and deepwater wave

steepness. Inside surf zone, the effect of deepwater wave steepness is likely to be

minimal. Therefore, a general power law functional form of N, is proposed as,

Nr (3.30)

From examining the equations given in Table 3.2, one may conclude that the value

of k is likely in the range from 0 to 1. In the case, k=0, the proposed modeling law

reduces to that of Wang's. On the other extreme if k=l, or N. is linearly proportional

to the local beach slope, then,

N = (3.31)

and Eqs. (3.28) and (3.29) become


NT = N( .2


(3.32)













Table 3.2: Summary of Wave Breaking Index (yb)


Author 7b note


McCowan
(1894)
Munk
(1949)
Galvin
(1968)
Collins and
Weir(1969)
Komar and
Gaughan(1972)
Weggel
(1972)

Singamsetti
and Wind(1980)
Sunamura
(1980)
Moore
(1982)
Larson and
Kraus(1989)
Smith and
Kraus(1990)
Wu
(1990)
Hansen
(1990)
Kampuis
(1991)


Yb = 0.78


7b = 10/3( )1/3

7% = 1.087mi
1 m 'Yb = 1.40-6.85m'
b = 0.72 + 5.5m

yb = 1/0.56(k)1/5

b = b(m) a(m) -
a(m) = 43.8(1.0 e-19m)
b(m) = 1.56(1.0 + e-195m)-1
7b = 0.568mO107( Hk-0.237

b= 1*[(Ho/7)1/2 1/6

b = b(m) a(m)( -)4/5
a and b same as Weggel
b =- 1.14[f m 10.21

Yb = b(m) a(m)( )

yb = 0.85 + 0.351og(H7L)

7b = 1.25m0.2

Yb = 0.56e3.5m


solitary


solitary

laboratory

linear

linear

laboratory


laboartory

laboratory

hybrid



80 10
0.007 < -" < 0.0921
laboratory

laboratory
laboratory
laboratory









and


N = (NT2/NN 2/5N4/5 (3.33)

Again, by using the two different hypotheses proposed by Wang on morphological

time scaling, two different scaling laws can be obtained. First, by assuming that the

number of incoming waves per unit time is preserved for the similitude of erosion rate,

we obtain,

Nt = NT = N2

Ns = (NsNw)2/5N4/5 (3.34)

Second, if one perserves the fallen particle trajectory, the following modeling laws are

arrived at,

NT = N/

N, = N/2

N6 = (NsNw)1N/3 /6 (3.35)

In summary, a new set of profile modeling law have been derived by using the same

approach of Wang et.al. This new modeling law contains an additional scale ratio of

wave height. It seems that Wang et.al's law represents one limiting condition of the

proposed law. The other limiting condition is also derived here and the modeling law

is also included in the Table 3.1.














CHAPTER 4
LABORATORY EXPERIMENTS


4.1 Test Facilities


Laboratory experiments were carried out in three different facilities all located

in the Department of Coastal and Oceanographic Engineering, University of Florida.

The main series of experiment was conducted in what is referred to as the air-sea wave

tank (ASW) and a limited number of cases were repeated in a different wave tank,

hereto referred to as the wave flume (WF). Finally, a set of experiment was carried in

a three-dimensional basin (WB) with varying input wave angles. The results under

normal wave incident angle were also reported in this thesis for comparison. Brief

descriptions of each facility is givn here.

4.1.1 Air-Sea Wave Tank

The ASW tank is 1.8-meter wide and 45.7-meter long. The wave generator section

occupies 3.4 meter and the wave absorbing beaches is 5.8 meter long. The remaining

36.6 meters are divided into two bays, each 0.86-meter wide and 1.9 meters deep. The

maximum allowable water depth is about 0.9 meters. The wave tank can be filled

from a well at the rate of 500 gallons per minute.

Wave generation in the Air-Sea tank is controlled electronically, hydraulically

driven wave paddle measuring 1.8-meter wide and 1.2-meter high. The wave generator

bulkhead is mounted on acarriage and is driven by two hydraulic rams governed

by hydraulic servo-valves. The system provides independent control of the top and

bottom rams in such a way that the bulkhead can move either as a piston on the

carriage or as a paddle. Any combination of piston and paddle motion is possible.







30
For the beach response modelling law verification tests, the piston type is used.

A moving instrument carriage was mounted on the railing system traversing on

top of the tank. The rails for the carriage was installed with a horizontal tolerance of

0.03 mm, providing an leveled reference platform from which precision beach profile

measurement can be performed. The carriage also serves to carry various sensing

instruments. The carriage drive train is powered by a 1/2HP electric motor capable

of moving the carriage at variable speed between 0 to 6.1 meters per second. A hand-

held remote control unit is used to start or stop the drive motor. A hand-operated

optic probe is used in this series of tests to measure beach profile elevations.

4.1.2 Wave Flume Facility

A limited number of experiments were repeated in the Wave Flume which is

considerably smaller than ASW. It is 0.6-meter wide, 0.9-meter high and 15.5-meter

long with one side of the wall made of glass panel and the other side of steel. The

tank is equipped with a piston type wave maker driven by a mechanically controlled

electric motor. A manually operated ponit gage was installed for profile measurement.

In order to avoid penetrating into the sand at the point of contact the gage was

constructed of light aluminium and the tip was modified by replacing the point with

a small rectangular base which rests flat on the sand.

4.1.3 Wave Basin Facility

Three-dimensional model tests were carried out in the wave basin of the Coastal

and Oceanographic Engineering Department, University of Florida. The dimension

of the basin is approximately 28 m x 28 m x 1 m. The basin is equipped with

a snake-type wave-maker, which consists of 88 independent wavepaddles of 24 cm

width each. By adjusting the phase of each individual paddle motion, it can generate

waves of various oblique angles. Also the amplitude can be adjusted individually to

meet different needs with wave heights ranging from 1 centimeter to 15 centimeter

and wave periods from 0.89 to 1.89 seconds.







31
4.2 Initial Beach Profile Design


In this laboratory study, a test series obtained from the Grosser Wellenkanal

(GWK) facility in Hannover, Federal Republic of Germany (Dette and Uliczka,1987)

was selected as the prototype-scale target condition. This was chosen on the basis that

GWK is among the largest tank facilities in the world and the experiments carried

out thereout can be considered as near prototype scale. The experiments were also

well documented with rather comprehensive time histories of profile evolution and

the associated wave transformation data. The GWK experiments, hereto referred as

prototype, used sand with a median diameter of 0.33 mm molded to a composite slope

of 1 on 4 on the upper portion of the slope and 1 on 20 on the lower portion of the

slope. This initial prototype profile is shown in figure 4.1. The tests were conducted

at water depth of 5.0 meters under the input wave condition of 1.5 meters wave height

and 6.0 seconds wave period.

In the ASW tank model tests, two types of sediment were used, one of natural fine

sand with median diameter (D50) of 0.20 mm, hereon referred to as natural sand and

the other a well sorted very fine quartz sand, hereon referred to as fine quartz sand,

with D50 equal to 0.09 mm. The former was used in the bulk of the experiments. The

latter was used only in one series of tests at undistorted model scale to see whether

very fine sand can be used in the model as this is one option to increase the geometrical

scale ratio between prototype and model without resorting to distorted models. The

size distributions of the two sand sizes obtained by sieve analysis are given in Figure

4.2. The sediment fall velocities corresponding to D50 = 0.09 mm and D50 = 0.2 mm

are, respectively, 0.675 cm/sec and 1.90 cm/sec at a water temperature 200C (see

Figure 4.3 after Rouse, 1937).

The modeling laws listed in Table 3.1 do not dictate the same geometrical distor-

tion ratio. The geometrical distortions based on LeMehaute's and Hughes' laws are

identical whereas the geometrical distortions based on Vellinga's, Wang's the newly












INITIAL PROFILE
Horizontal Scale=l:l Vertical Scale=l:l
Slope 1=4:1 Slope 2=20:1

Length in m


25.0




7.1 // ZS.W.L.


0.0 12.0 24.0 106.0

/


Figure 4.1: Initial Beach Profile In Prototype







33


SAND SIZE DISTRIBUTION


1.00
0.90

0.80

0.70
0.60
0.50
0.40

0.30

0.20
0.10
0.00
0.00


0.60 0.70 0.80 0.90


Figure 4.2: Cumulative Sand Size Distribution

proposed one are nearly the same. A choice has to be made here for the laboratory

initial profile design. The geometrical distortion based on the latter group, or the

Wang's modeling law is adopted. This is because the existing field and laboratory

data seemed to have better agreement using either the Vallinga's or the Wang's cri-

terion (Hughes, 1993), which are nearly the same in terms of geometrical distortion.

It should also be pointed out here that the geometrical distortion criteria of all the

modeling laws listed do no actually differ significantly from each other and that the

final test profile is not particularly sensitive to the initial profile.

The geometrical distortion law proposed by Wang is,


N-N4/5 21/5
N6 = N NW


(4.1)


The initial test profile is shaped according to the above equation based on the

prototype profile dimensions. Three different horizontal scales NA = 20, 30 and 40

were selected in the test. The relevant geometrical scale ratios and some of the


0.10 0.20 0.30 0.40 0.50
SAND SIZE, D50 (mm)





















































Figure 4.3: Fall Velocity Of Spherical Grains As A Function Of Size, Rouse (1937)









Table 4.1: Scale Ratios and Physical Dimensions in ASW Tests


Median Sand Size Dso 0.20 mm 0.09 mm

Median Fall Velocity W, 1.9 cm/s 0.675 cm/s

Fall Velocity Scale Nw 2.08 6.62

Horizontal Length Scale NA 20.0 30.0 40.0 20.0 30.0 40.0

Vertical Length Scale N6 14.46 20.00 25.18 20.00 30.00 40.00

Distortion (N6 : N) 1:1.38 1:1.5 1:1.59 1:1 1:1 1:1

Water Depth 34.6cm 25.0cm 19.9cm 25.0cm 16.7cm 12.5cm

Corresponding "A" Parameter 0.092 0.065



physical dimensions at different scale models are listed in Table 4.1. The physical

dimensions of these initial profiles are also shown in Figure 4.4 for the natural sand

models. As can be seen from Table 4.1, the fine quartz sand models are all close to

undistorted. Or, in other words, to achieve undistorted modeling very fine material

has to be used. To avoid too shallow water due to the increased scale ratios, shift

the whole profile to maintaining the water level around 40.0 centimeters but keep the

shape of the profile unchanged as designed.


The WF tank tests were design to repeat part of the experiment carried out in

the ASW, namely only the cases with 20:1 horizontal scale. A planar beach of initial

slope 1:2.9 at upper segment and 1:14.46 at the lower segment was formed such as

given in Figure 4.4. The beach material used here was well-sorted fine quartz sand

with a mean diameter of 0.21 mm (close to that used in the ASW) with a sorting

coefficient of 0.58. The corresponding fall velocity is approximately 2.0 cm/sec. The




































INITIAL PROFILE
Horizontal cale=l:30 Vertical cale=l:20
Slope 1=2.67:1 Slope 2=13.3:1


Length in cm

87.0







0.0 30.0 70.0 343.3







INITIAL PROFILE
Horizontal Ceale=l:40 Vertical scalesl:25.2
Slope 1=2.5:1 Slope 2=12.6:1


Unit in cm

87.0




28. S.W.L

0.0 30.0 60.0 285.0






Figure 4.4: Designed Initial Beach Profile in Model with Dso = 0.20mm







37
grain size distributions range between 0.1 mm and 0.5 mm. The water depth is 35.3

cm. A total 10 experiments was conducted with test conditions summarized in the

table 4.5.

Finally, in the 3D wave basin tests, the sediment used in the model was also fine

quartz sand with median diameter of 0.20 mm with size distribution given in Figure

4.2. The corresponding fall velocity is 1.9 cm/sec at water temperature 200C; this

yields a N,=2.0 which is the same as the natural sand experiment in the ASW tank.

The horizontal scale was again selected at 20 and the corresponding vertical scale is

14.46 according to the modeling law.

The beach built in the basin has a total length of 19 m with a width of 14 m and

contained 125 tons of quartz sand. Both ends of the beach were confined by rigid

block walls. The entire beach was molded into initial shape by wooden templates cut

into the desired shape.

4.2.1 Experimental Procedures

It is desirable to have set a standard procedure before conducting the experiments

so that the results from the three different setups can be consistent and to reduce the

operating error as much as possible. Hopefully the procedure will also be helpful for

future experiments of a similar nature. This procedures are outlined in the following:

Step 1. Mark the design profile and water level on the outside of the tank glass

wall. Close the drainage valves and fill air-sea tank with water to the required depth

and adjust the wave generating machine to the design test conditions including wave

height and wave period .

Step 2. While filling the tank with water, a wooden board cut to just slightly less

than the tank width is used to mold the profile from offshore to beach face according

to the profile line. The uniformity of the profile across the width of the tank is checked

with a leveler.

Step 3. Survey the initial profile after the beach attends saturation at the test








water level. Record the water level.

Step 4. The beach is first stablized by a series of small waves. The wave height

is gradually increased to the designated test height.

Step 5. In most of the two-dimensional tests, beach profiles are surveyed only

along the centerline of the tank at time intervals of 5 minutes, 10 minutes, 20 minutes,

40 minutes, 80 minutes. In the three-dimensional wave basin experiments, 5 profies

were regularly surveyed at any time interval.

A number of experimental errors are evident. The seaward position of closure

where sand transport stopped sometimes was difficult to define as a verneer of sand

was often transported beyond the end of the initial profile and deposited as a thin

layer over the horizontal floor of the tank. Also, profile variations across the tank

were common. Uniform sand compaction was also difficult to achieve. These errors

together with survey inaccuracy could lead to erroreous results that did not conserve

the total volume of material. In general, this errors was small. Nevertheless, caution

must be exercised in accepting the data.

4.2.2 Test Conditions

The test conditions were determined by the requirement that the beach should

be erosional under the given wave input. Various criteria have been proposed in the

past, some of them are given in Table 4.2.

From this table it can be seen that three non-dimensional parameters are often

used: the wave steepness parameter, Ho/Lo, the relative fall velocity parameter,

vrW/gT and the surf zone parameter, tanf//HO/Lo.

The test conditions for the two-dimensional and three-dimensional experiments

as well as the values of these three key paramters were given in Tables 4.3 to 4.7.

The ASW tank tests were the most comprehensive conisting of 26 cases at 3 dif-

ferent horizontal geometrical scales whereas 10 tests were performed in WF with a

horizontal scale of 20. In the three-dimensional basin, 4 sets of experiments were




















Table 4.2: Summary of Criteria Governing Beach Classification



Authors Parameters Erosional Criterion



Johnson, 1952 Hg HO >0.025-0.030
Lo Lo

Dean, 1973 W- > 1.7WW
Lo 9T Lo 9gT


Sunamura and O; Tan3; d HO = C(Tanp)-0.27( 067
Lo' Lo Lo LO
Horikawa, 1974

Wang and Hb rW Hb > 0.5(W)1/3
anTTanp gT /TTanp gT
Yang, 1980

Hattori and HoTan/; W _kTanO > 0.5W
Lo gT LO 9T
Kawamata, 1980

Kraus, 1991 (Ho/Lo)/( )3/2 (Ho/Lo)/(- )3/2 < 184













Table 4.3: Summary of Test Conditions in ASW


Test Wave Wave Water Grain Horizontal Vertical
No. period height depth size scale scale
(sec) (cm) (cm) (mm)

1 1.00 11.50 52.0
2 1.14 10.50 34.6
3 1.20 11.25 52.0
4 1.20 12.75 52.0
5 1.33 10.00 52.0
6 1.33 11.00 35.3
7 1.33 11.25 35.3 0.20 20.0 14.46
8 1.33 12.00 52.0
9 1.33 12.75 52.0
10 1.33 13.00 35.3
11 1.33 17.50 52.0
12 1.45 10.50 52.0
13 1.45 13.50 52.0
14 1.45 18.00 52.0

16 1.33 10.00 40.0
17 1.15 9.50 40.0 0.20 30.0 20.0
18 1.00 9.50 40.0

19 0.80 5.50 40.0
20 1.00 9.00 40.0 0.20 40.0 25.2
21 1.15 9.50 40.0

22 1.34 7.50 40.0 20.0 20.0
23 1.34 7.50 40.0 20.0 20.0
24 1.10 5.00 40.0 0.09 30.0 30.0
25 1.10 5.00 40.0 30.0 30.0
26 1.054 3.75 40.0 40.0 40.0












Table 4.4: Summary of Beach Profile Classification Parameter for ASW


Test Wave Wave Wave Wave Relative Fall Surf Zone Kraus
No. period height Length Steepness Velocity Parameter Parameter
(sec) (m) (m) (H_ (HT)/( W)3/2

(GWK) 6.00 1.50 56.18 0.0267 0.00239 0.3060 228
1 1.00 0.115 1.56 0.0737 0.00689 0.2547 129
2 1.14 0.105 2.03 0.0517 0.00604 0.3041 110
3 1.20 0.1125 2.25 0.0500 0.00574 0.3093 115
4 1.20 0.1275 2.25 0.0567 0.00574 0.2904 130
5 1.33 0.10 2.76 0.0362 0.00518 0.3635 97
6 1.33 0.11 2.76 0.0399 0.00518 0.3462 107
7 1.33 0.1125 2.76 0.0408 0.00518 0.3424 109
8 1.33 0.12 2.76 0.0435 0.00518 0.3316 117
9 1.33 0.1275 2.76 0.0462 0.00518 0.3217 124
10 1.33 0.13 2.76 0.0471 0.00518 0.3187 126
11 1.33 0.175 2.76 0.0634 0.00518 0.2747 170
12 1.45 0.105 3.28 0.0320 0.00475 0.3866 97
13 1.45 0.135 3.28 0.0411 0.00475 0.3411 126
14 1.45 0.18 3.28 0.0549 0.00475 0.2952 168

16 1.33 0.10 2.76 0.0362 0.00518 0.3942 97
17 1.15 0.095 2.06 0.0461 0.00600 0.3493 99
18 1.00 0.095 1.56 0.0609 0.00689 0.3039 120

19 0.80 0.055 1.00 0.0550 0.00861 0.3384 69
20 1.00 0.09 1.56 0.0577 0.00689 0.3304 101
21 1.15 0.095 2.06 0.0461 0.00600 0.3696 99

22 1.34 0.075 2.81 0.0267 0.00161 0.3060 413
23 1.34 0.075 2.81 0.0267 0.00161 0.3060 413
24 1.10 0.050 1.89 0.0265 0.00197 0.3071 303
25 1.054 0.0375 1.73 0.0217 0.00205 0.3394 233
26 1.10 0.050 1.89 0.0265 0.00197 0.3071 303









Table 4.5: Summary of Test Conditions in the WF


Test Wave Wave Water Grain Horizontal Vertical
No. period height depth size scale scale
(sec) (cm) (cm) (mm)

1 1.30 11.50
2 1.30 11.50
3 1.30 12.00
4 1.30 12.50
5 1.30 12.50 35.3 0.21 20.0 14.46
6 1.30 13.00
7 1.30 13.00
8 1.60 15.00
9 1.30 16.50
10 1.65 16.50


carried.

All the test conditions listed above should, in theory, satisfy the erosional condi-

tions given in Table 4.2, however, some cases dropped to the region of the accretional

profile according to one or two parameters, especially for the undistorted model tests

the profiles suppose to be accretional according to the Kraus parameter.


4.3 Test Results and Data Analysis


The experimental data consisted of a set of measured profiles for the three test

series. This data set is too voluminous to be included in this thesis. However, they

are archived on computer disks in the Department of Coastal and Oceanographic

Enginnering, University of Florida. In this thesis only reduced information related to

the specific study subject is reported.

Data anaylsis was performed for two objectives: a primary objective of establish-

ing the modeling law as stated in the "Introduction" and a secondary objective of

documenting profile evolution process under laboratory condition. To fulfill the first













Table 4.6: Beach Profile Classification Parameter for WF


Table 4.7: Test Conditions in Three-Dimensional Wave Basin


Test Wave Wave Wave Wave Relative Fall Surf Zone Kraus
No. period height Length Steepness Velocity Parameter Parameter
(sec) (m) (m) ( -H THo/o 1' 3/2

1 1.30 0.13 2.63 0.0494 0.00468 0.311 154
2 1.30 0.11 2.63 0.0418 0.00468 0.338 131
3 1.30 0.115 2.63 0.0418 0.00468 0.338 131
4 1.30 0.12 2.63 0.0456 0.00468 0.324 142
5 1.30 0.10 2.63 0.0380 0.00468 0.354 119
6 1.30 0.135 2.63 0.0513 0.00468 0.305 160
7 1.30 0.105 2.63 0.0399 0.00468 0.346 125
8 1.30 0.1125 2.63 0.0428 0.00468 0.337 134
9 1.30 0.165 2.63 0.0627 0.00468 0.276 196
10 1.65 0.165 4.24 0.0389 0.00370 0.350 173







44
objective, various quantities that can be used for comparisons between prototype

and model are computed; such quantities include the profiles themselves, the volume

of erosion and the bar characteristics. The procedures of computing these quantities

and the results are given here. The subject of modeling law will be treated separately

in the next chapter. The secondary objective, however, is more descriptive and will

be discussed here as an integral part of the data analysis process.

4.3.1 Profile Classifications of the Test Results

As stated earlier that all the test conditions were selected on the permise that

the beach should be erosional. An erosional beach generally is also associated with

the development of a bar-type of profile. This has been the case for practically all

the cases tested. Berm and foreshore erosion occurred in every cases. The develop-

ment of breaking bar also occurred, but in certain cases the breaking bar is not as

prominent but rather diffused; an example is shown in Figure 4.5. In the very fine

sand experiments (Dso=0.09 mm), no prominent breaking bar was formed in any of

the test case.

4.3.2 Volumetric Changes along the Profiles

The basic equation to compute the volumetric change along the profile is the

two-dimensional sediment conservation given by


S=-- (4.2)
9t 9O

where h is the elevation of the profile at a given point x and time t; x is on-off shore

direction pointing offshore and z-axis orients upward from an origin located at the

still water shoreline; q is the time-averaged volumetric sediment transport rate per

unit length of shoreline.

Integrate equation (4.2) from the landward reference, xo, to any other position,

x, gives the net volume change per unit time:












--- INITIAL PROFILE
1 ------ After 80min

NS.W.L.



E -1


-4 --- ----

I-6 -3----------------------1------------1-------------------1------------
-5

-6
-10 0 10 20 30 40 50 60 70 80 90 100
OFFSHORE DISTANCE (m)


Figure 4.5: Example of Beach Profile with Diffused Bar, D50 = 0.09mm



f 9q 9ah
Sqdx hdx (4.3)

Let q(xo) = 0 at landward closure we have:

q = h

q(x) = dx (4.4)

with
h [z(x, t2) z(, t)] (45)
Qt t2 tl
The quantities on LHS are measured. Thus, the spatial variation of transport

rate between any two time levels can be computed from Equation 4.4 and 4.5. In

theory, this transport rate should become zero at the offshore closure depth. Figure

4.6 illustrates a typical spatial variation of the transport rate for the erosional beach

and bar-type profile. In the computation transport to the offshore direction is defined

as positive.






46
The cumulative volumatric difference per unit width along the profile between

two type steps defined as VD(volumetric difference) is simply the integration of Ah

along the profile:


V.D. = Ahd (4.6)



Ah = z(x, t2) z(x, t1) (4.7)

If the profile is truly two dimensional and the sediment bulk density is unchanged

VD should be zero when the integration is carried out to the closure depth to conserve

the mass. In the experiments, non-zero values were often obtained owing to the

combined effects sediment losses to the offshore region and the three dimensional

tank effect.

The beach profiles evolution at different elasped time, the computed transport

rate and V.D. values are presented graphically in Appendix A.

4.3.3 Beach Erosion

There are a number of ways to define beach erosion. The two common ones are

shoreline retreat and volumetric sand loss. The former is clearly more direct and

the latter may be or more engineering concern. In the experiments, the shoreline is

not always easy to define in the final profile as the profile may undulate near mean

water level thus resulting in multiple intersects. To compute volumetric loss, one

must define an offshore cutoff point which also is not necessarily easy. In the present

experiment setups, the initial profile was composite and has a natural break. This

artificial point is chosen as the offshore limit in the volumetric integration based on

Equation 4.6. This volume is defined as the dune volume erosion and the results are

presented in Figure 4.7 to 4.10. As can be seen, most of the erosion took place in

the early period and the erosion rate decreased rapidly on later times. However, not

all cases had reached non-erosional state at the end of the tests (in most cases 80















ZA


SFinal
Initial
b


xz


-q 4


Initial
Final


+q Offshore
Offshore


Figure 4.6: Definition Of Net Sediment Transport Rate Across The Beach Profile


Initial


+q I


Offshore

Onshore x







48
minutes test time). In fact, the general trend as evidenced from the figures appeared

to indicate otherwise.

4.3.4 Profile Evolution and Bar Migration

As mentioned earlier, most of the profiles evolved into bar-type with erosion at

near the shore face and dune region. Initially the material eroded from the beach face

was deposited just seaward of the plunging point to form a breaking bar. A trough

would develop immediately landward of the breaking bar. As the bar grew, waves

started to break farther offshore, causing the location of the bar also to move offshore.

The volume of the bar would also grow as the bar elevation is mainly controlled by

the water depth. The material supply was taken from the region inshore of the

bar. Secondary bar(s) could also be developed shoreward of the breaking bar. The

breaking bar developed rather quickly in the early stage of the test. But the process

of bar migration was more gradual and the rate of offshore migration also slowed

down as time progressed. Analysis was performed here to quantify the process of bar

development and to examine whether a stable profile had been reached at the end of

the test.

First a definition of a bar feature is needed. In the laboratory a convienent

reference is the initial profile and a bar can be defined as material accumulated above

the initial profile. The limits of the bar can be expressed by the intersects with the

initial profile. A number of indices can be defined to charecterize the bar such as the

bar volume, the bar crest location and the mass center. These definions are given in

Figure 4.11. A number of difficulties were encountered in handling the actual test

profiles. The most frequent problem was that there existed no clear intersecting point

at the seaward end, and, at other occasions, the bar appeared reached beyond the toe

of the beach profile. The same problem was also encountered at the landward end

but of fewer cases. For these cases, the intersects were determined subjectively.

Each profile survey was, thus, visually examined for bar feature. The following













AIR-SEA TANK MODEL TEST

Horizontal Scale 20, Vertical Scale 14.46, D50=0.20 mm

0

STest No.1
S---------------------------------es-N.

" -4 -------- Test No.2
----- Test No.3
---- Test No.4
S........--- Test No.5
-8
-8 ----.-....... Test No.6
0 \ .". ". "-
.. .-.-- ............
g -12



-16



-20
0 10 20 30 40 50 60 70


0

-- Test No.8
S-4 ------ Test No.9
----- Test No.10
---- Test No.11
S-- Test No.12
-8 "-. ---- Test No.14
--- Test No.14

S-12 -'
0

-20 I I I ...
-20~-~~--`--- ------------------------"*****^^ ^

-20-

0 10 20 30 40 50 60 70
Elapsed Time (min)


Figure 4.7: Dune Erosion Evolution With Elapsed Time in ASW(1)


80















AIR-SEA TANK MODEL TEST

Horizontal Scale 30, Vertical Scale 20, D50=0.20 mm


10 20 30 40 50 60 70 80



Undistorted Model With Median Sand Size D50 = 0.09mm



Test No.22
-------- Test No.23
----- Test No.24
--- Test No.25
----- Test No.26


----------------------------------

"- - ------ ---- --


10 20 30 40 50
Elapsed Time (min)


60 70 80


Figure 4.8: Dune Erosion Evolution With Elapsed Time in ASW(2)


0


\ -4





0
o
n -12
O


Q -16








51



















Tilting Flume MODEL TEST

Horizontal Scale 20, Vertical Scale 14.46, D50=0.21 mm



Test No.l
---- Test No.2
- - - - - ----- Test No.3
---- Test No.4
\ --.... Test No.5
S....--.-- Test No.6
--- Test No.7
........... Test No..
S---Test No.8
..... Test No.9

--""-- -. ---... . -

..... .... ....



............ t-- -- -- -- -- -- -- -- -- -


10 20 30 40 50
Elapsed Time (min)


60 70 80


Figure 4.9: Dune Erosion Evolution With Elapsed Time in WF


? 1

-3

S-7

-11
0
.-n
-15
0
S-19

-23

-27

-31


-35 L
0














Wave Basin MODEL TEST
Horizontal Scale 20, Vertical Scale 14.46, D50=0.20 mm



----- Test No.2 (A) Test No.1 (A
--- (B) (B)
S- (C) ---- (c)
--- (D) ---- (D)
\ ----- (E) -------- (E)




. . L11111:::-- .. ... . .-.- -


10 20 30 40 50 60 70 80


10 20 30 40 50 60 70 80
Elapsed Time (min)


Figure 4.10: Dune Erosion Evolution With Elapsed Time in WB


)


-14


-18


-22





S-2


S-8


-10
0

o -14


-18


-22













10.0

0
V 0.0
Z
0
-4 10.0


,. -20.0
W


0.0 50.0 100.0 150.0 200.0 250.0 300.0 350.0 400.0 450.0 500.0 550.0 600.0
OFFSHORE DISTANCE (cm)

Figure 4.11: Definition of Longshore Bar With Respect to Initial Profile

properties are then calculated for every identified breaking offshore bar from the

profiles: bar volume = Vb, location of bar center of mass = xc, location of bar crest

=xc.

The results of these computed values are given in Figure 4.12 to 4.23 for the

natural fine sand (D50 = 0.20mm). As can be seen from the above figures, breaking

bar development can be broken down into two distinctive stages: the formation stage

and movement stage. During the formation stage the breaking bar grew rapidly as

can be seen from the growth curves of both bar crest and bar volume. The bar quickly

reached a stable condition usually within the first 10 to 20 minutes of the test. Once

the bar reached this mature stage it remained rather stable and only moved at a very

slow rate in the offshore while bar volume also grew. This can be witnessed from the

distinct breaks of the curves shown in the above figures. In most of cases, the bar

and the profile appeared to gradually reach a stationary condition near the end of the







54
tests. There were cases, however, the bar seemed to extend beyond the end of the

initial profile and an offshore intersecting point could not be established; consequently

, the bar volume could not be clearly defined. For these cases, a stationary condition

may or may not have been reached. It is also observed here that as indicators of

bar development, the bar crest and the bar mass center, particularly the bar crest,

appeared to be more stable than bar volume. Part of reason may be that the bar

crest is mainly controlled by the wave breaking point whereas the bar volume could

be rather diffused at times for lack of clear boundaries. As a consequence, the bar

crest usually approached to a stationary position in the test whereas the volume still

was undergone changes.

Similar anayalsis was performed for the very fine quartz sand (Dso = 0.09 mm)tests.

The results were shown in Figure 4.24 to 4.26. In most of these cases, a clean bar-

profile such as evidenced in the natural sand tests was not obtained. The bar(s), if

any, was rather diffused. This was likely due to the fact that the very fine material

which when suspended by the wave motion settled over a wider aera.

4.3.5 Eqilibrium Beach Profile

Equilibrium beach profile is an idealized stable beach profile under a given stable

wave condition. The permise is that under a constant wave condition, the profile will

eventually evolve into a shape such that the net sediment transport at any point along

the profile is zero, or in other words, the destructive and constructive forces reached

local balance. This idea is widely accepted and applied in coastal engineering In the

field, since the enviornmntal forces change constantly, the equilibrium profile, if exists,

should also be "dynamic" that might change its shape or shift its location from time

to time and are, therefore, more difficult to define or verify. In theory, the idea of

equilibrium profile can best be tested in a laboratory enviornment under controlled

test conditions. Therefore, although testing the concept of equilibrium profile is not

the main objective of this thesis analysis was performed here to contribute to this







55
topic. Basically, there are two issues; whether equilibrium condition is attainable or

has been attained in the tests and, if it is, what is the final shape?

Based on the analysis given above, one can clearly identify that the time-averaged

sediment transport rate along the profile deceased monotonically with increasing time.

This is illustrated here by the test case 8 which was tested for an extended period

up to 240 minutes. The profile change as well as transport rate are shown in Figure

4.27.

For most of test cases, the transport rate quickly approached to negilible value

after 40 to 80 minutes run time. This can be seen from the plots in A.1 to A.26.

Another stable feature is the bar profile which was generally achieved before the end

of 80 minutes test time after which the breaking bar maintained its shape with little

or no movement.

The quantity that appeared to have not reached stable condition at the end of

the tests were the dune erosion volume which still showed a trend of increasing. This

suggested that even when the profile appeared to have reached a stable form it may

shift as a whole.

As to the shape of the equilibrium profile, the results will be presented in chapter













AIR-SEA TANK MODEL TEST

Horizontal Scale 20, Vertical Scale 14.46, D50=0.198mm



-- Test No.1
-- Test No.2
----- Test No.3
---- Test No.4
........ Test No.5
Test No.6
--- Test No.7



-----------------------------------------------------------
-------------------------------------------
/......--








I 10 20 30 40 50 60 70 80



-- Test No.8
-- Test No.9
----- Test No.10
---- Test No.11
........ Test No.12
--- Test_ jq,3__---
Test No.14








------------------------------I---
I .
I


10 20


30 40 50
Elapsed Time (min)


60 70 80


Figure 4.12: Horizontal Movement Of Bar Crest With Horizontal Scale Equal to 20.

















TILTING FLUME MODEL TEST
Horizontal Scale 20, Vertical Scale 14.46, D50=0.21mm



--- Test No.l
Test No.2
-Test No.3
---- Test No.4
........ Test No.5


.............



-- -- -- -- -


100.
90.
80.
70.
60.
50.
40.
30.
20.
10.
0.


100.
90.
80.
70.
60.
50.
40.
30.
20.
10.
0.
0.


60. 70. 80.


Figure 4.13: Horizontal Movement Of Bar Crest With Horizontal Scale Equal to 20
In WF


10. 20. 30. 40. 50.
Elapsed Time (min)


Test No.6
--- Test No.7
-Test No.8
---- Test No.9
....-..- Test No.10




-7
. ,---
. ----


[


.







58


AIR-SEA TANK MODEL TEST

Horizontal Scale 20, Vertical Scale 14.46, D50=0.20 mm


t I I I I
0 10 20 30 40 50 60 70 80



Test No.8
-- Test No.9
----- Test No.10
---- Test No.11

Test No.13
--- ------" ------ -. ..-------




/ ..


10 20 30 40 50
Elapsed Time (min)


60 70 80


Figure 4.14: Horizontal Movement Of Bar Mass Center With Horizontal Scale Equal
to 20 In ASW


Test No.l
Test No.2
----- Test No.3
---- Test No.4
........ Test No.5
Test No.6
--- Test No.7
-------.------------------------
------------- ----------
__~_~_~___---------------------~~
..~~---- -------------~:,:J-~


--- -- ----
.... ... ...



















TILTING FLUME

Horizontal Scale 20, Vertical


MODEL TEST

Scale 14.46, D50=0.21mm


100.
90. -
Test No.l
80. Test No.2
70. --- Test No.3
---- Test No.4
60. ........ Test No.5
50.
fl40. ____ ^".^SJ'-----------^
40.
40 -- ----- ------- ---- -- -----------------

0
o 20.
S10.




0 90.
C) 100.
m 90- Test No.6
d 80. -- Test No.7
70 ----- Test No.8
0 ---- Test No.9
0 60. ....-- Test No.10
50. ------
40.------
30.
20.
10.
0. i I I
0. 10. 20. 30. 40. 50. 60. 70. 80.
Elapsed Time (min)









Figure 4.15: Horizontal Movement Of Bar Mass Center With Horizontal Scale Equal
to 20 In WF








60


AIR-SEA TANK MODEL TEST

Horizontal Scale 20, Vertical Scale 14.46, D50=0.20 mm

40

-35- Test No.l
-- Test No.2
----- Test No.3
30 -- Test No.4
S.....--- Test No.5
5--- Test No.6
25
--- Test No.7

20


STest No.10---
15










------ Test No.1
0 ,0 ..' ,-'-' _. ==. y--'"

5 -. .--" -- ................-- --........................

10 I












0
0 10 20 30 40 50 60 70

40

35 --- Test No.8
Test No.9
----- Test No.10
S30 --- Test No.ll
........ -- Test No.12
-- Test No.13
5--- Test No.14




20 -- -- ----------~ -----
0
dII. 10 ---- __-






0
0 10 20 30 40 50 60 70


80


80


Elapsed Time (min)


Figure 4.16: Growth of Bar Volume With Horizontal Scale Equal to 20 In ASW







61











TILTING FLUME MODEL TEST
Horizontal Scale 20, Vertical Scale 14.46, D50=0.21mm


Test No.l
Test No.2
---- Test No.3
---- Test No.4
........ Test No.5


0. 10. 20. 30. 40. 50. 60. 70. 80.
Elapsed Time (min)


Figure 4.17: Growth of Bar Volume With Horizontal Scale Equal to 20 In WF






62
AIR-SEA TANK MODEL TEST
Horizontal Scale 30, Vertical Scale 20, D50=0.20 mm


0 10 20 30 40 50 60 70 80
Elapsed Time (min)
Figure 4.18: Horizontal Movement Of Bar Crest With Horizontal Scale Equal to 30.


10 20 30 40 50 60 70 80
Elapsed Time (min)


Figure 4.19: Horizontal Movement Of Bar Mass Center With Horizontal Scale Equal
to 30.







63
AIR-SEA TANK MODEL TEST
Horizontal Scale 30, Vertical Scale 20, D50=0.20 mm


0 10 20 30 40 50 60 70 80
Elapsed Time (min)

Figure 4.20: Growth Of Bar Volume With Horizontal Scale Equal to 30.

Horizontal Scale 40, Vertical Scale 25.2, D50=0.20 mm


10 20 30 40 50 60 70 80
Elapsed Time (min)


Figure 4.21: Horizontal Movement Of Bar Crest With Horizontal Scale Equal to 40.







64
AIR-SEA TANK MODEL TEST
Horizontal Scale 40, Vertical Scale 25.2, D50=0.20 mm


0 10 20 30 40 50 60 70 80
Elapsed Time (min)


,Figure 4.22:
4to 40.


Horizontal Movement Of Bar Mass Center With Horizontal Scale Equal


0 10 20 30 40 50 60 70 80
Elapsed Time (min)


Figure 4.23: Growth Of Bar Volume With Horizontal Scale Equal to 40.













200

180

160

0 140

U 120
0
b- 100

a 80

C 60

S40

20

0


200

180

S160
0
1- 140
0
0 120

1 100
o
S80
so
60


0 40

20


AIR-SEA TANK MODEL TEST

Undistorted Model With Median Sand Size D50 = 0.09mm



Test No.22(Horizontal Scale 20)
Test No.23(Horizontal Scale 20)
----- Test No.24(Horizontal Scale 30)
Test No.25(Horizontal Scale 40)
---- Test No.26(Horizontal Scale 30)





..--............----------- ---
I-







D 10 20 30 40 50 60 70 80
Elapsed Time (min)

Figure 4.24: Horizontal Movement Of Bar Crest With Dso = 0.09mm


0 10 20 30 40 50 60 70 80
Elapsed Time (min)


Figure 4.25: Horizontal Movement Of Bar Mass Center With Dso = 0.09mm



















AIR-SEA TANK MODEL TEST
Undistorted Model With Median Sand Size D50 = 0.09mm

40

35- Test No.22(Horizontal Scale 20)
3- Test No.23(Horizontal Scale 20)
----- Test No.24(Horizontal Scale 30)
S30 ---Test No.25(Horizontal Scale 40)
----- Test No.26(Horizontal Scale 30)
* 25 -

20

s 15
P-4 -------------------
-------------------------------------------
10



0 S ---"; . .-,--

0 10 20 30 40 50 60 70 80
Elapsed Time (min)


Figure 4.26: Growth Of Bar Volume With Dso = 0.09mm








67


















AIR-SEA TANK TEST NO.15 (EROSION) X=1:20 6=1:14.46
(H=11.5cm, T=1.33sec, D=52.0cm, SCALE=9.0)


200. 400.
OFFSHORE DISTANCE (cm)


Figure 4.27: Beach Profile Evolution And Sediment Transport Rate


20.

10.

0.

S-10.

o -20.

-30.

-40.

-50.


-t.iUtiJl


0.000







a n nMF


V.D. .0274(m-3/m)



T^


V.D. 0230(m-3/m)


200.


400.


6000.


400.


600.


.














CHAPTER 5
EVALUATION OF SCALING LAWS


5.1 Methodology and Evaluation Criteria


As stated earlier a specific set of test results from GWK is treated here as the pro-

totype conditions. All the test results were compared with the GWK data set as

basis for evaluating the scaling laws. Basically four different scaling laws from Table

3.1 were selected for the purpose; they are, by first author's name, vallinga, Hughes,

Wang 1 and Wang 2. They practically cover the existing scope of the profile modeling

law. These four scaling laws are repeated here in Table 5.1.

To facilitate quantitative evaluation certain criteria are employed here. The entire

beach profile is first divided into two parts: from the shoreline to the end of the first

slope of the profile is defined as the dune profile region and from the beginning of the

second slope of the profile to the end of the toe is defined as the bar profile region

such as given in Figure 5.1. Six different quantities were used for evaluations, two

related to the dune region and four related to the bar region; they are:

A. Dune Region:

The RMS value of the dune region profile.

The dune erosion volme.

B. Bar Region:

The RMS value of the bar region profile.

The location of bar center of mass.

The location of bar crest.

The volume of bar.

























Bar Profile Region


-I-SWL


- Initial Profile
- Storm Profile


A SCHEMATIC OF BAR AND SHORE REGION


Figure 5.1: Definition of The Dune and Bar Regions


Shore Region









Table 5.1: Four Fall Speed Distorted Model Laws
Geometric Hydrodynamic Morphological
Author Distortion Time Scale Time Scale

Vellinga (1982) N = ( )0.28 NT



NN
Hughes (1983)) f = ( )1/2 Nt _


Wang, et.al (1990)) = (4 NT = ftm =
N6 (N gNW)2 FVN9 V Ng


Wang,et.al (1994) N ( Nl ,)1/4 NT = Ntm /




All the above quantities were evaluated relative to the reference prototype quan-

tites in terms of error such that the set with the least error represents the best fit.

Detailed formulas for computations will be presented later in the appropriate sec-

tions.

Geometrical scaling was evaluated first based on the RMS error of the profiles

in the two regions. Wave height and wave period scalings were then evaluated by

comparing the scaled final profiles of all the test cases with the prototype final profile.

Finally, the best-fit data sets from each horizontal-scale group, i.e., NA =20, 30 and

40, were selected to evaluate the morphological time scale.

5.1.1 Geometrical Scaling and Equilibrium Profile

The gerometrical scale was evaluated by comparing the RMS (root mean square)
error of the final test profiles with the prototype. The RMS error is defined as


= 1 n -h )2]
c = [n (h' h)2] (5.1)
i=1






71
where h' and hM are profile elevation of prototype and model, respectively. There

are basically only two geometrical scaling laws in the 4 modeling laws listed in Ta-

ble 5.1 as the Vellinga's and the two Wang's laws are nearly the same. These two

geometrical scaling laws are,


Ns = N /3 (5.2)

and


Ns = N1/5 (5.3)

The data were scattered but collective the latter scaling law appeared to perform

better. Figure 5.2 shows the comparisons of all the final profiles for the cases of N,

=20 with the prototype based on the scaling Equation 5.3.

From this figure one may also argue that the gross feature of the final profiles
may be expressed by a simple form which could be defined as the equilibrium profile.

A number of equilibrium profile forms have been proposed, notably by Bruun (1954),

Dean (1977), Vellinga(1982) and Wang (1990). They are all in the following general

form:
SW
h = a( S )nm (5.4)

where h is the water depth, x is distance from shoreline, S is the submerged specific

weight, W is the sediment fall velocity and a is non-dimensional coefficient. The value

of a( f)" is also known as the scale parameter. Moore (1982) analyzed 500 or so

beach profiles and proposed A to be a function of particle size. Later, Dean, Vellinga

and Wang all suggested that particle fall velocity is a more appropriate parameter

instead of the partial size. Vellinga (1982) proposed A to be equal to 0.39W0.44 from

analyzing field profile along the Dutch coast. Dean (1985) re-analyzed the values

complied by Moore (1982) and gave the best fit as A = 0.51W0.44; this formula was

also found suitable for GWK data by Wang (1990). As to the value m, Bruun and














WAVE TANK MODEL TESTS EQUILIBRIUM PROFILES


-10 0 10 20 30 40 50 60
OFFSHORE DISTANCE (m)


70 80 90 100


Figure 5.2: Equilibrium Profile Comparison Between Model Test Results and Model-
ing Laws







73
Dean suggested to be 2/3, Vellinga used 0.78 and Wang came up with 4/5. Equation

5.4 was also plotted in Figure 5.2 using two different values of n = 2/3 and 4/5. The

A parameter is equal to 0.131 for both cases based on the fall velocity equation given

above. It appeared that value of m=4/5 gave a better fit for the specific data set in

the inshore segment of the profile. It should be noted here that, to a certain degree,

irrespective to which value of m one selects, the equilbrium curve can also be adjusted

to fit any specific data set by adjusting the value A.

5.1.2 Wave Height and Wave Period Scaling

Based on the analysis given in the previous section, the basic goemetrical scaling

by Wang is selected for the subsequent analysis of wave height, wave period and mor-

phological time scalings. In this section, the scalings of the former two are addressed

and the latter will be addressed in the next section.

As mentioned earlier the analysis of wave height and wave period is based upon

final profiles. Figure 5.3 to figure 5.5 plots the scaled final profile of each test case for

the ASW test series against the protype. The results of the 10 WF tests are presented

in Figure 5.6







74
To establish the best scaling relationships from the data, the four of the criteria

given earlier were employed. The procedures are the same for analyzing each criterion.

It is explained here with the dune volume computation. The dune volume error is

defined as


Vm Vp
V p (5.5)
VP
where VP is the volume deficit (eroded volume) between the final and the initial

profile in the prototype and Vm is scaled-up volume deficit in the model. These values

are plotted against model wave heights, for different model wave periods, as shown in

Figure 5.7. These constitute a series of curves. The zero crossing(s) should represent

the best-fit model wave heights) and wave periodss. From them the best-fit scaling

ratios can be obtained. A rather clear trend between the dune volume error and wave

height can be detected. This trend is almost linear revealing a expected relationship

that increasing wave height resulted in increased erosional volume. The effect of wave

period on volumetric erosion is less clear revealing a rather weak relationship between

dune volumetric erosion and wave period. From this figure the best fit values of wave

height and wave period are determined to be 13.5 cm and 1.33 sec, respectively. The

corresponding scaling ratios based on this creterion are 11.1 and 4.5 for wave height

and wave period.

The above procedure was also applied to determine the best-fit modeling scales

for the other three criteria. Figure 5.8 to 5.10 show the plots of those other three

parameters: the RMS error of the bar profile, the bar volume and the bar mass

center. From these figures the best-fit scaling ratios based on different creteria are

determined. The results are summarized in Table 5.2.

5.1.3 Evaluation of Morphological Time Scale

To evaluate the morphological time scale one requires a comparison of the model

data with the prototype at each time step. This would be an unwiedy task if all the








75


AIRSEA TANK MODEL TEST AND GERMAN DATA COMPARISON


3.

2.

1.

0.



E--2.


S-4.

-5.

-6.

3.

2.

1.

0.




2-4.
I-2.

> -3.

M-4.

-5.

-6.


0. 10. 20. 30. 40. 50. 60.


70. 80. 90. 100.


OFFSHORE DISTANCE (m)


Figure 5.3: ASW Model Tests and Prototype Final Profile Comparison (1)


0. -









-5.


-10.








76


AIRSEA TANK MODEL TEST AND GERMAN DATA COMPARISON


1-- ',i. \ -------- TEST NO.12 (MODEL)
INITIAL PROFILE (GWK) S.1
S Q '^-N-V- - - - - - -NTARFLCI - :
0. - --- - -- - - - -
-- After 273min (GWK)
-1.

E--2.

>-3.

~-4.

-5. -.



3.

2. TEST NO.13 (MODEL)
,, ------ TEST N0.14 (MODEL)
S-------- TEST NO.16 (MODEL)
S INITIAL PROFILE (GiK) S.11
S o- - ^- - - - - - S
After 273min (GWK)




> -3.

S-4.



-6.

3.

2. -- TEST NO.17 (MODEL)
----- TEST NO.18 (MODEL)
S\ --------- TEST NO.19 (MODEL)
---- INITIAL PROFILE (GwI) S.1W
-- After 273min (GWK)
z-1.

E 2. .-... ..
-2.



S-4.

-5.


-10. 0. 10. 20. 30. 40. 50. 60. 70. 80. 90.

OFFSHORE DISTANCE (m)


Figure 5.4: ASW Model Tests and Prototype Final Profile Comparison (2)


100.








77


AIRSEA TANK MODEL TEST AND GERMAN DATA COMPARISON


3.

2.

1.

0.

-2.

0
.-3.

r-4.

-5.

-6.

3.

2.

1.

0.

-1.

-2.
r -3.


~ -4.

-5.

-6.


-6.1 10 I I I
-10. 0. 10. 20. 30. 40. 50. 60.


70. 80. 90. 100.


OFFSHORE DISTANCE (m)


Figure 5.5: ASW Model Tests and Prototype Final Profile Comparison (3)










TILTING FLUME MODEL TEST AND GERMAN DATA COMPARISON


0. 10. 20. 30. 40. 50. 60. 70. 80.

OFFSHORE DISTANCE (m)


Figure 5.6: WF Model Tests and Prototype Final Profile Comparison


3.

2.







-2.
-.



-W4.

-5.

-6.

3.

2.

1.

Sno.

2-1.
0
-3.-2.


1-4.

-5.

-6.


3. -



.








-4. -
Z-5.




-6. -

-10.
-6.'
-10.


90. 100.























A: Vellinga (1982)
B: Hughes (1983)
C: Wang, et al.(1990)
D: Wang, et al.(present)


2

0


0
w
0
'4;








-1


T=1.20(S)
T=1.3O(S)
T=1.33(S)
- c-T=1.45(S)


e T=1.00(S)
+ T=1.14(S)
* T=1.65(S)


9Wave Height, H (cm)
Wave Height, H (cm)


PLOT OF DUNE VOLUME ERROR (N\=20, N,=14.5 )


Figure 5.7: Dune Volume Erosion Error Criterion






















A: Vellinga (1982)
B: Hughes (1983)
C: Wang, et al.(1990)
D: Wang, et al.(present)


--x--T=1.20(S)
--- T=1.30(S)
-- T=1.33(S)
-x-- T=1.45(S)


o T=1.00(S)
+ T=1.14(S)
o T=1.65(S)


9 Wave Height, H (cm)


PLOT OF RMS ERROR OF BAR PROFILE ( Nx=20, N,=14.5 )


Figure 5.8: The RMS Error of The Bar Profile Criterion
























A: Vellinga (1982)
B: Hughes (1983)
C: Wang, et al.(1990)
D: Wang, et al.(present)


1




3-
0


So
I-



a)




-1


-1


--x--T=1.20(S)
-T=1.30(S)
- T=1.33(S)
--- T=1.45(S)


o T=1.00(S)
+ T=1.14(S)
* T=1.65(S)


Wave Height, H (cm) 19


PLOT OF BAR VOLUME ERROR (N =20, N =14.5 )


Figure 5.9: Bar Volume Error Criterion























A: Vellinga (1982)
B: Hughes (1983)
C: Wang, et al.(1990)
D: Wang, et al.(present)


.0.3





14
0










0


T=1.20(S)
T=1.30(S)
T=1.33(S)
m T=1.45(S)


o T=1.00(S)
+ T=1.14(S)
* T=1.65(S)


Wave Height, H (cm) 19


PLOT OF BAR LOCATION CENTER ERROR ( Nx=20. N,=14.5)


Figure 5.10: Bar Location Error Criterion
















Table 5.2: Comparison of Model Performances


Ex.1: Given N = 20, Nw = 2.

Author N6 NH NT Nt
Vellinga (1982) 14.5 14.5 3.8 3.8
Hughes (1983) 14.5 14.5 5.3 5.3
Wang, et al.(1990) 14.5 14.5 5.3 3.8
Wang(present) 14.5 10.5 4.5 4.5
Experimental data Ns NH NT Nt
Bar location 14.5 11.5 4.5 4.5
Bar volume change 14.5 11.3 4.5 4.5
Dune volume change 14.5 11.1 4.5 4.5
Ex.2: Given NX = 40, Nw = 2.

Author N6 NH NT Nt
Vellinga (1982) 25.2 25.2 5.0 5.0
Hughes (1983) 25.2 25.2 7.8 7.8
Wang, et al.(1990) 25.2 25.2 7.8 5.0
Wang(present) 25.2 15.9 6.3 6.3
Experimental data N6 NH NT Nt
Bar location 25.2 16.7 6.0 6.3
Bar volume change 25.2 16.7 6.0 6.3
Dune volume change 25.2 16.7 6.0 6.3







84
data sets were used. In here, the best-fit data set from the three different horizontal

scale groups (NA = 20, 30, and 40) were selected from the ASW and WF tests results.

The morphorlogical scale was then examined from this data set. The selection

of the best-fit data set was guided by the results of the previous sections. The error

quantities established above are now plotted for each test case.

Figure 5.11 shows the results of dune region error parameters (dune erosion vol-

ume and dune profile RMS) for the cases in the ASW test.

Figure 5.12 gives the results of bar region error parameters for the ASW tests.

From these two figures, the best-fit data sets selected (judged to have the smallest

overall error) are No.8 for NA = 20, No.18 for NA = 30 and No.20 for NA = 40.

Similarly, Figures 5.13 and 5.12 give the dune and bar parameters results for the WF

tests. From here, No.9 is selected as a compromise for the best overall fit. These data

sets are then used to establish the best-fit morphorlogical scale. In theory, this can

be accomplished by the same procedure as described in the previous section except

that the comparisons are to be made at each time step for the three selected cases.

In practice, this is rather tidious and there is not sufficient data points at each time

step. An alternative procedure is employed.

There are three different morphological time scaling laws guided by the mor-

phological time scales given in Table 5.1. Wang(1990) suggested that the particle

trajectory should be preserved which leads to Nt = \/fN-. Both Vellinga (1982) and

Hughes (1986) modeling laws give Nt = NA/VN6. The study referred to as Wang 2

suggests that both motion time scale and morphological time scale are governed by

the scaling law, or, Nt = VNWA.

Now, the time elaspsed changes of the 6 quantities, i.e., the dune erosion volume,

bar volume the RMS values of profiles, etc., are plotted in accordance with the three

morphological scaling laws and are compared with the GWK results. The GWK data

contained 21 different elapsed time at 5, 13, 20, 27, 34, 48, 62, 76, 90, 111, 132, 162,








AIR-SEA TANK DISTORTED MODEL TESTS
(Shore and Dune Profile)
80
0 ERROR OF VOLUME EROSION
75
75 A RMS VALUE OF DUNE PROFILE (*25)

70 ........... WAVE PERIOD SCALE
----- WAVE HEIGHT SCALE
65

60

55
Nx=20 30 40
50 0 -
N6 =14.5 20 25.2
45

40

35 00


ACA
30 -

25 -

20

o-----------------------------------------------
pA- (D -

10 A A




1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21
TEST CASE NUMBER


Figure 5.11: Summary of ASW Test Results Based On Dune Profile Parameter







AIR-SEA TANK DISTORTED MODEL TESTS
(Nearshore and Bar Profile)
70
0 ERROR OF BAR LOCATION(center of mass)
65 A RMS ERROR OF PROFILE ('50)
---- WAVE PERIOD SCALE
60
------ WAVE HEIGHT SCALE

55
NX =20 A 30 40
50
N6 =14.5 20 25.2
45

40 A

35 A A A

30 A A00



20A

00
o i ,0



5 : ---- -----------



0 I I
0 (D Q) ) (TG_(D o__- 9) - (D
1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21
TEST CASE NUMBER


Figure 5.12: Summary of ASW Test Results Based On Bar Profile Parameter







87
176, 190, 204, 217, 231, 245, 259, 273 minute, respectively. From these comparisons,

the best-fit morphorlogical time scale is obtained.

Dune Region

There are two criteria in the dune region, the dune volume erosion and the profile

RMS value.

For dune erosion, a number of observations can be made. From the ASW results

(Figure 5.15) all three scaling laws over predict the total erosional volume and the

larger the scale ratio, or the smaller the model, the larger the over-prediction. The

over prediction largely occurred in the initial stage (0 to 100 minutes prototype time).

Also, it appears that none of the tests including the prototype has reached equilibrium

at the end of the runs.

The results from WF test are shown in Figure 5.16. All modeling laws also over

predict the total erosional volume.

Therefore, these results suggest that the best-fit morphological time scale ratio

has to be smaller than any of the 3 modeling laws.

The comparisons of profile RMS error are given in Figure 5.17 for ASW cases

and in Figure 5.18 for the WF case. For this criterion all 3 modeling laws appeared

to perform reasonably well as the scaled values all custered in a narrow range around

the prototype results. Overall the Wang 2 model may be slightly better.

Bar Profile Region

Four different criteria have been developed for this region, the profile RMS value,

the bar volume, the bar mass center and the bar crest location. The results of these

four criteria are plotted in Figure 5.19 to 5.22 for the ASW tests and Figure 5.23 for

the WF tests.

From these figures a number of observations are made. The bar mass center is

the most stable and consistent criterion. All three modeling laws appeared to give

reasonable results for all three data sets. The bar crest location is next consistent








TILTING


FLUME DISTORTED MODEL TEST
(Shore and Dune Profile)


0 ERROR OF VOLUME EROSION
A RMS VALUE OF DUNE PROFILE (*30)
--- WAVE PERIOD SCALE
------ WAVE HEIGHT SCALE




NX =20

N6 =14.5





(


A A A


0--------------- -----
------------------------------------------------- ---------------------------




2 3 4 5 6 7 8 9
TEST CASE NUMBER


Figure 5.13: Summary of WF Test Results Based On Dune Profile Parameter









TILTING FLUME DISTORTED MODEL TEST
(Nearshore and Bar Profile)

0 ERROR OF BAR LOCATION(center of mass)
A RMS ERROR OF PROFILE (*50)
---...... WAVE PERIOD SCALE
----- WAVE HEIGHT SCALE


NX=20

N6=14.5


(D0_ _- _ __ (D- -- -- ------- - -
0r --.---"' ..........--(


2 3 4 5 6 7 8 9
TEST CASE NUMBER


Figure 5.14: Summary of WF Test Results Based On Bar Profile Parameter


-1 -111-^1-------1~-~-1-11---11-~-1------ ~~_~







90











COMPARISON OF SHORE/DUNE VOLUME EROSION
(Distorted Model, AirSea Tank, D50 = 0.20mm)


0 50 100 150 200 250 300 350 400
Prototype Time (min)


450 500 550 600


Figure 5.15: Dune Profile Evolution Scaling from ASW results


- German GWK data
WaveTank Nt = N = Nt=
Test (NA) VN vN NA,/4v
No.8 (20) -A- - -X-
No.18 (30) - -- -*-
No.20 (40) --Q- --Z- -_ -


.....Z-.7...... .... ...... .

.-~~ ~~~~ ----;.---.----------"--------'"--......
.......---- ------
-' r I I .i I
-^/^Y




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