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Nearshore Infragravity Wave Generation: A Numerical Model and Parametric Study

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Permanent Link: http://ufdc.ufl.edu/UFE0015500/00001

Material Information

Title: Nearshore Infragravity Wave Generation: A Numerical Model and Parametric Study
Physical Description: Mixed Material
Copyright Date: 2008

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Holding Location: University of Florida
Rights Management: All rights reserved by the source institution and holding location.
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Permanent Link: http://ufdc.ufl.edu/UFE0015500/00001

Material Information

Title: Nearshore Infragravity Wave Generation: A Numerical Model and Parametric Study
Physical Description: Mixed Material
Copyright Date: 2008

Record Information

Source Institution: University of Florida
Holding Location: University of Florida
Rights Management: All rights reserved by the source institution and holding location.
System ID: UFE0015500:00001


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Full Text













NEARSHORE INFRAGRAVITY WAVE GENERATION: A NUMERICAL MODEL
AND PARAMETRIC STUDY















By

EILEEN M. CZARNECKI


A THESIS PRESENTED TO THE GRADUATE SCHOOL
OF THE UNIVERSITY OF FLORIDA IN PARTIAL FULFILLMENT
OF THE REQUIREMENTS FOR THE DEGREE OF
MASTER OF SCIENCE

UNIVERSITY OF FLORIDA


2006






























Copyright 2006

by

Eileen M. Czarnecki

































This document is dedicated to my father, William John Czarnecki.
















ACKNOWLEDGMENTS

First and foremost, the author wishes to thank her advisor and supervisory

committee chairman, Dr. Andrew Kennedy, for his support, patience, guidance,

instruction, and assistance throughout this study. Gratitude is extended to the other

members of the committee, Dr. Robert Dean and Dr. Robert Thieke, for their assistance.

The author also wishes to thank the entire faculty of the Civil and Coastal

Engineering Department, who helped to shape her intellectual development as an

engineer, both during undergraduate and graduate studies.

Finally, the author would like to thank her family and friends for their love and

support. Special thanks go to Elaine Czarnecki, Billy Czarnecki, Barbara Lewis, and

Xiaoyan Zheng.
















TABLE OF CONTENTS

page

ACKNOW LEDGM ENTS ........................................ iv

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

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

ABSTRACT.................................... xii

CHAPTER

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

1.1. Definition and Importance of Infragravity W aves.................................................1
1.2 Objectives ................... ...................................... ............ ........ 1
1.3 Literature Review ................................................ ........ 1
1.4 Thesis O outline ...................................... ......................... .... ....... .4

2 NUMERICAL MODEL .................6............. .......... 6

2.1 C onceptual O verview .................................................. ...............6
2.2 Bathymetry ........................................ ........6
2.3 W ave Spectrum ................... ...... .... .... ........ ............... .......... 7
2.4 Wave Transformation ........................ ............... ...............9
2.5 Long W ave G eneration................................................. 12
2.5.1 Governing Equations .................................... ...... ............ ........ 12
2.5.2 Infragravity W ave Surface Elevation.............. .................................... 13
2.5.3 Boundary Conditions...................................................... 17
2.5.3.1 Shoreline boundary condition ................. ............................17
2.5.3.2 Offshore boundary condition .................................. ....18
2.5.4 Derivation of Radiation Stress..................................23
2.5.4.1 Steady radiation stress ........................ ...... ................... 26
2.5.4.2 Low frequency radiation stress ................ ................. ...........27
2.6 Root Mean Square Long Wave Surface Elevation................ .................28
2.7 M ean W after Level ...................... ........ .... ..................28
2.8 Model Validation ......... ......... ......................30






v










3 NUMERICAL SIMULATION OF LOW FREQUENCY WAVE CLIMATE..........34

3.1 Use of the M odel ......................................... ...... ..... ...34
3.2 Parameters.............................. ...... ......... 35
3.3 Results...................... .... .. ............ ......... 35
3.3.1 B ase C ase....................................35
3.3.2 Offshore Significant Wave Height and Peak Period ................................37
3.3.3 Jonswap Peak Enhancement Factor............ ....................49
3.3.4 Deep Water Directional Width...............................50
3.3.5 Peak Wave Direction ............... .... ...................51
3.3.6 B ottom Friction .............................. ............................. 53
3.3.7 Bar Amplitude ............................................. .... .....54
3.3.8 Bar Width .......................................... .........56
3.3.9 Distance of Bar from Shore........................................... 57
3.3.10 W ater Depth at Offshore Boundary............ ....................58
3.3.11 Domain Length ...........___ ............ ......... .60

4 CONCLUSIONS ...................................................62

4.1 Summary...................... .. .......................62
4.2 D discussion and Conclusions ........................................... ............... 63
4.3 Recommendations for Further Work................................67

APPENDIX

A DERIVATION OF EQUATION FOR INFRAGRAVITY WAVE SURFACE
ELEVATION ...................................... ................................. ........ 69

A. 1 Second Order Partial Differential Equation..............................................69
A.2 Second Order Ordinary Differential Equation in the Frequency Domain...........70

B DERIVATION OF EQUATIONS FOR BOUNDARY CONDITIONS....................72

B 1 Shoreline B boundary Condition.............................................. 72
B.2 Offshore Boundary Condition............................... ................... 73
B.2.1 Characteristic Equations ............................... ............... 73
B.2.1.1 Incom ing bound wave ........................... ..... ............... 73
B.2.1.2 Outgoing free wave ............................. ............... 74
B.2.1.3 Combined Characteristic Equation................. .................74
B.2.2 Incoming Bound W ave Amplitude.................................. ...... ........75
B.2.3 Offshore Boundary Condition Equation............................................... 77

C VALUES OF ROOT MEAN SQUARE LONG WAVE SURFACE ELEVATION
FOR EACH TEST CA SE .............................................................................79

LIST O F R EFER EN CE S ..................................... ....................................................... ....... 83









SUPPLEM ENTARY REFERENCES ....................................................... 86

BIOGRAPHICAL SKETCH .................................................. ............... 90
















LIST OF TABLES


Table page

3-1 List of test cases with corresponding results section and equations ........................34

C-i Root mean square wave surface elevation for each test case, at the offshore
boundary and at 25 m seaward of the shoreline cutoff depth............... ...............79
















LIST OF FIGURES


Figure page

2-1 Definition sketch of coordinate axes............. ....... .................... 13

2-2 Definition sketch of the incoming short wave direction 0 ........................15

2-3 Definition sketch of infragravity wave direction: incoming bound wave angle
Oin, outgoing free wave angle ,,ut, and actual outgoing free wave angle Oout,actual
= ot + 7 ................................. .................. ..............19

2-4 Overlay of analytic and numerical solutions................................................ ...... 32

3-1 Model results for the base case: (a) root mean square long wave surface
elevation (r-hatrms), (b) significant wave height (Hs), and (c) bathymetric profile. 36

3-2 Effect of variation of peak wave period (Tp) (for offshore Hs=0.4 m) on (a) root
mean square long wave surface elevation (r-hatrms) and (b) significant wave
height (H). ......................................................38

3-3 Effect of variation of peak wave period (Tp) (for offshore Hs =0.7 m) on (a) root
mean square long wave surface elevation (r-hatrms) and (b) significant wave
height (H). ......................................................39

3-4 Effect of variation of peak wave period (Tp) (for offshore Hs =1.0 m) on (a) root
mean square long wave surface elevation (r-hatrms) and (b) significant wave
height (H). ......................................................40

3-5 Effect of variation of peak wave period (Tp) (for offshore Hs =2.0 m) on (a) root
mean square long wave surface elevation (r-hatrms) and (b) significant wave
height (H). ......................................................42

3-6 Effect of variation of peak wave period (Tp) (for offshore Hs =3.0 m) on (a) root
mean square long wave surface elevation (r-hatrms) and (b) significant wave
height (H). ......................................................43

3-7 Effect of variation of offshore significant wave height (Hs) (for T,=4 s) on (a)
root mean square long wave surface elevation (r-hatrms) and (b) significant wave
height (H). ......................................................44









3-8 Effect of variation of offshore significant wave height (Hs) (for T,=6 s) on (a)
root mean square long wave surface elevation (r-hatms) and (b) significant wave
height (H). ......................................................45

3-9 Effect of variation of offshore significant wave height (Hs) (for T,=8 s) on (a)
root mean square long wave surface elevation (r-hatms) and (b) significant wave
height (H). ......................................................46

3-10 Effect of variation of offshore significant wave height (Hs) (for T,=10 s) on (a)
root mean square long wave surface elevation (r-hatms) and (b) significant wave
height (H). ......................................................47

3-11 Effect of variation of offshore significant wave height (Hs) (for T,=12 s) on (a)
root mean square long wave surface elevation (r-hatms) and (b) significant wave
height (H). ......................................................48

3-12 Effect of variation of Jonswap peak enhancement factor (y) on (a) root mean
square long wave surface elevation (r-hatms) and (b) significant wave height
(H ). ............................................................... 49

3-13 Effect of variation of deep-water directional width (dir-widtho) on (a) root mean
square long wave surface elevation (r-hatms) and (b) significant wave height
(H ).. ............................. .................. ........ 51

3-14 Effect of variation of peak wave direction (0,) on (a) root mean square long
wave surface elevation (r-hatms) and (b) significant wave height (Hs).................52

3-15 Effect of variation of bottom friction coefficient (ff) on (a) root mean square
long wave surface elevation (r-hatms) and (b) significant wave height (Hs)...........53

3-16 Effect of variation of bar amplitude (a2) on (a) root mean square long wave
surface elevation (r-hatms), (b) significant wave height (Hs), and (c) bathymetric
profile. ............................. .................. ......... 55

3-17 Effect of variation of bar width on (a) root mean square long wave surface
elevation (r-hatms), (b) significant wave height (Hs), and (c) bathymetric profile.
......................................... ........................................ . 5 6

3-18 Effect of variation of distance of bar from shore (x,) on (a) root mean square
long wave surface elevation (r-hatms), (b) significant wave height (Hs), and (c)
bathym etric profile.. ............................... ............................... 58









3-19 Effect of variation of water depth at offshore boundary offshorer) on (a) root
mean square long wave surface elevation (r-hatrms), (b) significant wave height
(Hs), and (c) bathym etric profile.. .............................................. 59

3-20 Effect of variation of domain length (ld) on (a) root mean square long wave
surface elevation (r-hatrms), (b) significant wave height (Hs), and (c) bathymetric
profile. .........................................................61















Abstract of Thesis Presented to the Graduate School
of the University of Florida in Partial Fulfillment of the
Requirements for the Degree of Master of Science

NEARSHORE INFRAGRAVITY WAVE GENERATION: A NUMERICAL MODEL
AND PARAMETRIC STUDY

By

Eileen M. Czarnecki

August 2006

Chair: Andrew Kennedy
Major Department: Civil and Coastal Engineering

The purpose of this study was to develop and present a linear frequency-domain

numerical model of nearshore infragravity wave generation on an alongshore-uniform

beach, and then to utilize this model to investigate the importance of various parameters

in the generation of these infragravity waves. The numerical model was composed of

two parts: wave transformation and infragravity wave generation. Wave transformation

was modeled using linear wave theory. Infragravity wave generation was based on the

theory that these waves are forced by spatial changes in the radiation stresses associated

with the incoming short wave groups, then released to become free waves when these

short waves break near the shoreline, and subsequently reflected at the shoreline to

become outgoing free infragravity waves. The total infragravity wave surface elevation

was determined by summing all of the infragravity contributions due to difference

interactions between pairs of incoming short wave spectral components with frequency

differences in the infragravity range ( Af <: 0.05Hz). The results of the numerical









simulation of the low frequency wave climate indicated the relative importance of various

parameters in the generation of nearshore infragravity waves. These parameters affect

the infragravity wave response in the following manner: a higher peak wave period leads

to a higher magnitude of response; a higher offshore significant wave height leads to a

higher magnitude of response; a narrower directional width leads to higher magnitude of

response; increased bottom friction leads to a decreased magnitude of response; a

shallower bathymetric profile leads to an increased magnitude of response; a higher bar

amplitude leads to decreased magnitude of response, especially near the shoreline; a

wider bar leads to a slightly higher magnitude of response; the bar being closer to the

shore results in a narrower response pattern; obliquely incident waves lead to a decreased

magnitude of response at the offshore boundary, although peak wave direction has little

effect on response near the shoreline; a narrower frequency spectrum leads to a slightly

decreased magnitude of response.















CHAPTER 1
INTRODUCTION

1.1. Definition and Importance of Infragravity Waves

Infragravity waves, also known as long waves or surf beat, are defined as low-

frequency waves, with periods typically between 20 and 200 seconds (Henderson and

Bowen, 2002). In contrast to short-period waves, infragravity, or long-period, waves are

not obvious from visual observation because they cause a very slow variation of sea

surface elevation. Nevertheless, they are important in shallow water and contribute to the

majority of water surface elevation variance at the shoreline (Holman and Bowen, 1984).

Infragravity waves are thought to be important in the generation of nearshore currents

(Bryan and Bowen, 1998), harbor resonance (Janssen et al., 2003), nearshore sediment

transport, and bar formation (Bowen and Inman, 1971; Holman and Bowen, 1982).

1.2 Objectives

The objectives of the current study are two-fold. The first objective is to develop

and present a linear frequency-domain numerical model of nearshore infragravity wave

generation on an alongshore-uniform beach. The second objective is to utilize the model

to investigate the effects of various parameters on nearshore infragravity wave

generation.

1.3 Literature Review

The slow temporal variation of sea surface elevation in the nearshore zone was first

observed by Munk (1949) and Tucker (1950). Their observations showed that the low-

frequency infragravity motion was correlated with the incoming short-wave groups.









Longuet-Higgins and Stewart (1962, 1964) later hypothesized a mechanism for the

generation of infragravity waves: that these waves are forced, or bound, by spatial

changes in the radiation stresses associated with the incoming short wave groups, then

released to become free waves when these short waves break near the shoreline, and

subsequently reflected at the shoreline to become outgoing free infragravity waves.

Since that time, this theory has been explored extensively in analytical, numerical, field

and laboratory studies. Recently, an extensive cross-correlational study of laboratory

data conducted by Janssen et al. (2003) confirmed that the incoming bound infragravity

waves travel at the group velocity Cg of the incoming short wave groups and that the

outgoing free infragravity waves travel at the shallow water wave velocity gh The

numerical model presented in this thesis is based upon this radiation stress theory.

The other main theory of long wave generation by incoming short wave groups

involves a time-varying breakpoint (Symonds et al., 1982). The variation in wave

amplitude due to the wave groups would cause these incoming short waves to break at

different locations in a periodic manner. Theoretically, the time varying breakpoint could

generate free waves radiating both in the onshore and offshore directions. However,

research has shown that the long waves generated by a time-varying breakpoint are only a

small contribution to the total infragravity wave energy, compared to those generated by

spatial variation in radiation stresses associated with short-wave groups (List, 1992a,

1992b). In their cross-correlational study, Janssen et al. (2003) found no indications of

infragravity waves being generated at the breaker bar. Therefore, the model presented in

this thesis does not include a time-varying breakpoint.









As mentioned previously, the incoming infragravity waves are bound by the

incoming short wave groups. The outgoing free infragravity waves, depending on their

frequency and alongshore wave number, may refract repeatedly and be trapped near the

shoreline, traveling in the alongshore direction as edge waves, or they may continue to

travel in the offshore direction as leaky waves (Schaffer, 1994). Free waves are more

energetic than bound waves, both near the shore and in deeper water (Okihiro et al.,

1992; Herbers et al., 1994). The cross-shore structure of infragravity waves shows an

outgoing progressive wave at the offshore boundary and partial standing waves near the

shoreline, where edge waves often predominate (Symonds et al., 1982). The model

developed in this thesis produced the same cross-shore pattern of infragravity waves.

Lippmann et al. (1999) found that shear waves (instabilities in the alongshore current)

contribute to infragravity velocity variance; however, since shear waves do not

significantly affect the infragravity wave surface elevation, they are not considered as a

factor in the present model. Edge waves of the same frequency can resonate with each

other, and thus, it is important to include friction in numerical models in order to prevent

unbounded growth of infragravity waves (Reniers et al. 2002, Schaffer, 1993).

Bathymetry is another important factor in infragravity waves. Herbers and

colleagues (1995b) found that shoreline morphology affects the generation and reflection

of free infragravity waves and that the shelf-wide topography affects the propagation and

trapping of free infragravity waves. On barred beaches, edge waves tend to be trapped at

the location of the bar (Bryan and Bowen, 1998). Sallenger and Holman (1987) found

that the dominant peak of the infragravity wave surface elevation occurs at the bar crest.

Edge waves, which propagate in the alongshore direction, may be either progressive or









standing. Standing edge waves may be generated by topographic changes or obstructions

in the seabed which can act as reflectors (Huntley et al., 1981). Obviously, when

modeling infragravity waves, it is important to take into account the local bathymetry.

The numerical model presented in this thesis is based upon the two-dimensional

numerical model of infragravity wave generation developed by Reniers et al. (2002).

Reniers and colleagues (2002) assumed an alongshore uniform bathymetry in their model

and found that results of their numerical simulation compared well with field data

gathered at Duck, North Carolina. Later, in 2003, Van Dongeren and colleagues

explored whether modeling the bathymetry in two or three dimensions significantly

affects the numerical simulation of low frequency wave climate at Duck, North Carolina.

They found that long-shore variability in bathymetry had little effect on their results and

concluded that, for bathymetries that do not have much long shore variability, it is valid

to model infragravity wave generation in two dimensions.

1.4 Thesis Outline

The current Chapter 1 begins with a brief description of infragravity waves and

their importance. Next, the objective of the study is stated, followed by a literature

review of research on infragravity waves. Chapter 2 presents a detailed description of the

numerical model. Chapter 3 presents results of the model, used to investigate the low

frequency wave climate under varying conditions, in order to determine the importance

of various parameters and their effects on infragravity wave generation. Chapter 4

includes a summary, conclusions, a discussion of results, and recommendations for

further work. Appendix A and Appendix B give detailed derivations of the main

equations that constitute the numerical model. Appendix C tabulates the results of the

numerical model for each test case described in Chapter 3. The list of references cited in







5


this thesis is followed by supplementary references pertinent to the topic of infragravity

waves.














CHAPTER 2
NUMERICAL MODEL

2.1 Conceptual Overview

The numerical model developed in this chapter is composed of two main parts: (1)

wave transformation, and (2) infragravity wave generation.

The two main inputs for the wave transformation model were the bathymetry and

the wave spectrum (which was composed of many frequencies and directions).

Equations for wave transformation were based on linear wave theory.

The numerical model of infragravity wave surface elevation was based upon the

model presented by Reniers et al. (2002), with some modifications. This model

mathematically describes the generation of infragravity waves, which are composed of

incoming bound waves generated by pairs of incoming short wave components and

outgoing free waves that are generated by reflection of the incoming waves at the

shoreline.

2.2 Bathymetry

The bathymetric profile was assumed to be uniform in the alongshore (y) direction

and was modeled in the cross-shore (x) direction as an equilibrium beach profile with an

alongshore bar superimposed. The equation for the equilibrium beach profile (Dean and

Dalrymple, 2002) is

h(x)= Axy (2.2.1)









where h represents water depth, x represents the cross-shore coordinate, and A is the

profile scale factor. The equation for the bar, given by Yu and Slinn (2003) to

approximate the alongshore bar measured at Duck, North Carolina, is


h(x) = -a, exp 5 x x (2.2.2)


where a2 is the bar amplitude and xc is the distance of the center of the bar from the

shoreline. In equations (2.2.1) and (2.2.2), x = 0 at the onshore boundary. However,

since the numerical model requires that x = 0 at the offshore boundary, the order of the x

vector was reversed according to

x = Xshore -xe (2.2.3)

in order to satisfy this condition. Equations (2.2.1) through (2.2.3) were combined to

form the equation for the bathymetric profile


h(x') = Ax' -a exp (2.2.4)


with an onshore water depth of 0.25 m and a maximum onshore slope of 1/20. In

equation (2.2.4), c, is the bar width coefficient.

2.3 Wave Spectrum

The wave spectrum describing the incoming short waves was composed of a

frequency spectrum and a directional spectrum. The frequency spectrum was modeled as

a Jonswap frequency spectrum. The expression for the Jonswap spectrum is given by

Kamphius (2000) as

-4
ag y2 exp(a) 5 f
SA, f )= aexp -2 (2.3.1)
(2;r)45 4 fp









In the above equation,fis the frequency,f, is the peak frequency, g is the gravitational

constant, y is the peak enhancement factor (with a higher value of y implying a narrower,

more peaked frequency spectrum), a is a coefficient related to frequency, and aj is a

coefficient related to the wave-generating conditions. The coefficient a is given by


a 22 (2.3.2)


where

3 = 0.07 for f < fp, and 3 = 0.09 for f > fp. (2.3.3)

The coefficient aj is given by


a = 0.076 gFJ 022 (2.3.4)


where F is the fetch length and U is the wind velocity. In this model, fetch length was

assigned the value of F = 1000 m, and wind velocity was assigned the value of U= 5 m/s.

The offshore significant wave height Hs was specified as an input value, which was

then converted to the root mean square wave height (Hrm,).

H,,,,, = H,2 (2.3.5)

The frequency spectrum was then proportioned to the root mean square wave height

(Hrm,) according to the equation


H,,,,, = (2.3.6)


where p is the density of seawater and E is the total spectral energy, equal to the sum of

the energies of each individual frequency component. The spectral frequency resolution

was set at 0.00083 Hz, to give a total of 602 components.









The directional spectrum was calculated as

D(O)= cos"(0-0) (2.3.7)

In the above equation, m determines the directional width of the spectrum (with a higher

value of m corresponding to a narrower spectrum), 0 is the incoming short wave

direction, and O, is the peak incoming short wave direction. The peak wave direction (0p)

and the deep water directional width (dir-widtho) were specified as input for the

directional spectrum. The deep water directional width (dir-widtho) was related to the

directional width at the offshore boundary (dir-widthi) by the following equation:

ko sin(dir 1i /,h.,) = k, sin(dir 1i //h,) (2.3.8)

where ko and k1 are the wave numbers in deep water and at the offshore boundary,

respectively. The value of m in equation (2.3.7) was chosen to match the directional

width at the offshore boundary. The directional spectrum was then normalized such that

the area under the spectrum was equal to one.

Finally, the frequency and directional spectrums were combined into one spectrum,

with one direction per frequency, according to the following equation:

S(f,0)= S,(f)D(O) (2.3.9)

2.4 Wave Transformation

The two main inputs for the wave transformation program are the bathymetry and

the wave frequency-directional spectrum. For each component of the frequency-

directional spectrum, the wave length, celerity, and wave number, wave angle, and

energy dissipation were calculated.

From linear wave theory (Dean and Dalrymple, 1991), deep water wave length Lo

and deep water wave group velocity cgo were










L= gT(2.4.1)


Cgo = L1T (2.4.2)

where Tis the wave period (s), calculated as the inverse of the wave frequency (Hz).

The wave length L, the wave celerity c, the wave number k, and the wave group velocity

cg were calculated (from linear wave theory) for each component frequency, at each

cross-shore location:


L = L, tanh 2z (2.4.3)


c= LT (2.4.4)


k =2 (2.4.5)


c = c I+-kh (2.4.6)
g 2 sinh(2kh) (2.4.6)

The wave angle 0 was calculated for each wave component, at each cross-shore

location, from Snell's law, as


i = sin- C *sin (2.4.7)


where j represents the cross-shore location.

Energy dissipation was based upon the model presented by Reniers and Battjes

(1997). The dissipation S is given by the differential equation


d (Ecg cos)= S (2.4.8)
dx

where










S = aH 2Qb (2.4.9)
4T max
P

In the above equation, p is the density of water, g is the gravitational constant, Tp is the

peak period, a is a coefficient (equal to one in this model), Qb is the fraction of breaking

waves, and Hmax is the maximum wave height. The fraction of breaking waves Qb

(Battjes and Janssen, 1978) is given by the implicit relationship


Qb = exp b )2 (2.4.10)
Hrms1 max

The maximum wave height is given as


H 0.88 tanhi2 (2.4.11)
k k 0.88)

with the wave breaking parameter yb given as


b =0.5 + 0.4tanh 3Hrso"" (2.4.12)


In the above equation, Lo and Hrmso (root mean square wave height in deep water) were

defined from the peak values in the spectrum, with


rms0 rms,offshore Cg peak (2.4.13)
cg0, peak

The Newton-Raphson method of root-finding (Hornbeck, 1975) was used to solve

equation (2.4.10).

The energy dissipation and thus the wave height at each cross-shore location was

calculated for each wave component by using forward differences to estimate the

differential equation (2.4.8).









2.5 Long Wave Generation

2.5.1 Governing Equations

The continuity equation and the cross-shore and alongshore momentum equations

form the basis of the numerical model. The equation for infragravity wave surface

elevation was derived from these three basic linearized long wave equations, given

below. These equations assume that q, u, and v are small and therefore, that the nonlinear

terms can be neglected.

Long wave continuity equation:

aq 0(hu) 0(hv)
+ + = 0 (2.5.1)
at x 9y

Cross-shore momentum equation:

au a7n aSxx aSx
ph -+pgh (2.5.2)
at ax ax ay

Alongshore momentum equation:

Qv Qy 9Sxy 9Syx
ph +pgh- as aS- (2.5.3)
at 9y y ax

In the above equations, r represents the infragravity wave surface elevation, u represents

the cross-shore velocity component, v represents the along-shore velocity component, t

represents time, and x and y represent the coordinate axes. In this model, the x-axis is

oriented in the cross-shore direction, with x=0 at the offshore boundary. The y-axis is

oriented in the along-shore direction. A definition sketch of coordinate axes is given in

Figure 2-1. S Sy, and Syy represent the radiation stresses, which force the infragravity

waves. Radiation stress symbolized as Smn represents the flux of the m-component of









momentum in the n-direction. Thus, for example, Sy represents the flux of the x-

component of momentum in the y-direction.


y





10
O c





Figure 2-1. Definition sketch of coordinate axes

2.5.2 Infragravity Wave Surface Elevation

Equations (2.5.1)-(2.5.2) were combined into one equation. This resulted in the

second order partial differential equation for infragravity wave surface elevation:

1 a2u dh7 a8 ch 1 aS 2a2S 5$2S(
+h + +h + + (2.5.4)
g t2 g at X2 dx ax ay pg dx 8x8y ay 2


with the linear damping term a7 added in order to prevent unbounded growth in the
g at

case of infragravity wave resonance. The term [t is a resistance factor, given by

p(x) = f,/V(x) (2.5.5)

and ff is an empirical coefficient of bottom friction. The derivation of equation (2.5.4)

is given in Appendix A.

Equation (2.5.4) was transformed into a series of second order ordinary differential

equations (2.5.6) in the frequency domain so that it could later be solved using finite

difference representations of derivatives with respect to x.









h d dh d + 4;-2Af2 iu27rAf hAk2 2
h-+- + --- hAk 7
dx2 dx dx) g g Y

drA d2S +2iAk y +k 2S (2.5.6)
dx2 y dx y

The derivation of equation (2.5.6) is given in Appendix A.

This transformation necessitates defining functional representations of infragravity

wave surface elevation r, and radiation stresses Sx, Sx, and Syy:


)(x, y, t, f,, f,, k,,, k,2) = I r(x, f,, f2, k,,, k,,) exp[i(2rAft Aky)+ (2.5.7)


Sx(x,y,t, fl, f2k,k,ky2) l=SI(x, f,ky,ky2)exp[i(2;Aft -Ak yY)]+* (2.5.8)


S,(x,y,t, f,, f,1,f,,k,2)= I (x, f,, f,k,k 2)exp[i(2Aft-Ak y )]* (2.5.9)
2


S,(x, y, t,,, f,, k, k2) = (x, f,, f, k, k) exp[i2Aft Ak y)]+* (2.5.10)
2

where is the complex conjugate, and frequency and wave number are from a

combination of two incoming short wave spectral components (indicated by the

subscripts 1 and 2).

The infragravity wave frequency is defined as

Af = f, f2 (2.5.11)

The radial frequency is defined as

cr = 2.Af (2.5.12)

The alongshore wave number is defined as

Aky = ky = ky2 = k sin -k sin (2.5.13)









where 0 represents the incoming short wave direction. The cross-shore wave number

(which will later be used to calculate the amplitude of infragravity wave surface elevation

77 and the amplitudes of the radiation stresses S, Sx,, and S,) is defined as

Ak, = k, k = k, cosO, -k, cosO, (2.5.14)

A definition sketch of the incoming short wave direction 0 is given in Figure 2-2. The

wave direction of each incoming short wave component was between -7T/2 and 7T/2

radians. Wave angles were measured with respect to the positive x-axis, according to the

right-hand-rule (counterclockwise positive and clockwise negative).

7c/2




x






7/2

Figure 2-2. Definition sketch of the incoming short wave direction 0

In order to numerically solve equation (2.5.7), derivatives of i (and similarly of S, and
S,) were estimated using second order central differences.

= -(2 .5.15)
9x 2 Ax


(2.5.16)
2x Ax2

where the subscript j represents the cross-shore (x) location and Ax represents the grid

resolution, which was set to 5 m in this model. The central difference equations were









substituted into equation (2.5.7), in order to obtain the solution for (7 at a typical

cross-shore locationj.

h, dh 1 4iA2 f2 i2rAf 2 2h, h, dh 1
Ax2 dx 2Ax 1 g g x 2 x2 dx 2AxJ+ 1


I -S +2S -S S -S
I -(+1) + 2xj) XX-1) +iAk xy+1) xy1-)/ Ak 2
Pg A2 A y

(2.5.17)

In equation (2.5.17), r, is unknown, the right hand side consists of known quantities

which may be calculated numerically, and the coefficients of Q^, 77, and ,,,1 may also

be calculated numerically.

Equation (2.5.17) is valid at all interior points in the cross-shore grid. It was solved in

matrix form and was represented as

a _1 + bj + c 1 = Rj (2.5.18)

with additional coefficients at the onshore and offshore boundaries.

The coefficients of equation (2.5.18) are

h dh 1
a _2 dx 212 (2.5.19)



bi = f- h, Ak _2 (2.5.20)
[ g g J y Ax 2


= h dh\ 1
cJ 2 d+ 2AX- (2.5.21)


and the right-hand-side is










R =1 SJ+)+2J) + 2-) + iAk xy(J+) xy(J-1)+ 2 (2.5.22)
pg 2 A Ax


Note that j goes from 1 to n, with j = n at the shoreline and j = 1 at the offshore boundary.

Forj = 1 to n, if n = 6, the matrix would be set up as such:

bi c, d, 0 0 0 I R,~
a2 b2 c2 0 0 0 72 R2
0 a b3 3 0 0 3 R
3 3 3 3 3 (2.5.23)
0 0 a4 b4 4 0 4 R4
0 0 0 a5 b5, c,5 R,
O 0 0 z6 a6 b,6 R

The coefficients b c1, and d6 and z,, an, and b, as well as right-hand-sides R1 and Rn will

be defined in the following section on boundary conditions.

2.5.3 Boundary Conditions

Boundary conditions were needed because: (1) at the shoreline, equation (2.5.17)

would have terms with the subscript (j+1), and atj = n, (j+1) does not exist; and (2) at the

offshore boundary, equation (2.5.17) would have terms with the subscript (j-1), and atj

=1, (j-1) does not exist. Thus, boundary condition equations were formed by

mathematically describing the conditions at both the shoreline and at the offshore

boundary. Second order backward differences were used to estimate the derivatives at

the shoreline boundary; second order forward differences were used to estimate the

derivatives at the offshore boundary.

2.5.3.1 Shoreline boundary condition

At the shoreline boundary, where j = n, it was assumed that there exists a "wall" at

a very small depth. Then, obviously, un = 0, since there could be no x-directed velocity

through that wall. This assumption was applied to equation (2.5.2) in the frequency









domain, using the second order backward difference representation for derivatives with

respect to x, to obtain

(1 2 3 1 3,(n 4S + 2) Sn)
2 + -- + 1 "=i -QA -- --;M. Sln)
K2Axj 2 Ax I 2Axf pghn 2Ax

(2.5.24)

The complete derivation of this equation is given in Appendix B.

Equation (2.5.24) forms the shoreline boundary condition for the matrix (2.5.23)

and may be represented as

zA-2 + ank-I +b,,A = Rn (2.5.25)

with coefficients






( =(2.5.27)
-22













2.5.3.2 Offshore boundary condition

At the offshore boundary, it was assumed that the overall long wave surface

elevation was formed by the superposition of the incoming bound and outgoing free

waves, such that

r = -r +routS (2.5.30)
)7 = )7b +)out (2.5.30)









where wave surface elevation for the incoming bound wave subscriptt b) and the

outgoing free wave subscriptt out) were defined as


7b = 7 exp(i[ot K,, (x cos O,, + y sin 8, }+ (2.5.31)



2ou = 2 q,,, exp{i[ot + K0o, (x cos 6,,, + y sin )] + *(2.5.32)



Wave angles 0,, and O,,t were measured with respect to the positive x-axis,

according to the right-hand-rule (counterclockwise positive and clockwise negative). A

definition sketch of infragravity wave direction is given in Figure 2-3.

7c/2





Oout,actual in X

out a




-7t/2

Figure 2-3. Definition sketch of infragravity wave direction: incoming bound wave angle
Oin, outgoing free wave angle Oout, and actual outgoing free wave angle
Oout,actual = 0out + 71

The value of the incoming bound wave angle 0,n was between -7T/2 and 7T/2 radians. The

outgoing free wave angle O0ut was defined such that its value was also between -7T/2 and

7T/2 radians. This was done because, for inverse trigonometric functions, Matlab returns a

value between -7T/2 and 7T/2 radians, and But would have to be calculated using the









inverse sine function (according to equation (2.5.39)). However, the actual value of 0out

was

outactual = out + (2.5.33)

The wave number of the incoming bound wave, Kn, was defined as


K,, = Ak+ Ak2 (2.5.34)

where

Ak = K,,, cosO,, (2.5.35)

Ak, = K,, sin 8,, (2.5.36)

The wave number of the outgoing free wave, Kout, was defined as


Kot = k +kk. (2.5.37)

where

kx,,, = Ko,, cos0B,, (2.5.38)

Ak5 = -Ko,, sin 6,,, (2.5.39)


Equivalently, since the speed of the outgoing free wave is Vgh ,

Ko,, = 2TAf/ gh (2.5.40)

Given the above expressions, equations (2.5.31) and (2.5.32) may be expressed

equivalently in terms of wave numbers:


7b = 1 exp(- iAkx)exp[i(2;TAft Ak,y)]* (2.5.41)
2


7out 17b exp(kxoux)exp[i(2'Aft Ak,y) +* (2.5.42)









The offshore boundary condition was formed by starting with characteristic

equations for both the incoming bound wave and the outgoing free wave. The

characteristic equation for the surface elevation of the incoming bound wave is

a77b 2.'zAf a77b 2.'zAf a77b
+ cos + sinO = 0 (2.5.43)
at K rn Ox K y

The characteristic equation for the surface elevation of the outgoing free wave is

077o t k amut Aut Ak out
- gh k+ gh k =0 (2.5.44)
at Kout ax K0 Qy

Equations (2.5.43) and (2.5.44) were combined with 7 = b, + out to obtain


7 gh kx j7+ V-Ak^au
ig h ~ a7 + gh K 0 1a
at Kou ') Kout C
St 2Af cs Ak 2Af O 17b (2.5.45)
+ cosrn + sgh K -0 sin J
Kou8 Kaot K I y

Equation (2.5.45) was the starting point for forming the offshore boundary condition. The

derivation of this equation as well as proof that equations (2.5.43) and (2.5.44) are

characteristic equations for rb and fout are given in Appendix B.

The amplitude ?b of the incoming bound wave was obtained analytically by

applying equation (2.5.4) to the incoming bound wave at the offshore boundary.

Akxt) 21 2 ) + 2Akx1)AkS + Ak2,, (1)
4p;r2Af2 2ipu,Af pghAkx()2 pgh, Ak2

In the above equation, the subscript 1 represents the cross-shore location at the offshore

boundary. The radiation stress amplitudes Sx, S, and S, were also found analytically

and will be discussed in section 2.5.4. The derivation of equation (2.5.46) is given in

Appendix B.









Finally, equation (2.5.45) was transformed into the frequency domain. Then, using

the second order backward difference representation for the derivative of 7 with respect

to x, the offshore boundary condition equation (2.5.47) was obtained.

S 3 k A 2 Vgh\ r Vgh kx0, t ( g
i;rAf +- gh k + + 77
4Ax Kout 2 Ko) Ax K) y 4Ax Ko)
2ld 2 2ld Old

= iAkx + cosV + iAk + sin 8,
2 Kout Kin 2 1 K out Kin)

(2.5.47)

The complete derivation of this equation is given in Appendix B.

Equation (2.5.47) forms the shoreline boundary condition for the matrix (2.5.23)

and may be represented as

b,7, +c,, +dI, =3 RI (2.5.48)

with coefficients


b Af xough Ak1 2 gh (2.5.49)
4Ax K 2 Ko)


c, = h (2.5.50)



d= 4 Kagh (2.5.51)


and the right-hand-side


2 K in 2 (out n 2.5.52)

(2.5.52)









2.5.4 Derivation of Radiation Stress

Radiation stresses were derived from the wave energies of the incoming short

waves. The free surface elevation C of a component incoming short wave is

1H
= exp(iyV)+* (2.5.53)
22

where the component wave height H is a real number, and where the short wave phase

function x is defined by its derivatives, as follows:


= -kcosO (2.5.54)


= -k sin 0 (2.5.55)
ay


S=a (2.5.56)


Recall that the wave number k and the wave angle 0 of the incoming short wave are

functions of x. Also, the long wave phase q is

0 = (2TAf Akyy) (2.5.57)

where AkA = K,,, sin 0,,, and neither K,, nor 0,r are functions of x.

The numerical model employs a large number of component incoming short waves,

such that the free surface elevation is


S= Y,. (2.5.58)
m=l

where m is the individual component and Nis the total number of components. The

square of the free surface elevation C2 can be represented in summation notation. The









following formula shows that C2 can be reduced to two-component interactions of

incoming short waves.

N N-1 N
=2 ;- 2 + 2V Y, ;, (2.5.59)
m=l m=1 n=m+l

where

2i H f2 2
r2n = m exp(2iVy)+ m exp(- 2i V,) + H (2.5.60)
16 16 8


2-m(,-n HmHn exp[i(ym + V, )+ H n exp[i(y, -V n)]
8 8 (2.5.61)
+ HmHn exp[- i (ym + l, )+ H exp[i(V, m )]
8 8

Terms involving summing the phases of the two component incoming short waves, such

as Vf, + n, or 2 Vf, are high frequency terms. Terms involving the difference of the

phases of the two component incoming short waves, such as Vm f, or Vf, Vm, are low

frequency terms. Terms with no exponential are steady terms. High frequency terms will

be discarded, since this numerical model involves radiation stresses that force the long

waves, which are, by definition, low frequency waves. From equations (2.5.60) and

(2.5.61), keeping only the low frequency and steady terms,


2 ow = mn exp[i(Vy Vn)]+* (2.5.62)
8

fi 2
msteady =- (2.5.63)


Next, the radiation stresses S, S, and S, were derived in terms of the

component wave heights. The general equations for radiation stress, valid only for steady

or slowly varying waves, (Dean and Dalrymple, 1991) are










S, = En(cos20+1) -1 (2.5.64)



S, =E n(sin20+1)-1 (2.5.65)


S = Sy = nsin20 (2.5.66)
"2

where

n = c c (2.5.67)

As mentioned previously, S., is the wave momentum flux in the x-direction of the x-

component of momentum, Syis the wave momentum flux in the y-direction of the y-

component of momentum, and Sy is the wave momentum flux in the x-direction of the y-

component of momentum. Since the general equation for wave energy is


E = pgH2 (2.5.68)
8

then the radiation stresses are proportional to the wave heights squared. The component

wave heights H were obtained from the component energies of the input wave energy

spectrum according to equation (2.5.68).

The radiation stresses S^,S S, and S, were calculated at each cross-shore location,

for each arbitrary combination of two incoming short wave components. Low frequency

radiation stresses were derived from the interaction between two different components,

for difference frequencies within the infragravity range ( Af: < 0.05Hz). Steady radiation

stresses were derived from component self-self interactions.

For the low frequency components of radiation stresses, the average incoming

wave angle 0a, and the average ratio nv were used, where









o,, = (, +O)/2 (2.5.69)


n2= [cg +fcg /2 (2.5.70)


The low frequency wave energy is

Eow =Pg;lw (2.5.71)

In terms of wave heights, this may be written as


EHow = pg ,, exp[i(,m -V ,)]+* (2.5.72)

The steady wave energy is

1
Eteady = PgCseady =1 2 m (2.5.73)
8

Equations (2.5.8)-(2.5.10) give functional representations of the low frequency

components of radiation stress. However, the total radiation stress at any cross-shore

location is composed of both the steady and low frequency (unsteady) components,

which can be represented in summation notation as


Stota = ZS steady + S,,ow exp[i(2Aft Ak)] + (2.5.74)


Syotal = Soysteady + IS ,,ow exp[i(2rAft Aky)]+* (2.5.75)
2


S0,tot0 =Sns.Ptearp +- nZSo exp[i(2'Aft -Aky)]+* (2.5.76)

2.5.4.1 Steady radiation stress

The steady component radiation stresses are


Smstea = Esteady nm(cos2 m +1)- ] (2.5.77)









Symea = Estea [n (sin2 Om +1)- (2.5.78)
om,steady sey 21


.nymsrtea = -- (n1 sin 20,) (2.5.79)

2.5.4.2 Low frequency radiation stress

The low frequency (unsteady) component radiation stress amplitudes are

Sxx low = lw no,(cos Ol, + 1)- (2.5.80)


w = ow na(sin 2a, +1)- (2.5.81)


E, = w (n sin 2O a) (2.5.82)


It can be seen from equation (2.5.72) that the low frequency wave energy E1ow is a

function of the incoming short wave phase Vy(equations (2.5.54)- (2.5.56)), which is a

function of both x, y, and t. In order to obtain the low frequency components of radiation

stress at each cross-shore or x-location, it was necessary to know the phase at each cross-

shore location. In the numerical model, it was assumed that y = 0 and t = 0 for all x and

that Vf= 0 at the offshore boundary. Thus, with this simplifying assumption, the short

wave phase ywas considered to be a function of x only. Then, from equation (2.5.54)

for y'/8x and from forward differences, Vwas calculated at each location in the cross-

shore, beginning at the offshore boundary and continuing towards the shoreline, using the

following formula (where j represents the cross-shore location)

y,1 = Ax(- k, cosO )+ y, (2.5.83)









2.6 Root Mean Square Long Wave Surface Elevation

As stated previously, this numerical model combines two component incoming

short waves from the input frequency-directional spectrum. Every possible combination

of components was calculated, such that each component was combined with every other

component, including itself. When two different components, with difference

frequencies within the infragravity range ( Af < 0.05Hz), were combined, the result was

the forcing of a long wave. When a component was combined with itself, the result was

setup or setdown, as will be described in the following section on mean water level.

Since the long wave surface elevation 7 is a periodic function, it is appropriate to

represent its amplitude as a root mean square. Thus, the root mean square wave surface

elevation, is given by


ms(j) ( m jO) 2 (2.6.1)

where m,n indicates the combination of two different components andj represents the

cross-shore location. Note that the term r,,,,( in equation (2.6.1) is equivalent to r,

from equation (2.5.17).

2.7 Mean Water Level

As stated in the previous section, when a component was combined with itself, the

result was setup or setdown. At the offshore boundary, the mean water level is given by

linear wave theory (Dean & Dalrymple, 1991) as

a2k + C() (2.7.1)
2sinh2kh g

where a = H/2 and C(t) = 0 if the mean water level is zero in deep water. Thus, the

mean water level for each wave component at the offshore boundary is given by









i= k (2.7.2)
8 sinh 2kh

The mean water level at each location in the cross-shore was derived from the

cross-shore momentum equation (2.5.2), where r is the water surface elevation, and S,

and Sx are the steady components of radiation stress. Taking the time average,

9u/at = 0, and thus the equation reduces to

a1steady 1 Sx,steady aSxy,steady |, -
h 1(2.7.3)
ax pg x y

where the long wave phase 0 = 0 for a steady wave and thus

o7steady 1 steady
(2.7.4)
ax 2 ax

sxx, steady 1 x,steadyv 7
ax 2 ax

dS 1
asxy, steady 1 I
xystea = --iykS (2.7.6)
ay 2 xysteady(

Then, using forward differences to estimate derivatives with respect to x, one obtains

h hj 1 xxsteady, xx,steady .
steady+=1 steady Ak Sxy,steady j (2.7.7)
Ax A Ax 9x Ax


where j represents the cross-shore location. Since AkA = 0 when the two incoming short

wave components are the same, the above equation reduces to


steady ~ = steady xx,stead vj+ xx,steady) (2.7.8)


Thus, the mean water level or setup is calculated from steady, for each self-self

interaction of incoming wave components, at each cross-shore location, beginning with










steady = r at the offshore boundary. Then, the sum of seady for all components gives the

mean water level at each cross-shore location.


IWL(J) I'tea-(j) (2.7.9)
m

where m represents the self-self combination of an incoming wave component,andj

represents the cross-shore location.

The accuracy of this calculation was checked by assuring that the mean water level

at the shoreline was approximately 15% of the breaking wave height and also

approximately equal to the magnitude of root mean square infragravity wave surface

elevation multiplied by F2 .

2.8 Model Validation

The model was validated by analytically solving the second order partial

differential equation for infragravity wave surface elevation (equation (2.5.4)) for a

simple test case: a simple input spectrum of two incoming wave components each with

wave direction 0 = 0O, no bottom friction ([t = 0), a flat bed with a constant water depth of

3 m, and a reflecting boundary condition at the shoreline. The simplified version of

equation (2.5.4) for these given conditions is given by equation (2.8.1). Additional

criteria for the simple test case were fi = 0.19 Hz, f2 = 0.20 Hz, and domain length = 7000

m.

The governing second order partial differential equation for infragravity wave

surface elevation was

1 02 7 21 1 02S.
g +h pg (2.8.1)
g Ot2 a2 2g a2


which is satisfied everywhere in the domain by









1 = 7b + 1f (2.8.2)

where 1ib (bound wave) is the particular solution to equation (2.8.1), given by


7b = Ib exp[i(2;Aft Akx)]+ (2.8.3)
2

and where ?if (free wave) is the homogeneous solution to equation (2.8.1), given by


r7f = j exp 2 2fAft 2, f x] + 2- 2f exp i 2rAft + 2f x +* (2.8.4)
2 2 _gh

The amplitude ?b of the incoming bound wave was already solved analytically (equation

(2.5.46)), which simplifies for this test case to

Ak 2
b = S (2.8.5)
2+ 2. 2Af2 2+ g


where Sxx is equivalent to S^ at x = 0 and is constant across the domain because of the

constant depth.

The shoreline boundary condition was taken from the cross-shore momentum

equation (2.5.2), for u = 0 (for perfect reflection at the shoreline) and Aky = 0 (from all 0

= 00), reduced to

07 dx pgh x

The offshore boundary condition was taken from equation (2.5.45), reduced to


d- gh r a2AfBb (2.8.7)

with K,, = Akx since Aky = 0. By substituting equations (2.8.2) (2.8.4) into the

boundary conditions, one obtains ,jf = 0 and










2f() exp -i KAkx + 2fx 1 (2.8.8)
2;TAf pgh [h

where the subscript j represents the cross-shore location. Then, making substitutions into

equation (2.8.2), the analytic solution for the infragravity wave surface elevation is


= Iexp(i2zAf) k exp(- iAkx) + ) exp .2,Af (2.8.9)
2 L I gh J_

The root mean square wave surface elevation for the analytic solution was then calculated

as


77rs(J) = -exp(- iAkx- )+ 2f exp igh x (2.8.10)


The results of the analytic solution (7r,,,,) were then compared to the results of the

numerical solution used by the model (7,,, ), equation (2.6.1). Figure 2-4 shows an

overlay of the analytic and numerical solutions for the simple test case discussed in this

section. Both solutions show an almost complete standing wave across the entire cross-


0.2

E 5 I I I I I I fI
0.1 I I I
I I I I I I I I I
005 I I I

0 1000 2000 3000 4000 5000 6000 7000
x(m)

Figure 2-4. Overlay of analytic (77,r ) and numerical (7,, ) solutions. Legend: -- 7,,,,

Irmp









shore domain. A test of errors in the numerical solution showed that errors in the root

mean square infragravity wave surface elevation converged to the exact solution with

second-order accuracy.














CHAPTER 3
NUMERICAL SIMULATION OF LOW FREQUENCY WAVE CLIMATE

3.1 Use of the Model

The model described in Chapter 2 was used to investigate the low frequency wave

climate under varying conditions. Conditions were varied according to eleven basic

parameters: offshore significant wave height, offshore peak period, the Jonswap peak

enhancement factor, deep water directional width, peak wave direction, bottom friction,

bar amplitude, bar width, distance of the bar from the shore, water depth at the offshore

boundary, and domain length. Table 3-1 lists the test cases with the corresponding results

section and relevant equations for each case. The base case was the basis against which

all other test cases were compared. The parameters for the other test cases are reviewed

in section 3.2.

Table 3-1. List of test cases with corresponding results section and equations
Test Case Results Section Relevant Equations
Base Case 3.3.1
Offshore Significant Wave Height (Hs) 3.3.2 (2.3.5)
Offshore Peak Period (Tp) 3.3.2 (2.3.1)
Jonswap Peak Enhancement Factor (y) 3.3.3 (2.3.1)
Deep Water Directional Width (dir-widtho) 3.3.4 (2.3.8)
Peak Wave Direction (Op) 3.3.5 (2.3.7)
Bottom Friction (ff) 3.3.6 (2.5.4)-(2.5.5)
Bar Amplitude (a2) 3.3.7 (2.2.4)
Bar Width (c,) 3.3.8 (2.2.4)
Distance of Bar From Shore (xc) 3.3.9 (2.2.4)
Water Depth at Offshor Boundary offshorer) 3.3.10 (2.2.4)
Domain Length (ld) 3.3.11 (2.2.4)









3.2 Parameters

Significant wave height (Hs) at the offshore boundary, peak period (Tp), and the

Jonswap peak enhancement factor (y) were specified as input for the Jonswap frequency

spectrum. The offshore significant wave height (Hs) is given by equation (2.3.5). The

peak period (Tp) was calculated as the inverse of the peak frequency (f,). Both the peak

frequency (fp) and the Jonswap peak enhancement factor (y) are given in equation (2.3.1),

which defines the Jonswap frequency spectrum. The deep water directional width (dir-

widtho) and peak wave direction (0p) were specified as input for the directional spectrum

(equations (2.3.7)-(2.3.8)). The coefficient of bottom friction ff influenced the

infragravity wave response (see equations (2.5.4)-(2.5.5)) and served to prevent

unbounded growth in the case of infragravity wave resonance. The remaining parameters

were specified as input for the bathymetric profile (equation (2.2.4)): bar amplitude (a2),

bar width coefficient (c,), distance of the bar from the shore (xc), domain length, and

water depth at the offshore boundary, which was varied by varying the profile scale

factor (A).

3.3 Results

3.3.1 Base Case

The base case was the basis against which all other test cases were compared. The

parameters for the base case were as follows: offshore significant wave height Hs = 1 m,

offshore peak period Tp = 8 s, Jonswap peak enhancement factor y = 3.3, deep water

directional width dir-widtho = 150, peak wave direction O, = 0O, coefficient of bottom

friction ff= 1/200 s-1, bar amplitude a2 = 1.5 m, bar width coefficient c, = 5, distance of

the bar from the shore xc = 120 m, water depth at the offshore boundary offshore = 10.09 m

(from the profile scale factor A = 0.1 m), and domain length Id = 1000 m.










Figure 3-1 shows the model results for the base case. Part (c) of this figure displays

the bathymetric profile. Unless otherwise noted, this is the bathymetric profile used in the

subsequent test cases. Part (b) of this figure shows the transformation of significant wave

height (Hs); as the incoming short waves approach the shore, they shoal and break.


0.2


0.1


100 200 300 400 500 600 700
x(m)


800 900 1000


100 200 300 400 500 600 700 800 900
x(m)


1000


-5-


-10


-15
0 100 200 300 400 500 600 700 800 900 1000
x(m)


Figure 3-1. Model results for the base case: (a) root mean square long wave surface
elevation (r-hatrms), (b) significant wave height (Hs), and (c) bathymetric
profile.


(a)II I




-









As expected, wave breaking is pronounced in the region of the bar. Part (a) of Figure 3-1

displays the root mean square long wave surface elevation (r-hatms), calculated from

equation (2.6.1)*. As expected, at the offshore boundary, the infragravity wave has a

small magnitude, and near the wave breaking region, the infragravity wave has a larger

magnitude; a time animation of model results showed the pattern of a small outgoing

infragravity wave at the offshore boundary and a larger magnitude partial standing wave

near the wave breaking region. The vertical line near the shoreline indicates the cutoff

depth. The cutoff depth was calculated, for each case, as the shallowest depth greater

than 0.5 m; shoreward of this cutoff depth, the model results are considered to be invalid.

For the base case, the cutoff depth was 0.59 m. At the offshore boundary, the root mean

square long wave surface elevation was 0.042 m; 25 m seaward of the shoreline cutoff

depth, the root mean square wave surface elevation was 0.140 m. Appendix C tabulates

the values of the root mean square long wave surface elevation at the offshore boundary

and at 25 m seaward of the shoreline cutoff depth, for each test case.

3.3.2 Offshore Significant Wave Height and Peak Period

Figures 3-2 3-6 show the effect of variation of peak wave period (Tp) on model

results, for offshore significant wave heights (Hs) of 0.4 m, 0.7 m, 1.0 m, 2.0 m, and 3.0

m, respectively. These figures clearly show that, for all cases, a higher peak wave period

leads to a higher magnitude of long wave response (r-hatms), across the entire cross-

shore (x) domain. This seems to be consistent with results of a numerical study by

Battjes et al. (2004), in which it was found that incoming bound infragravity waves

*In this chapter, the root mean square infragravity wave surface elevation is denoted as
r-hatms in order to be consistent with axis labels in the figures. This is equivalent to r,,,
in equation (2.6.1).










generated by higher frequency incoming wave components experience significantly more

dissipation than the incoming bound waves generated by lower frequency incoming wave

components.

Figures 3-7 3-11 show the effect of variation of offshore significant wave height

(Hs) on model results, for peak wave periods (Tp) of 4 s, 6 s, 8 s, 10 s and 12 s,

respectively. These figures clearly show that, for all cases, a higher offshore significant

wave height leads to a higher magnitude of long wave response (r-hatms), across the

entire cross-shore (x) domain. This makes sense, because the radiation stresses that force


0.1


0.05


0 100 200 300 400 500
x(m)


600 700 800 900 1000


0.8

0.6

E 0.4

0.2

0


O 100 200 300 400 500 600 700 800 900 1000


x(m)

Figure 3-2. Effect of variation of peak wave period (Tp) (for offshore H,=0.4 m) on (a)
root mean square long wave surface elevation (r-hatms) and (b) significant
wave height (Hs). Legend: -T,=4 s, Tp=6 s, -- Tp=8 s, Tp=10 s,
..... T,=12 s.


(I)










the infragravity waves are proportional to the wave heights squared; thus, more energetic

(higher) incoming short waves lead to greater forcing and thus higher amplitudes of the

infragravity waves.

Figure 3-2 shows the effect of the variation of peak wave period for an offshore

significant wave height of 0.4 m. In Figure 3-2 (a), the offshore value of the root mean

square long wave surface elevation (r-hatms) ranges from 0.006 m for Tp = 4 s to 0.025

m for Tp = 12 s. The value of the root mean square long wave surface elevation at 25 m

seaward of the shoreline cutoff depth ranges from 0.024 m for Tp = 4 s to 0.073 m for




0.2 (a)
E 0.15 -

m 0.1

0.05

0 100 200 300 400 500 600 700 800 900 1000
x(m)





E0.5




0 100 200 300 400 500 600 700 800 900 1000
X(m)

Figure 3-3. Effect of variation of peak wave period (Tp) (for offshore Hs =0.7 m) on (a)
root mean square long wave surface elevation (r-hatms) and (b) significant
wave height (Hs). Legend: -T,=4 s, Tp=6 s, -- Tp=8 s, Tp=10 s,
..... T,=12 s.










T, = 12 s. Figure 3-2 (b) clearly shows that, for an offshore significant wave height of

0.4 m, a higher peak wave period leads to a higher significant wave height, particularly in

the wave shoaling region.

Figure 3-3 shows the effect of the variation of peak wave period for an offshore

significant wave height of 0.7 m. In Figure 3-3 (a), the offshore value of the root mean

square long wave surface elevation (r-hatms) ranges from 0.010 m for Tp = 4 s to 0.042

m for Tp = 12 s. The value of the root mean square long wave surface elevation at 25 m

seaward of the shoreline cutoff depth ranges from 0.040 m for Tp = 4 s to 0.128 m for




0.3 (a)

f 0.2





0 100 200 300 400 500 600 700 800 900 1000


1.5
(b) x



0.5 -



0 100 200 300 400 500 600 700 800 900 1000
x(m)

Figure 3-4. Effect of variation of peak wave period (Tp) (for offshore Hs =1.0 m) on (a)
root mean square long wave surface elevation (r-hatms) and (b) significant
wave height (Hs). Legend: -Tp=4 s, Tp=6 s, Tp=8 s, Tp=10 s,
..... T,=12 s.









T, = 12 s. Figure 3-3 (b) clearly shows that, for an offshore significant wave height of

0.7 m, a higher peak wave period leads to a higher significant wave height, particularly in

the wave shoaling region.

Figure 3-4 shows the effect of the variation of peak wave period for an offshore

significant wave height of 1.0 m. The base case (Tp = 8 s) is shown as a bold black line.

In Figure 3-4 (a), the offshore value of the root mean square long wave surface elevation

(r-hatms) ranges from 0.012 m for Tp = 4 s to 0.065 m for Tp = 12 s. The value of the

root mean square long wave surface elevation at 25 m seaward of the shoreline cutoff

depth ranges from 0.053 m for Tp = 4 s to 0.197 m for Tp = 12 s. Figure 3-4 (b) clearly

shows that, for an offshore significant wave height of 1.0 m, a higher peak wave period

leads to a higher significant wave height, particularly in the wave shoaling region.

Figure 3-5 shows the effect of the variation of peak wave period for an offshore

significant wave height of 2.0 m. In Figure 3-5 (a), the offshore value of the root mean

square long wave surface elevation (r-hatms) ranges from 0.018 m for Tp = 4 s to 0.130

m for Tp = 12 s. The value of the root mean square long wave surface elevation at 25 m

seaward of the shoreline cutoff depth ranges from 0.072 m for Tp = 4 s to 0.357 m for Tp

= 12 s. Figure 3-5 (b) shows that, for an offshore significant wave height of 2.0 m,

values of Hs through the cross-shore domain for Tp = 6 to 12 s are quite similar, although

there is still a general trend for higher peak wave period leading to a higher significant

wave height. However, when Tp = 4 s, the model causes the waves to break near the

offshore boundary, limiting the wave height to Hmax, which is dependent upon wave

period (equation (2.4.11)).






42




0.6


I 0.4

S0.2 -


0 100 200 300 400 500 600 700 800 900 1000
x(m)










0 100 200 300 400 500 600 700 800 900 1000
x(m)

Figure 3-5. Effect of variation of peak wave period (Tp) (for offshore Hs =2.0 m) on (a)
root mean square long wave surface elevation (r-hatms) and (b) significant
wave height (Hs). Legend: -T,=4 s, Tp=6 s, -- Tp=8 s, Tp=10 s,
..... T,=12 s.

Figure 3-6 shows the effect of the variation of peak wave period for an offshore

significant wave height of 3.0 m. In Figure 3-6 (a), the offshore value of the root mean

square long wave surface elevation (r-hatms) ranges from 0.047 m for Tp = 4 s to 0.193

m for Tp = 12 s. The value of the root mean square long wave surface elevation at 25 m

seaward of the shoreline cutoff depth ranges from 0.105 m for Tp = 4 s to 0.443 m for Tp

= 12 s. Figure 3-6 (b) shows that, for an offshore significant wave height of 3.0 m,

values of Hs through the cross-shore domain for Tp = 8 to 12 s are quite similar. When Tp

= 6 s, significant wave height is less than that for the higher wave periods through most









of the cross-shore domain. When Tp = 4 s, the model causes significant wave breaking

near the offshore boundary, limiting the wave height to Hmax (equation (2.4.11)).



0.8
0 6. (a)


S0.4 --------^ -- ^ .**-\



0 100 200 300 400 500 600 700 800 900 1000
x(m)


(b)




0..


0 100 200 300 400 500 600 700 800 900 1000
x(m)
Figure 3-6. Effect of variation of peak wave period (Tp) (for offshore Hs =3.0 m) on (a)
root mean square long wave surface elevation (r-hatms) and (b) significant
wave height (Hs). Legend: -T,=4 s, Tp=6 s, -- Tp=8 s, Tp=10 s,
..... T,=12 s.

Figure 3-7 shows the effect of the variation of offshore significant wave height for

a peak wave period of 4 s. In Figure 3-7 (a), the offshore value of the root mean square

long wave surface elevation (r-hatms) ranges from 0.006 m for Hs = 0.4 m to 0.047 m for

Hs = 3 m. The value of the root mean square long wave surface elevation at 25 m

seaward of the shoreline cutoff depth ranges from 0.024 m for Hs = 0.4 m to 0.105 m for

Hs = 3 m. Figure 3-7 (b) shows that, in general, a higher offshore significant wave height







44



0 .2 II IIiII








O 100 200 300 400 500 600 700 800 900 1000
x(m)
0.15 -




















x(m)

Figure 3-7. Effect of variation of offshore significant wave height (Hs) (for T,=4 s) on
(a) root mean square long wave surface elevation (r-hatrms) and (b) significant
wave height (Hs). Legend: Hs=0.4 m, Hs=0.7 m, -- Hs=l m,
Hs=2 m, ..... Hs 3 m.

corresponds to a higher Hs in the entire cross-shore domain, although wave heights tend

to converge in the nearshore after the waves have broken. It is notable that, when the

offshore H1 = 3 m, the model causes significant wave breaking near the offshore

boundary, limiting the root mean square wave height Hons (equation (2.3.5)) to Hmax

(equation (2.4.11)); this causes convergence of Hs with the case of offshore Hs = 2.0 m.

However, although wave heights (Hs) are identical throughout most of the cross-shore

region for these two cases (offshore Hs = 2 m and 3m), it can be seen from Figure 3-7 (a),

that a higher offshore significant wave height leads to a higher magnitude of long wave

response (-hato a highe), across the entire cross-shore domain. Mathematically, this can be
response (q-hatrm,), across the entire cross-shore domain. Mathematically, this can be









explained by the fact that the offshore boundary condition is affected by the offshore

significant wave height, due to the amplitude of the incoming bound wave rb (equation

(2.5.46)) increasing with increasing radiation stress at the offshore boundary. However,

since radiation stresses are proportional to wave heights squared, and since, for cases

where the offshore Hrms is greater than Hmax (such as in the case where Hs, = 3 m and Tp =

4 s), the radiation stresses at the offshore boundary are most likely overestimated and

thus the results for the long wave response (in such cases) are most likely invalid.




0.3 -

U0.2





0 100 200 300 400 500 600 700 800 900 1000
x(m)


(b)







0 100 200 300 400 500 600 700 800 900 1000
x(m)

Figure 3-8. Effect of variation of offshore significant wave height (Hs) (for T,=6 s) on
(a) root mean square long wave surface elevation (r-hatrms) and (b) significant
wave height (Hs). Legend: Hs=0.4 m, Hs=0.7 m, -- Hs=l m,
Hs,=2 m, ..... H 3 m.

Figure 3-8 shows the effect of the variation of offshore significant wave height for

a peak wave period of 6 s. In Figure 3-8 (a), the offshore value of the root mean square






46


long wave surface elevation (r-hatms) ranges from 0.011 m for Hs = 0.4 m to 0.060 m for

Hs, = 3 m. The value of the root mean square long wave surface elevation at 25 m

seaward of the shoreline cutoff depth ranges from 0.045 m for Hs, = 0.4 m to 0.193 m for

Hs, = 3 m. Figure 3-8 (b) shows that, for a peak wave period of 6 s, a higher offshore

significant wave height corresponds to a higher Hs, in the entire cross-shore domain.





0.4 -


0.2



0 100 200 300 400 500 600 700 800 900 1000
x(m)

4

3






0 100 200 300 400 500 600 700 800 900 1000
x(m)

Figure 3-9. Effect of variation of offshore significant wave height (Hs) (for T,=8 s) on
(a) root mean square long wave surface elevation (r-hatms) and (b) significant
wave height (Hs). Legend: Hs=0.4 m, Hs=0.7 m, H,_ Hs= m,
Hs,=2 m, ..... H 3 m.

Figure 3-9 shows the effect of the variation of offshore significant wave height for

a peak wave period of 8 s. The base case (Hs = 1 m) is shown as a bold black line. In

Figure 3-9 (a), the offshore value of the root mean square long wave surface elevation (r-

hatms) ranges from 0.017 m for H, = 0.4 m to 0.106 m for H, = 3 m. The value of the









root mean square long wave surface elevation at 25 m seaward of the shoreline cutoff

depth ranges from 0.059 m for Hs = 0.4 m to 0.282 m for Hs, = 3 m. Figure 3-9 (b) shows

that, for a peak wave period of 8 s, a higher offshore significant wave height corresponds

to a higher Hs in the entire cross-shore domain.




0.6 (a)

0.4

0.2


0 100 200 300 400 500 600 700 800 900 1000











0 100 200 300 400 500 600 700 800 900 1000
x(m)

Figure 3-10. Effect of variation of offshore significant wave height (Hs) (for T,=10 s) on
(a) root mean square long wave surface elevation (r-hatms) and (b) significant
wave height (Hs). Legend: -Hs=0.4 m, Hs=0.7 m, -- Hs=l m,
Hs=2 m, .... Hs 3 m.

Figure 3-10 shows the effect of the variation of offshore significant wave height for

a peak wave period of 10 s. In Figure 3-10 (a), the offshore value of the root mean

square long wave surface elevation (r-hatms) ranges from 0.021 m for Hs = 0.4 m to

0.149 m for Hs = 3 m. The value of the root mean square long wave surface elevation at

25 m seaward of the shoreline cutoff depth ranges from 0.067 m for Hs = 0.4 m to 0.356







48


m for Hs = 3 m. Figure 3-10 (b) shows that, for a peak wave period of 10 s, a higher

offshore significant wave height corresponds to a higher Hs in the entire cross-shore

domain.



0.8
(a)
0.6

0.4




0 100 200 300 400 500 600 700 800 900 1000
x(m)

















Hs=2 m, .... Hs 3 m.

Figure 3-11 shows the effect of the variation of offshore significant wave height for

a peak wave period of 12 s. In Figure 3-11 (a), the offshore value of the root mean

square long wave surface elevation (r-hatms) ranges from 0.025 m for Hs = 0.4 m to

0.193 m for Hs = 3 m. The value of the root mean square long wave surface elevation at

25 m seaward of the shoreline cutoff depth ranges from 0.073 m for Hs = 0.4 m to 0.443

m for Hs = 3 m. Figure 3-11 (b) shows that, for a peak wave period of 12 s, a higher







49


offshore significant wave height corresponds to a higher Hs in the entire cross-shore

domain.

3.3.3 Jonswap Peak Enhancement Factor

Figure 3-12 shows the effect of the variation of the Jonswap peak enhancement

factor y (equation (2.3.1)) on model results. According to Kamphius (2000), y has an

average value of 3.3 and typically ranges between 1.0 and 7.0. A higher value of y

implies a narrower, more peaked frequency spectrum. The base case (y = 3.3) is shown

as a bold black line. Figure 3-12 (b) shows that the variation of y has little effect on


E 0.2






O
0
0


100 200 300 400 500 600 700 800
x(m)


900 1000


0 100 200 300 400 500 600 700 800 900 1000
x(m)

Figure 3-12. Effect of variation of Jonswap peak enhancement factor (y) on (a) root
mean square long wave surface elevation (r-hatrms) and (b) significant wave
height (Hs). Legend: -y=1.0, y=3.4, y=5.0, -- y=7.0.

significant wave height (Hs). This is expected, since the total wave energy for each case

was the same. Figure 3-12 (a) shows that a narrower frequency spectrum (increased y)


(. .









leads to a slightly decreased root mean square long wave surface elevation (r-hatrms).

This is unexpected, and further investigation would have to be done to explain this

pattern of results. The offshore value of the root mean square long wave surface

elevation (r-hatrms) ranges from 0.043 m for y = 1.0 to 0.036 m for y = 7.0. The value of

the root mean square long wave surface elevation at 25 m seaward of the shoreline cutoff

depth ranges from 0.147 m for y = 1.0 to 0.120 m for y = 7.0.

3.3.4 Deep Water Directional Width

Figure 3-13 shows the effect of the variation of deep water directional width, dir-

widtho, (equation (2.3.8)) on model results. The deep water directional width was varied

from 5' to 300. The base case, with dir-widtho = 15', is shown as a bold black line.

Figure 3-13 (a) shows that a narrower directional width leads to a greater magnitude of

long wave response. This finding is consistent with those of Van Dongeren et al. (2003);

in employing a numerical model (SHORECIRC), it was found that eliminating

directional spreading from the incoming wave spectrum caused significant amplification

of infragravity wave heights. In analyzing field data, Herbers et al. (1995a, 1995b) found

a similar relationship between directional spreading and infragravity wave response. The

offshore value of the root mean square long wave surface elevation (r-hatrms) ranges

from 0.051 m for dir-widtho = 5' to 0.030 m for dir-widtho = 300. The value of the root

mean square long wave surface elevation at 25 m seaward of the shoreline cutoff depth

ranges from 0.159 m for dir-widtho = 50 to 0.110 for dir-widtho = 300. Figure 3-13 (b)

shows that deep water directional width has little effect on significant wave height

throughout the cross-shore domain.







51





(a)
0.2 -


0.1



0 100 200 300 400 500 600 700 800 900 1000
x(m)
1.5





0.5



O 100 200 300 400 500 600 700 800 900 1000
x(m)
Figure 3-13. Effect of variation of deep-water directional width (dir-widtho) on (a) root
mean square long wave surface elevation (r-hatrms) and (b) significant wave
height (Hs). Legend: -dir-widtho=50, dir-widtho=150,
dir-widtho=300.

3.3.5 Peak Wave Direction

Figure 3-14 shows the effect of the variation of peak wave direction, O,, (equation

(2.3.7)) on model results. Peak wave direction was varied from 0O (shore-normal, base

case) to 600 (oblique incidence). Figure 3-14(a) shows that peak wave direction has little

effect on long wave response near the shoreline. However, at the offshore boundary,

more oblique waves (higher Op) lead to a decreased magnitude of long wave response.

One possible explanation for this is that more obliquely incident short waves lead to more






52






0O.2


J_ 0.1



0 100 200 300 400 500 600 700 800 900 1000
x(m)
1.5 1








O 100 200 300 400 500 600 700 800 900 1000


Figure 3-14. Effect of variation of peak wave direction (,p) on (a) root mean square long
wave surface elevation (r-hatms) and (b) significant wave height (Hs).
Legend: O,=0o, p=200, O,=400, -- =600.

trapping of the outgoing free infragravity waves and thus less leaky waves reaching the

offshore boundary. The offshore value of the root mean square long wave surface

elevation (r-hatms) ranges from 0.042 m for O, = 00 to 0.029 m for O, = 600. Figure 3-

14(b) shows that the obliquely incident waves (O, = 600) have a lower significant wave

height; this is due to greater refraction and less shoaling than the non-obliquely incident

waves. It is important to note that, although the significant wave height (Hs) and thus the

wave energy of the obliquely incident waves (O, = 600) is lower than the Hs for all of the

other cases as the waves approach the bar, the magnitude of the infragravity wave

response in the nearshore region is similar in all cases. This is consistent with the

explanation that more obliquely incident waves generate more edge waves (trapped










infragravity free waves), and thus the case of O, = 600 shows similar nearshore

infragravity wave energy as the other cases, although it shows less incoming short wave

energy than the other cases.

3.3.6 Bottom Friction

Figure 3-15 shows the effect of the variation of the bottom friction coefficient,ff,

(equations (2.5.4)-(2.5.5)) on model results. The bottom friction coefficient was varied

from ff= 1/400 s-1 to 1/50 s-1. The base case, with ff= 1/200 s-1, is shown as a bold black

line. Figure 3-15 (a) shows that increased bottom friction decreased the magnitude of

long wave response across the entire cross-shore domain. This is expected, because





E 0.2 -





0 100 200 300 400 500 600 700 800 900 1000
x(m)

1.5-





0.5 -


0 100 200 300 400 500 600 700 800 900 1000
x(m)

Figure 3-15. Effect of variation of bottom friction coefficient (ff) on (a) root mean square
long wave surface elevation (r-hat,,s) and (b) significant wave height (Hs).
Legend: ff=/50 s-1, ff=l/100 s1, ffl1/200 s1, -- ff=/300 s1,
ffl1/400 s1.









bottom friction serves to damp the long wave response (equations (2.5.4)- (2.5.5)). The

offshore value of the root mean square long wave surface elevation (r-hatms) ranges

from 0.048 m for ff = 1/400 s-1 to 0.016 m for ff = 1/50 s-1. The value of the root mean

square long wave surface elevation at 25 m seaward of the shoreline cutoff depth ranges

from 0.150 m for ff = 1/400 s-1 to 0.098 m for ff = 1/50 s-1. Figure 3-15 (b) shows that the

bottom friction coefficient has no effect on significant wave height throughout the cross-

shore domain. This is because bottom friction was not a factor in the wave-breaking

portion of the model.

3.3.7 Bar Amplitude

Figure 3-16 shows the effect of the variation of bar amplitude, a2, (equation 2.2.4)

on model results. The bar amplitude was varied from a2 = 0 m to 2.14 m. The base case,

with a2 = 1.5 m, is shown as a bold black line. The variation of the bathymetric profile

due to bar amplitude is shown in Figure 3-16 (c). The maximum bar amplitude of 2.14 m

was chosen in order to limit the minimum water depth over the bar to 0.3 m. Figure 3-16

(b) shows that an increased bar amplitude leads to stronger wave breaking and a

decreased significant wave height from the bar to the shoreline. Figure 3-16 (a) shows a

more complex pattern of results for the long wave response. In general, a higher bar

amplitude leads to a decreased magnitude of long wave response, especially near the

shoreline; however, this pattern seems to be reversed at the peak of the bar for the

maximum bar amplitude of 2.14 m. One explanation for this is the trapping of edge

waves due to the bar. Also, it is notable that, for the case of no bar (a2 = 0 m), r-hatms

shows a sharp increase at a location approximately 40 m seaward of the shoreline cutoff










depth. This may be due to the predominance of infragravity wave reflection at the

shoreline but an absence of trapping due to a bar.


E 0.2
E

0.1


0



1.5


0 100 200 300 400 500 600 700 800 900 1000
x(m)


0 100 200 300 400 500 600 700 800 900 1000
x (m)












0 100 200 300 400 500 600 700 800 900 1000
x(m)


Figure 3-16. Effect of variation of bar amplitude (a2) on (a) root mean square long wave
surface elevation (r-hatrms), (b) significant wave height (Hs), and (c)


bathymetric profile. Legend:


a2=0 m, a2=0.5 m, -- a2=1.0 m,


az=2.0 m, ***** az=2.14 m.


a2=1.5 m,







56


3.3.8 Bar Width

Figure 3-17 shows the effect of the variation of bar width on model results.

Equation (2.2.4) shows how the bar width coefficient c, affects the bathymetric profile.

The bar width coefficient was varied from c, = 2 to 8. A lower c, implies greater width.


0.2


0.1


100 200 300 400 500 600 700
x(m)


100 200 300 400 500
x(m)


800 900 1000


600 700 800 900 1000


-5


-10


-15
0 100 200 300 400 500 600 700 800 900 1000
x(m)

Figure 3-17. Effect of variation of bar width on (a) root mean square long wave surface
elevation (r-hatrms), (b) significant wave height (Hs), and (c) bathymetric
profile. Width coefficient is c,. Legend: c,=2, c,=5, w=8.


IIIa)







I I I I I III









The base case, with c, = 5, is shown as a bold black line. The variation of the

bathymetric profile due to bar width is shown in Figure 3-17 (c). Figure 3-17 (b) shows

that a wider bar leads to a more gradual pattern of wave breaking. Figure 3-17 (a) shows

that a wider bar leads to a slightly increased magnitude of long wave response, especially

near the shoreline. One possible explanation for this is that bars tend to trap edge waves;

therefore, a wider bar might lead to more trapping of these edge waves near the shoreline.

The value of the root mean square long wave surface elevation at 25 m seaward of the

shoreline cutoff depth ranges from 0.150 m for c, = 2 to 0.124 m for c, = 8.

3.3.9 Distance of Bar from Shore

Figure 3-18 shows the effect of the variation of the distance of the bar from shore,

xc, (equation (2.2.4)) on model results. The distance xc was varied from 80 m to 150 m.

The base case, with xc = 120 m, is shown as a bold black line. The variation of the

bathymetric profile due to the distance of the bar from shore is shown in Figure 3-18 (c).

Figure 3-18 (b) shows that the bar being closer to shore leads to waves breaking closer to

shore. Figure 3-18 (a) shows that the bar being closer to shore results in a narrower long

wave response pattern near the shoreline. This makes sense, because the bar trapped

edge waves would be nearer to shore if the bar is nearer to the shore; as the bar is located

further from the shoreline, the long wave response pattern becomes more spread out in

the near-shore region.














0.2


0.1


100 200 300 400 500 600 700 800
x(m)


0 1 I 1 1 1 1
0 100 200 300 400 500
x (m)


600 700 800 900 1000


-156
0 100 200 300 400 500 600 700 800 900 1000
x(m)

Figure 3-18. Effect of variation of distance of bar from shore (x,) on (a) root mean
square long wave surface elevation (r-hatrms), (b) significant wave height
(Hs), and (c) bathymetric profile. Legend: xc=80 m, xc=100 m,
xc=120m, --xc=150m.

3.3.10 Water Depth at Offshore Boundary

Figure 3-19 shows the effect of the variation of water depth at the offshore

boundary offshorer) on model results. The water depth at the offshore boundary was


(III)I


900 1000







59


varied by varying the profile scale factor A (equation (2.2.4). The bar amplitude was

scaled to the offshore water depth by multiplying the bar amplitude a2 (in equation

(2.4.3)) by the ratio A/Abase where A is the profile scale factor and Abase is the profile


E 0.2
E

- 0.1


100 200 300 400 500 600 700 800 900 1000
x(m)


0 100 200 300 400 500 600 700 800 900 1000
x(m)


0 100 200 300 400 500 600 700 800 900 1000
x(m)

Figure 3-19. Effect of variation of water depth at offshore boundary offshorer) on (a) root
mean square long wave surface elevation (r-hatrms), (b) significant wave
height (Hs), and (c) bathymetric profile. Legend: -hoffshore=7.19 m,

hoffshore=8.16 m,-- hoffshore=9.13 m, hoffshore=10.09 m,
hoffshore=l 11.97 m, ***** offshore= 12.91 m.









scale factor for the base case. The offshore water depth was varied from offshore = 7.19 m

(for A = 0.07) to offshore = 12.91 m (for A = 0.13). The base case, with offshore = 10.09 m

(for A = 0.1), is shown as a bold black line. The variation of the bathymetric profile is

shown in Figure 3-19 (c). Figure 3-19 (b) shows waves breaking farther from shore for

the shallower bathymetric profiles. Figure 3-19 (a) shows that a shallower bathymetric

profile (smaller offshore and bar amplitude) results in a higher amplitude of long wave

response in the entire cross-shore domain. This makes sense conceptually because

infragravity waves tend to be predominant in shallow water. The offshore value of the

root mean square long wave surface elevation (r-hatrms) ranges from 0.047 m for offshore

= 7.19 m to 0.037 m for offshore = 12.91 m. The value of the root mean square long wave

surface elevation at 25 m seaward of the shoreline cutoff depth ranges from 0.151 m for

offshore = 7.19 m to 0.131 m for offshore = 12.91 m.

3.3.11 Domain Length

Figure 3-20 shows the effect of the variation of the domain length (ld) on model

results. The distance Id was varied from 750 m to 1625 m. The base case, with Id = 1000

m, is shown as a bold black line. Figures 3-20 (a) (c) were plotted such that for all

cases, x = 1625 m at the onshore boundary. These figures show convergence of the

results for all cases. This indicates that the chosen cross-shore domain of 1000 m was

adequately long to give accurate results.












(a)

S0.2





0
0 200 400 600 800 1000 1200 1400 160C
x(m)

1.5
(b)




0.5-


0.
0 200 400 600 800 1000 1200 1400 160OC
x(m)

0


-5
0P

-o10r
I I5 I I" "


0 200 400 600 800
x (m)


1000 1200 1400


1600


Figure 3-20. Effect of variation of domain length (ld) on (a) root mean square long wave
surface elevation (r-hatrms), (b) significant wave height (Hs), and (c)


bathymetric profile. Legend:
ld=1625 m


ld=750 m, d=1000 m, -- 1d=1375 m,















CHAPTER 4
CONCLUSIONS

4.1 Summary

The purpose of this study was to develop and present a linear frequency-domain

numerical model of nearshore infragravity wave generation on an alongshore-uniform

beach, and then to utilize this model to investigate the importance of various parameters

in the generation of these infragravity waves. The model of infragravity wave generation

was based upon the model presented by Reniers et al. (2002), which was found by the

same researchers to agree well with field data from Duck, North Carolina. Chapter 2 of

this thesis presented detailed derivations of this numerical model, as well as a validation

of the numerical model against an analytical solution for a simple test case. The results

presented in Chapter 3 of this thesis demonstrate the relative importance of various

parameters in the generation of nearshore infragravity waves.

The results of the numerical simulation of the low frequency wave climate

indicated that the most important parameters in the generation of nearshore infragravity

waves are: peak wave period (Tp), offshore significant wave height (Hs), bottom friction

(ff), deep water directional width (dir-widtho), and water depth at the offshore boundary

offshorere. These parameters affect the infragravity wave response in the following

manner:

* A higher Tp leads to a higher magnitude of response;

* A higher Hs leads to a higher magnitude of response;

* A narrower directional width leads to higher magnitude of response;









* Increased bottom friction leads to a decreased magnitude of response;

* A shallower bathymetric profile leads to an increased magnitude of response.

The remaining parameters investigated in the numerical simulation were found to

be moderately important in the generation of nearshore infragravity waves. These

parameters are: bar amplitude (a2), the bar width coefficient (cw), the distance of the bar

from the shoreline (xc), peak wave direction (,p), and the Jonswap peak enhancement

factor (y). These parameters affect the infragravity wave response in the following

manner:

* A higher bar amplitude leads to decreased magnitude of response, especially near
the shoreline;

* A wider bar leads to a slightly higher magnitude of response;

* The bar being closer to the shore results in a narrower response pattern;

* Obliquely incident waves (higher Op) lead to a decreased magnitude of response at
the offshore boundary, although peak wave direction has little effect on response
near the shoreline;

* A narrower frequency spectrum (increased y) leads to a slightly decreased
magnitude of response.

4.2 Discussion and Conclusions

One of the main findings in this study is that a larger peak wave period (Tp) of the

incoming short waves leads to a greater magnitude of infragravity wave surface

elevation. It is important to note that this pattern is evident for small incident waves (i.e.

Hs=0.4m), where Hs is higher across the domain for higher peak periods (i.e. greater

dissipation of short wave energy for lower Tp), and also for large incident waves (i.e.

Hs=2.0 m) where Hs is similar across the domain for all peak periods. This indicates that,

regardless of the dissipation of the primary (short) waves, there is still greater dissipation

of infragravity wave energy when the peak period of the incident short waves is lower.









This seems to be consistent with results of a numerical study by Battjes et al. (2004), in

which it was found that incoming bound infragravity waves generated by higher

frequency incoming wave components experience significantly more dissipation than the

incoming bound waves generated by lower frequency incoming wave components.

Another parameter that has an important impact on infragravity wave surface

elevation is offshore significant wave height (Hs). Results of the numerical simulation of

the low frequency wave climate show that higher offshore significant wave height leads

to higher magnitude of infragravity wave response. This is consistent with the findings

of Ruessink (1998a) that the infragravity wave energy is significantly positively

correlated with the wave energy of the incoming short waves. This also makes sense

mathematically, because the radiation stresses that force the infragravity waves are

proportional to the wave heights squared; thus, more energetic (higher) incoming short

waves lead to greater forcing and thus higher amplitudes of the infragravity waves.

However, as seen in Figure 3.3.2.6, it is important to specify a realistic wave height at the

offshore boundary. If the offshore Hrms exceeds Hmax at the offshore boundary, then the

value of the radiation stresses at the offshore boundary will be unrealistically high, and

the model results for infragravity wave surface elevation will be inaccurate.

Results of the numerical simulation of the low frequency wave climate also show

that a narrower directional width leads to a greater magnitude of long wave response.

This finding is consistent with that of Van Dongeren et al. (2003); in employing a

numerical model (SHORECIRC), it was found that eliminating directional spreading

from the incoming wave spectrum caused significant amplification of infragravity wave









heights. In analyzing field data, Herbers et al. (1995a, 1995b) found a similar

relationship between directional spreading and infragravity wave response.

As expected, increased bottom friction decreased the magnitude of long wave

response across the entire cross-shore domain. Bottom friction serves to damp the long

wave response (equations (2.5.4)- (2.5.5)) and is necessary to prevent unbounded growth

in the case of infragravity wave resonance.

The bathymetric parameter that seems to most significantly affect the long wave

response is the offshore water depth offshorere, which was varied in the numerical

simulation by varying the profile scale factor (A, equation (2.2.4)). A shallower

bathymetric profile (smaller offshore and bar amplitude) results in higher amplitude of

long wave response in the entire cross-shore domain. This makes sense conceptually

because infragravity waves tend to be predominant in shallow water.

Results of the numerical simulation of the low frequency wave climate show that,

in general, a higher bar amplitude leads to a decreased magnitude of long wave response,

especially near the shoreline; however, this pattern seems to be reversed at the peak of the

bar for the maximum bar amplitude. One explanation for this is the trapping of edge

waves due to the bar. Also, it is notable that, for the case of no bar, the root mean square

infragravity wave surface elevation shows a sharp increase at a location approximately 40

m seaward of the shoreline cutoff depth. This may be due to the predominance of

infragravity wave reflection at the shoreline but an absence of trapping due to a bar.

The variation of bar width also affects the low frequency wave climate. Results of

the numerical simulation show that a wider bar leads to a slightly increased magnitude of

long wave response, especially near the shoreline. One possible explanation for this is









that bars tend to trap edge waves; therefore, a wider bar might lead to more trapping of

these edge waves near the shoreline.

Results of the numerical simulation of the low frequency wave climate also show

that the bar being closer to shore results in a narrower long wave response pattern near

the shoreline. This makes sense, because the bar trapped edge waves would be nearer to

shore if the bar is nearer to the shore; as the bar is located further from the shoreline, the

long wave response pattern becomes more spread out in the near-shore region.

Findings also indicate that peak wave direction has little effect on long wave

response near the shoreline. However, at the offshore boundary, more oblique waves

(higher Op) lead to a decreased magnitude of long wave response. One possible

explanation for this is that more obliquely incident short waves lead to more trapping of

the outgoing free infragravity waves and thus less leaky waves reaching the offshore

boundary. It is important to note that, although the significant wave height (Hs) and thus

the wave energy of the obliquely incident waves (Op = 600) is lower than the Hs for all of

the other cases as the waves approach the bar, the magnitude of the infragravity wave

response in the nearshore region is similar in all cases. This is consistent with the

explanation that more obliquely incident waves generate more edge waves (trapped

infragravity free waves), and thus the case of O, = 600 shows similar nearshore

infragravity wave energy as the other cases, although it shows less incoming short wave

energy than the other cases.

The one result of this numerical simulation of low frequency wave climate that is

not consistent with expectations is that a narrower frequency spectrum (increased y) leads









to a slightly decreased root mean square long wave surface elevation (r-hatrms). Further

investigation would have to be done to explain this pattern of results.

4.3 Recommendations for Further Work

It is possible to expand this numerical model to include solutions for the velocities

u and v, in the cross-shore and alongshore directions, respectively. In order to do this,

rather than combining equations (2.5.1)- (2.5.3) into a single equation for infragravity

wave surface elevation fl (2.5.4), one would transform equations (2.5.1)- (2.5.3) into the

frequency domain and solve for the three unknowns 7, ui, and i. This would

necessitate formulating more complex boundary conditions and would also entail more

computational time. The benefit of this expansion would be the ability to analyze the

relationships between infragravity waves and nearshore currents or vorticity.

Another possibility is to expand the model to include an alongshore-varying

bathymetry. Thus, the model would be valid for cases other than those with an

alongshore uniform bathymetry. Perturbation expansions could be used to generate this

alongshore-varying bathymetry. This would provide results showing the alongshore

variation of infragravity wave surface elevation and would thus allow for the depiction of

edge waves.

With the model in its current state, one could analyze the output in order to separate

the incoming (bound) and outgoing (free) long waves. It would also be possible to

further analyze the model output to separate the outgoing long waves into edge waves

and leaky waves by forming a frequency alongshore wave number spectrum. This

would allow one to analyze which factors or parameters are most important in the







68


generation of the long waves traveling in each direction, and in trapped versus leaky

waves.














APPENDIX A
DERIVATION OF EQUATION FOR INFRAGRAVITY WAVE SURFACE
ELEVATION

This appendix gives the derivations of the two forms of the equation for

infragravity wave surface elevation: the second order partial differential equation,

equation (2.5.4), and the second order ordinary differential equation in the frequency

domain, equation (2.5.6).

A.1 Second Order Partial Differential Equation

Equation (2.5.4), the second order partial differential equation for infragravity wave

surface elevation,

1 8a2 Pa a2 7 dh a a2 1 SX 22S, 2S
+h + +h + +
g at2 g t x2 dx& x y pg dx2 9xy 2 j

was obtained by combining equations (2.5.1)-(2.5.3), as follows.

1. Differentiate equation (2.5.1) with respect to time:

+- h- +- h = 0 (A. 1)
9t2 ax at) 9 y at)

2. Differentiate equation (2.5.2) with respect to x:

a 2, SB^ 92SX
p- h -+pg --ah (A.2)
ax at ax ax axay

3. Differentiate equation (2.5.3) with respect to y:

a ( av a99 8 7 2S 2S(
p- h -+pg h-- (A.3)
S \y at yq ( y Ay .x y

4. Rearrange equation (A. 1):









-h- -- --7 ha (A.4)
ax at 9t2 9y at

5. Substitute equation (A.4) into equation (A.2) to obtain:

0 2 7 9 2h7 0 92S. 02S"
S 9y ajt t ax ax x a2 2 x 9xy

6. Substitute equation (A.5) into equation (A.3) to obtain:

1 2r 9h 9r 1 9 h 9r 92r 12Sy 2S
-+ +h + --+h- -+2- (A.6)
g at Ox ax a2x 9hy y 2y pg da2x 9xy 2 y 2

7. Assuming h varies only with x, not with y:

1 a2h7 a7+ dha 17 +h, +2 +a) (A.7)
g at2 9x2 dxax 9 y pgK dx2 9xay ay 2


This is the same as equation (2.5.4), except for the added term on the left hand
g at

side.

A.2 Second Order Ordinary Differential Equation in the Frequency Domain

Equation (2.5.6), the second order ordinary differential equation for infragravity

wave surface elevation,

d + dh du + 4.2Af2 iu2zAf hAk2 2
dx dx dx g g

1 dXS dSd 2
d + 2iAk + Ak 2
pg 2 dx dx

was obtained by transforming equation (2.5.4) into the frequency domain, as follows:

1. Symbolize the infragravity wave phase q as

S= (2zAft Aky) (A.8)


2. From equation (2.5.7) for q:









S= iTzAfiexp[i0]+* (A.9)
at


at -2;r2A 2exp[i]+* (A.10)
8t

a7 1 ^ expli]+* (A.11)
cx 2 cx

2 exp[iO]+* (A.12)
ax2 2 ax2

a27 1
-- Ak 2exp[li]+* (A.13)
ay 2

3. From equation (2.5.10) for Syy:

1 Ak 2 exp[iq ]+* (A.14)
y 2 2

4. From equation (2.5.9) for Sxy:

02S 1 dS i i
=iAk, exp[iq]+*
8x-y 2 dx (A.15)


5. From equation (2.5.8) for S,,xx:

a2SX 1 d2S x
S 2 exp[i*]+* (A.16)
x 2 2 dxC2

6. Equations (A.9)-(A. 16) were substituted into equation (2.5.4) to obtain equation
(2.5.6).














APPENDIX B
DERIVATION OF EQUATIONS FOR BOUNDARY CONDITIONS

B.1 Shoreline Boundary Condition

The cross-shore momentum equation (2.5.2) was the starting point in deriving the

reflecting boundary condition at the shoreline.

au a as8xx as,
ph-+ pgh
at ax ax ay

The following steps were followed in order to obtain the shoreline boundary

condition equation (2.5.24).

1. Assume that there is perfect reflection at the shoreline (x=n). Therefore, let Un = 0.
Equation (2.5.2) then becomes

7 1 as as (B.1)
dx pgh d x Sy )

2. Transform equation (B. 1) to the frequency domain. Recall that the infragravity
wave phase is represented as

= (27rAft -Aky) (B.2)

From equations (2.5.7)-(2.5.9) for 7, Sxx, and Sxy:

a7 1 a^ exp(i)+* (B.3)
ax 2 ax

as lasexp(io)+* (B.4)
ax 2 ax

as -iAk
= Y S, exp(i)+* (B.5)
Sy 2

Substitute equations (B.3)-(B.5) into equation (B.1) to obtain










a- iAk, S
pgh Ox "


(B.6)


3. Use second order backward differences to estimate the derivatives with respect to
x:

897 9,_ 4^-i + 39
Na n2 -4 +n (B.7)
ax 2Ax


a ., ":(n-2) ~4xx(n-l) +3S(n) (B.8)
Ax 2Ax

4. Substitute equations (B.7) and (B.8) into equation (B.6) to obtain equation (2.5.24):

1 -( 2 3 1 r3 -(n) 4S,(nl) + Sxn iAk Sy(n)
2Ax A x 2Axj pghn 2Ax



B.2 Offshore Boundary Condition

B.2.1 Characteristic Equations

B.2.1.1 Incoming bound wave

Equation (2.5.43) can be proven to be a characteristic equation for the surface

elevation of the incoming bound wave.

1. Given equation (2.5.43):

a77b 2zAf a7b 2'zAf a 8qb
7, + cosO 0 + 2 sino 7 = 0
at K x K y

2. Substitute c=27zAf and take the analytic derivatives of rb from equation (2.5.31) to
obtain


iyCb + cos 8O (- iK,,, cos ,,, )7b + sin 8O, (- iK, sin 8,)17b = 0


3. Cancel terms to obtain the trigonometric identity

cos2 O,, + sin2 O,, = 1


(B.9)


(B.10)









which is true, by definition.

B.2.1.2 Outgoing free wave

Equation (2.5.44) can be proven to be a characteristic equation for the surface

elevation of the outgoing free wave.

1. Given equation (2.5.44):

d07,,, kxout dr0,, Aky 07o 0
gh + gh 0
St Kot ax Kout y

2. Take the analytic derivatives of r,,ut from equation (2.5.42) to obtain


iuuou kgxoh (ik-xo0u)u0i + gh -ihk( ik =) 0 (B.l)
Kout Kout


3. Substitute Ko,, = then cancel and rearrange terms to obtain
Vgh

K = Ak+kxo (B.12)

which is true by definition ofKout (equation (2.5.37)).

B.2.1.3 Combined Characteristic Equation

The combined characteristic equation (2.5.45) was the starting point for forming

the offshore boundary condition. It was obtained by the following steps:

1. Substitute 77o = 1r rb (from equation 2.5.30) into equation (2.5.44) to obtain


d- r boa Sbb- 0 (B.13)
at at Ko,, x x ) K aout

2. Add together equations (B.13) and (2.5.43) and rearrange terms to obtain equation
(2.5.45):










a gh k, a. + gh 7k ja7
at Ko,,, x Ko0t

gh + os,, O + gh Kout- f sin 8,,


B.2.2 Incoming Bound Wave Amplitude

Equation (2.5.46) gives the analytic solution of the incoming bound wave

amplitude rb It was obtained by the following steps:

1. Apply equation (2.5.4) to the incoming bound wave at the offshore boundary.

1 82 b 8b a2 1b dh b 2b 1a0Sxx 22x + 2S
+h + +h +a +
g t2 g at a2 dxax y2 pg2 dx2 axay ay2

(B.14)

Note that the radiation stresses force the incoming bound wave and not the

outgoing free wave, and thus it was not necessary to apply the subscript b to the

radiation stresses in the above equation.

2. In order to take the analytic derivatives of radiation stresses with respect to x,
radiation stresses were defined at the offshore boundary as


Sxx = S x exp(-iAkxx)expi(2Aft Aky) +* (B.15)


S, = exp(- iAkxx)exp [i (2Aft Aky)]+ (B.16)


SA = 1 exp(- iAkx)exp[i(2Aft Aky)] +* (B.17)
2

Equations (B.15)-(B.17) are similar in form to equation (2.5.41), which defines the

surface elevation of the incoming bound wave at the offshore boundary.

3. By comparing the above three equations with equations (2.5.8)-(2.5.10), it can be
seen that









S, = S exp(- iAkx) (B.18)

S, = S, exp(- iAk,x) (B.19)

Sy = S,, exp(- iAkx) (B.20)

4. Take the analytic derivatives of r7b from equation (2.5.41) and of radiation stresses
from equations (B. 15)- (B. 17). Recall that = (27TAft-Akyy).

a-7b = izAf exp(- iAkx)exp(i) +* (B.21)
at

= -2zi f Ar2b exp(- iAkxx)exp(i) +* (B.22)
at2

ax2 AkX2 7b exp(- iAkx)exp(io) + (B.23)
X2 2

a -7b Ak 2 exp(- iAkxx)exp(io) + (B.24)
oy 2

12S -Ak1 exp(- iAkxx)exp(i) + (B.25)
na2 2


SAkxAk, S exp(- iAkx)exp(i) + (B.26)
axay 2


a2 -1 Ak, 2S exp(- iAkxx)exp(ij) +* (B.27)
Cy 2

dh
5. Assume a flat bed at the offshore boundary; therefore, the term = 0 in equation
dx
(2.5.4). Substitute into equation (2.5.4) the above analytic derivatives from
equations (B.21)-(B.27). Note that since x = 0 at the offshore boundary, the term
exp(-iAkx) = 1. Rearrange terms to obtain

Akx S + 2Ak AkSA + Ak S
17b = x) xx -x(l ) 2 (B.28)
4p'r Af2 2ippnf' pghAk ) pghAk









6. As can be seen from equations (B.18)- (B.20), since x = 0 at the offshore boundary,
S, S,y, and S., are equivalent to S, S,,, and SY, respectively, at the offshore
boundary. Therefore, the above equation becomes equation (2.5.46):

Akxct) + 2AkrM)+AkS,( + 2Ak .2 ,
4 pr;2Af2 2ip1n, Af pgh, Ak (2 pgh, AkY

B.2.3 Offshore Boundary Condition Equation

The offshore boundary condition equation (2.5.47) was obtained by taking the

following steps:

1. Begin with equation (2.5.45).


gh 0a7 + gV- a7k
at K0ut ax K0ut jy

g- + cos O,, + gh
K, ] ,,L


Ksin O y


2. Take the analytic derivates of r (from equation 2.5.7).


=7 izAf exp(i )+*
at

ar 1 a;7
exp(if)+*
ax 2 ax

= -- iAk, exp(i) + *
cy 2


(B.29)


(B.30)


(B.31)


3. Equation (2.5.45) was transformed into the frequency domain by substitution of the
above equations (B.29)-(B.31).


Af k xo
2 KOut Cx


1 Ak ,
2gh K iAky
2 Kout


K 2'Af (1
gh- + cos Akxb exp(-iAkxx)


+ gh 2Af sin*,, 1 iAkyb exp(-iAkxx)
Kout Kin 2


(B.32)









4. Use the second order forward differences representation of at the offshore

boundary.

S 3-i1+472(B.373)
Ox 2Ax

5. Substitute equation (B.33) into equation (B.32) and rearrange terms to obtain the
offshore boundary condition equation (2.5.47).

3 r k 1 2 gh ( ghkxout kxout g
irrAf +- -gh Ak + + 3
y 4Ax K4A 2 K ) Ax K 4Ax Kou
lOut ~Ofrt 2OA/ l ~2
= iAkx + g cos + iAkn sin 8,n
2 out Kin 2 Iout Kin















APPENDIX C
VALUES OF ROOT MEAN SQUARE LONG WAVE SURFACE ELEVATION FOR
EACH TEST CASE

Table C-1. Root mean square wave surface elevation ( 7ms) for each test case, at the
offshore boundary and at 25 m seaward of the shoreline cutoff depth.

Root mean square wave surface elevation (rms) (m)
At offshore boundary At 25 m seaward of shoreline cutoff depth
3.3.1 Base Case
0.0417 0.1400
3.3.2 Offshore Significant Wave Height and Peak Period
HI(m), Tn(s)
0.4, 4 0.0056 0.0239
0.4,6 0.0110 0.0448
0.4, 8 0.0167 0.0587
0.4, 10 0.0212 0.0669
0.4, 12 0.0249 0.0734
0.7, 4 0.0096 0.0398
0.7, 5 0.0189 0.0736
0.7, 6 0.0279 0.0975
0.7,7 0.0358 0.1126
0.7, 8 0.0419 0.1277
1,4 0.0122 0.0526
1,6 0.0284 0.1050
1,8 0.0417 0.1400
1, 10 0.0524 0.1646
1, 12 0.0651 0.1966
2,4 0.0176 0.0717
2,6 0.0442 0.1581
2, 8 0.0716 0.2220
2, 10 0.1036 0.2945
2, 12 0.1295 0.3569










Table C-1. Continued


Root mean square wave surface elevation (r,,) (m)
At offshore boundary At 25 m seaward of shoreline cutoff depth
3.3.2 Offshore Significant Wave Height and Peak Period (continued)
H, (m), T,(s)
3,4 0.0465 0.1053
3,6 0.0598 0.1927
3, 8 0.1063 0.2821
3, 10 0.1492 0.3562
3, 12 0.1925 0.4428
3.3.3 Jonswap Peak Enhancement Factor

1 0.0433 0.1469
2 0.0412 0.1405
3 0.0417 0.1405
3.3 0.0417 0.1400
4 0.0381 0.1290
5 0.0374 0.1225
6 10.0358 10.1195
7 10.0358 10.1200
3.3.4 Deep Water Directional Width
dir-width_0 (deg)
5 0.0510 0.1587
10 0.0451 0.1461
15 0.0417 0.1400
20 0.0343 0.1208
25 0.0340 0.1212
30 0.0302 0.1099
3.3.5 Peak Wave Direction
O, (deg)
0 0.0417 0.1400
10 0.0378 0.1322
20 0.0393 0.1359
30 0.0379 0.1361
40 0.0384 0.1393
50 0.0331 0.1417
60 0.0288 0.1316










Table C-1. Continued


Root mean square wave surface elevation ( mrm) (m)
At offshore boundary At 25 m seaward of shoreline cutoff depth
3.3.6 Bottom Friction
ff
1/50 0.0156 0.0982
1/100 0.0278 0.1149
1/150 0.0345 0.1267
1/200 0.0417 0.1400
1/250 0.0432 0.1418
1/300 0.0460 0.1424
1/350 0.0434 0.1419
1/400 0.0484 0.1504
3.3.7 Bar Amplitude
a2
0 0.0420 0.1336
0.5 0.0441 0.1394
1.0 0.0442 0.1435
1.5 0.0417 0.1400
2.0 0.0333 0.1200
2.14 0.0277 0.1093
3.3.8 Bar Width
Cw
2 0.0426 0.1500
3 0.0435 0.1489
4 0.0407 0.1411
5 0.0417 0.1400
6 0.0410 0.1352
7 0.0381 0.1265
8 0.0381 0.1241










Table C-1. Continued


Root mean square wave surface elevation (r,,) (m)
At offshore boundary At 25 m seaward of shoreline cutoff depth
3.3.9 Distance of Bar from Shore


80 0.0373 0.1371
90 0.0358 0.1277
100 0.0397 0.1325
110 0.0397 0.1339
120 0.0417 0.1400
130 0.0399 0.1343
140 0.0422 0.1400
150 0.0434 0.1432
3.3.10 Water Depth at Offshore Boundary


7.19 0.0474 0.1506
8.16 0.0437 0.1413
9.13 0.0395 0.1343
10.09 0.0417 0.1400
11.97 0.0367 0.1284
12.91 0.0368 0.1308
3.3.11 Domain Length
Id (m)__ _
750 0.0455 0.1379
1000 0.0417 0.1400
1375 0.0377 0.1389
1625 0.0359 0.1411
















LIST OF REFERENCES


Battjes, J. A., and Janssen, J. P. F. M., Energy loss and set-up due to breaking of random
waves, Proceedings of the 16th International Coastal Engineering Conference,
Hamburg, pp. 569-587, American Society of Civil Engineers, New York, 1978.

Battjes, J. A., Bakkenes, H. J., Janssen, T. T., and van Dongeren, A. R., Shoaling of
subharmonic gravity waves, Journal of Geophysical Research, 109, C02009, 2004.

Bowen, A. J., and Inman, D. L., Edge waves and crescentic bars, Journal of Geophysical
Research, 76(36), 8662-8671, 1971.

Bryan, K. R., and Bowen, A. J., Bar-trapped edge waves and longshore currents, Journal
of Geophysical Research, 103(C 12), 27,867-27,884, 1998.

Dean, R. G., and Dalrymple, R. A., Water Wave Mechanics for Engineers and Scientists,
World Scientific Publishing Co., River Edge, NJ, 1991.

Dean, R. G., and Dalrymple, R. A., Coastal Processes n i/l Engineering Applications,
Cambridge University Press, New York, NY, 2002.

Henderson, S. M., and Bowen, A. J., Observations of surf beat forcing and dissipation,
Journal of Geophysical Research, 10 7(C 11), 14-1-14-10, 2002.

Herbers, T. H. C., Elgar, S., and Guza, R. T., Infragravity-frequency (0.005-0.05 Hz)
motions on the shelf, part I, Forced waves, Journal of Physical Oceanography, 24,
917-927, 1994.

Herbers, T. H. C., Elgar, S., and Guza, R. T., Generation and propagation of infragravity
waves, Journal of Geophysical Research, 100(C12), 24,863-24,872, 1995a.

Herbers, T. H. C., Elgar, S., Guza, R. T., and O'Reilly, W.C., Infragravity-frequency
(0.005-0.05 Hz) motions on the shelf, part II, Free waves, Journal of Physical
Oceanography, 25, 1063-1079, 1995b.

Holman, R. A., and Bowen, A. J., Bars, bumps, and holes: models for the generation of
complex beach topography, Journal of Geophysical Research, 87(C 1), 457-468,
1982.

Holman, R. A., and Bowen, A. J., Longshore structure of infragravity wave motions,
Journal of Geophysical Research, 89, 6446-6452, 1984.






84


Hornbeck, R. W., Numerical Methods, Quantum Publishers, Inc., New York, NY, 1975.

Huntley, D. A., Guza, R. T., and Thornton, E. B., Field observations of surf beat 1.
Progressive edge waves, Journal of Geophysical Research, 86(C7), 6451-6466,
1981.

Janssen, T. T., Battjes, J. A., and van Dongeren, A. R., Long waves induced by short-
wave groups over a sloping bottom, Journal of Geophysical Research, 108(C8),
2003.

Kamphius, J. W., Introduction to Coastal Engineering and Management, World
Scientific Publishing Co., River Edge, NJ, 2000.

Lippmann, T. C., Herbers, T. H. C., and Thornton, E. B., Gravity and shear wave
contributions to nearshore infragravity motions, Journal of Physical
Oceanography, 29, 231-239, 1999.

List, J. H., Breakpoint-forced and bound long waves in the nearshore: a model
comparison, Proceedings of the 23rd International Coastal Engineering
Conference, Venice, Italy, pp. 860-873, American Society of Civil Engineers, New
York, 1992a.

List, J. H., A model for the generation of two-dimensional surf beat, Journal of
Geophysical Research, 97(C4), 5623-5635, 1992b.

Longuet-Higgins, M. S., and Stewart, R. W., Radiation stresses and mass transport in
gravity waves, with application to "surf beats," Journal ofFluidMechanics, 13,
481-504, 1962.

Longuet-Higgins, M. S., and Stewart, R. W., Radiation stresses in water waves: a
physical discussion with applications, Deep Sea Research, 11, 529-562, 1964.

Munk, W.H., Surf beats, EOS Transactions, American Geophysical Union, 30, 849-854,
1949.

Okihiro, M., Guza, R. T., and Seymour, R. J., Bound infragravity waves, Journal of
Geophysical Research, 97(C7), 11,453-11,469, 1992.

Reniers, A. J. H. M., and Battjes, J. A., A laboratory study of longshore currents over
barred and non-barred beaches, Coastal Engineering, 30, 1-22, 1997.

Reniers, A. J. H. M., van Dongeren, A. R., Battjes, J. A., and Thornton E. B., Linear
modeling of infragravity waves during Delilah, Journal of Geophysical Research,
107(C10), 3137, 2002.

Ruessink, B. G., The temporal and spatial variability of infragravity energy in a barred
nearshore zone, Continental ShelfResearch, 18, 585-605, 1998a.






85


Sallenger, A. H., and Holman, R. A., Infragravity waves over a natural barred profile,
Journal of Geophysical Research, 92(C9), 9531-9540, 1987.

Schaffer, H. A., Infragravity waves induced by short-wave groups, Journal of Fluid
Mechanics, 247, 551-588, 1993.

Schaffer, H. A., Edge waves forced by short-wave groups, Journal ofFluid Mechanics,
259, 125-148, 1994.

Symonds, G., Huntley, D.A., and Bowen, A. J., Two-dimensional surfbeat: Long wave
generation by a time varying breakpoint, Journal of Geophysical Research, 87,
492-498, 1982.

Tucker, M. J., Surf beats: sea waves of 1 to 5 min. period, Proceedings of the Royal
Society ofLondon, Series A, Mathematical and Physical Sciences, 202, 565-573,
1950.

Van Dongeren, A., Reniers, A., and Battjes, J., Numerical modeling of infragravity wave
response during DELILAH, Journal of Geophysical Research, 108(C9), 3228,
2003.

Yu, J., and Slinn, D. N., Effects of wave-current interaction on rip currents, Journal of
Geophysical Research, 108(C3), 33-1-33-19, 2003.
















SUPPLEMENTARY REFERENCES


Baldock, T. E., and Simmonds, D. J., Separation of incident and reflected waves over
sloping bathymetry, Coastal Engineering, 38, 167-176, 1999.

Battjes, J. A., and Stive, M. J. F., Calibration and verification of a dissipation model for
random breaking waves, Journal of Geophysical Research, 90(C5), 9159-9167,
1985.

Elgar, S., Herbers, T. H. C., Okihiro, M., Oltman-Shay, J., and Guza, R. T., Observations
of Infragravity Waves, Journal of Geophysical Research, 9 7(C 10), 15,573-15,577,
1992.

Foda, M. A., and Mei, C. C., Nonlinear excitation of long-trapped waves by a group of
short swells, Journal ofFluid Mechanics, I]], 319-345, 1981.

Gallagher, B., Generation of surf beat by non-linear wave interactions, Journal of Fluid
Mechanics, 49, 1971.

Guza, R. T., and Davis, R. E., Excitation of edge waves by waves incident on a beach,
Journal of Geophysical Research, 79(9), 1285-1291, 1974.

Guza, R. T., and Bowen, A. J., Finite amplitude edge waves, Journal ofMarine
Research, 34(2), 269-293, 1976.

Guza, R. T., and Thornton, E. B., Observations of surf beat, Journal of Geophysical
Research, 90(C2), 3161-3172, 1985.

Henderson, S. M., Elgar, S., and Bowen, A. J., Observations of surf beat propagation and
energetic, Proceedings of the 27th International Coastal Engineering Conference,
Sydney, pp. 1412-1421, American Society of Civil Engineers, New York, 2000.

Herbers, T. H. C., Elgar, S., Guza, R. T., and O'Reilly, W.C., Infragravity-frequency
(0.005-0.05 Hz) motions on the shelf, Proceedings of the 23rd International
Coastal Engineering Conference, Venice, Italy, pp. 846-859, American Society of
Civil Engineers, New York, 1992.

Holman, R. A., Infragravity energy in the surf zone, Journal of Geophysical Research,
86(C7), 6442-6450, 1981.

Holman, R. A., and Sallenger, A. H., Setup and swash on a natural beach, Journal of
Geophysical Research, 90(C1), 945-953, 1985.









Howd, P. A., Oltman-Shay, J., and Holman, R. A., Wave variance partitioning in the
trough of a barred beach, Journal of Geophysical Research, 96(C7), 12,781-12,795,
1991.

Huntley, D. A., Long-period waves on a natural beach, Journal of Geophysical Research,
81(36), 6441-6449, 1976.

Janssen, T. T., Kamphius, J. W., Van Dongeren, A. R., and Battjes, J. A., Observations of
long waves on a uniform slope, Proceedings of the 27th International Coastal
Engineering Conference, Sydney, pp. 2192-2205, American Society of Civil
Engineers, New York, 2000.

Kostense, J. K., Measurements of surf beat and set-down beneath wave groups,
Proceedings of the 19th International Coastal Engineering Conference, Houston,
pp. 724-740, American Society of Civil Engineers, New York, 1984.

Lippmann, T. C., Holman, R. A., and Bowen, A. J., Generation of edge waves in shallow
water, Journal of Geophysical Research, 102(C4), 8663-8679, 1997.

List, J. H., Wave groupiness variations in the nearshore, Coastal Engineering, 15, 475-
496, 1991.

Liu, P. L.-F., A note on long waves induced by short-wave groups over a shelf, Journal
ofFluid Mechanics, 205, 163-170, 1989.

Longuet-Higgins, M. S., and Stewart, R. W., Changes in the form of short gravity waves
on long waves and tidal currents, Journal ofFluidMechanics, 8, 565-583, 1960.

Madsen, 0. S., On the generation of long waves, Journal of Geophysical Research,
76(36), 8672-8683, 1971.

Madsen, P. A., Sorensen, 0. R., And Schaffer, H. A., Surf zone dynamics simulated by a
Boussinesq type model. Part II: surf beat and swash oscillations for wave groups
and irregular waves, Coastal Engineering, 32, 289-319, 1997.

Masselink, G., Group bound long waves as a source of infragravity energy in the surf
zone, Continental ShelfResearch, 15(13), 1525-1547, 1995.

Mei, C. C., The Applied Dynamics of Ocean Surface Waves, World Scientific Publishing
Co., River Edge, NJ, 1992.

Mei, C. C., and Benmoussa, C., Long waves induced by short-wave groups over an
uneven bottom, Journal ofFluidMechanics, 139, 219-235, 1984.

Nakamura, S., and Katoh, K., Generation of infragravity waves in breaking process of
wave groups, Proceedings of the 23rd International Coastal Engineering
Conference, Venice, Italy, pp. 990-1003, American Society of Civil Engineers,
New York, 1992.