Phenomenology of breaking waves

n

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deift hydraulics

CLIENT: MARIN

TITLE: Phenomenology of breaking waves

ABSTRACT:

Iii this report an overview is giveI of literature concerning the subject of breaking waves. The literature survey

discusses three different aspects The first aspect is the classification and physics of breaking waves The second aspect

concerns the research on models for the statistics of breaking waves and the third aspect is the influence of

environmental conditions on the occurence of breaking waves The classification and physics of breaking waves is given

the most attention. Literature discussing the latter aspect is rare and only a few references are given. In this overview

the relevance with respect .to the influence. ofbreäkhig waves in the sea-regime on sailing ships has been kept in mind;

Letters:

REFERENCES: 1) 14578.100 (dated October 23, 1998) of ir S.G. Tan .

ÖIGINATOR DATE REMARKS REVIEW . APPROVEDBY

O P C A de Maas December 1998 G Klopman W M K.. Tiirnans

P C A de Haas Februaty 1999 G Klopman W M K Tiirnans

KEYWORDS CONTENTS STA11JS

BREAKThIGWAVES,UTERATURE,SURVEY,CLASSICATION - -TEXi PAGES: TABLES: FIGURES: APPENOICES: 12 -. 3 O

EI

E

Contents

Abstract

i

i

2 Classification, dynamics and kinematics of breaking waves -

-2.1

C1sifcaticp

2.2 Dynamics and kinematics

3 Statisticsof breaking waves 6

3.1 Introduction : 6

3.2 Wave statistics - 6

3.3 Statistics of breaking waves - 9

4 The influence of environmental conditions

li

4.1 Introduction 11

4.2 Wave grouping 11

4.3 Directional spreading

il

---

5 Conclusions and recommendations 13

References

deift hydra.alia

Abstract

In this report an overview is given of literature conerning the subject of breaking waves. The literature survey discusses three different aspects. The first aspect is the classiflcàtion

and physics of breaking waves. The second aspect concerns the research on models for the

statistics of breaking waves and the third aspect is the influence of environmental

conditions on the occurrence of breaking waves. The classification and physics of breaking

waves is given the most attention. Literature disdussing the latter aspect is rare 'and oniy a few references are'gi'ven. In this overview the relevance with respect to the influence of

breaking waves on sailing ships has been kept in mind.

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I

Introduction

In this report a literature survey is presented concerning the subject of breaking waves.

Emphasis is put on the present state of affairs with respect to the phenomenology of

breaking waves and the corresponding (non-linear) wave statistics. Some attention is paid to

environmental conditions, which influence breaking waves such as directional spreading and wave grouping. The study is focused on breaking waves related to periods between say 6 and 12 seconds in a field of wind waves on deep water.

First in Section 2 the literature concerning definition, dynamics and kinematics of breaking

waves is discussed. The most relevant quantities to characterise breaking waves are

summarised. In Section 3 literature related to the statistics of breaking waves is reviewed. This section starts with a short introduction in wave statistics with special attention for

conditions in which (large) breaking waves can occur. The influence of some environmental conditions is discussed in Section 4. Finally, in Section 5, results of the literature survey are

summarised and recommendations are given.

This report is intended as an introduction to the subject of breaking waves with special attention to the subjects mentioned above. A less specific introduction to the subject of

breaking waves in deep water can be obtained from the review paper by Banner and Peregrine (1993) which has served as one of the starting points of this report. A large number of references are made to studies dealing with thephysics of breaking waves- and therefore the article gives a good overview of the present work on this subject. A quite general recent introduction is the book by Masse! (1996). A review of literature in the

context of offshore structure design can be found in Easson (1997).

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2

Classification, dynamics and kinematics of

breaking waves

2.1

Classification

In engineering manuals such as the 'Shore protection manual' (Volume 1, pp. 2-129..2-136) breaking waves have been classified as spilling, plunging or surging depending on the way in which they break. Spilling breakers break gradually and are characterised by white water at the crest. Plunging breakers curl over at the crest with a plunging forward of the mass of water at the crest. Surging breakers build up as if to forniapltinging breaker but the base of

the wave surges up the beach before the crest can plunge fòrward. The nnie surging breaker is in fact misleading because these they do not break, but they fully reflect. In

actuality, the transition from one breaker type to another is gradual without distinct dividmg

lines. In the context of wave breaking inside the surf zone Massel (1996) (Section 6.2.10)

also identifies the collapsing type as a special type of plunging breaking.

plunging

collapsing

surging

Figure 1: Classification of breaking waves

In deep water only spilling and plunging breakers occur. Although plunging breakers are

less common on deep water, they do occur naturally there. In Banner and Peregrine

reference is made to Coles (1991) for a distillation of an expenenced yachtsman's account

of waves at sea..

2

PbenomenoIog cfbreng wv H3466 Fetruary. 1999

This classification is used for investigations in the dynamics and kinematics of breaking

waves. For applications the typical flow characteristics of plunging breakers are of

importance in determining the loading on constructions and ships, see forexample Chan

(1994). The typical flow characteristics of spilling breakers are more often used in

describing the energy loss due to wave breaking in wave propagation models. However, Banner and Peregrine (1993) remark that the distinction between both types of breakers

cannot yet be quantified Bonmann (1989), in a detailed laboratory experiment, used the criterion of a vertical crest slope to identify plunging breakers and the occurrenceof foam

to identify spilling breakers.

The visual óharacterisation of breaking waves, which is most often used, is that of the

presénce of whitecaps. Although not always explicitly stated, whitecapping is considered to

be associate4 with spilling breakers only. A definition of whiteçapping is for example the one adopted by Huang et al. (1986) as 'Oceanic whitecapping is a consequence of wave breaking and occurs when a patch of white watèr, which is the turbulent air-water mixturç at the crest, runs down the forward face of the wave.' Most definitions of whitecapping used in literature are similar to this one (see e.g. Holthuijsen and Herbers, 1986). A further classification of whitecapping for the purpose of optical detection methods is mentioned in Banner and Peregrine (1993).

2.2

Dynamics and kinematics

For the description of the dynamics and kinematics of breaking waves we use the

distinction between plunging and spillmg breaking waves In most experimental and

numerical work on plunging breakers, use is made of packet-focusing techniques.

For a predictable and reliable packet-focusing technique it is important that all the components coincide in phase at a certain pre-specified position and time instance.

Therefore, the usê of an accurate (non-linear) phase velocity of the wave compònents is

important, especially when the desiréd focusing position is located far from the wave

generating boundaries. In the laboratory it.is important to have either enough stilling time in

between tests or active wave absorption iii order to have highly repèatable packet-focusing events Otherwise, the phase speed of especially the shorter wave components is influenced by remnant spurious lng4vave components from a previous focusing event

The work on spilling breakers seems to be concentrated more on the study öf instabilities of

random Waves leading to breaking. The origin of such instabilities has been related in literatUre to criterion's for wave breaking and we therefore discuss such criterion's in the

context ofspilling breakers.

Plunging breakers

From Banner and Peregrine (1993), p. 386, we summarise the following:

Some progress has been made towards analytical descriptions fOr the motion of the free surface. We refer to Longùet-Higgins (1980), New (1983), Greenhow (1983) and Jillians (1988). However, close inspection of these solutions reveals that little agreement exists

between them. Numerical computations employing boundary integral methods can be used

I

to investigate the full details of many important aspects of wave breaking (up to the

re-enterñg of the breaker in the free surface). A striking: feature discovered from such

computatiOns (Peregrine et L, (1980)) is that the water rising up the front of the wave into the jet is subject to large accelerations. Typical computed maximum values are around 5g,

where g is the gravitational acceleration. We remark that such a boundary integral method

has been developed at MARIN and WL I DELFT HYDRAULICS in which both in 2D and3D

breaking waves have been simulated See Broeze (1993) for simulation of plunging

breakers due to bottom topography and WL I DELFT HYDRAULICS (1997) for simulation of

experiments in a wave flume. An example of a detailed study on the flow in a plunging

breaker can be found in Longúet-Higgins (1995)

-Dommermuth et al. (1988) made a detailed comparison between the deep-water plunging

breaker as computed with a boundary integral method and kinematics measurements using wave gauges and Laser-Doppler vlócimetry. The numerical results agree very well with. the

measurements, proving the usefulness of the boundary integral equation models up to the point where the plunging breaket jet re-enters the free-surface in front of the crest.

Detailed experiments with plunging breakers have been reported recently by Kjeldsen et al.

(1998) and by Perlin et al. (1996). In the experiments desiribed in the latter paper it was

observed that the flow is esseiltially irrotational up to the jet's re-entry into the forward face

of the water surface, supporting the assumption made in the boundary integral methods

mentioned above Kjeldsen et al

(1998) reports the occurrence of total

acceleratións up to 1.5g. Note that there is a large difference with the computed maximum of 5g by Peregrine et aL (1980) but since the way in which the plunging breaker is created is completely different, a direct comparison is not appropriate. Still it is striking that such

large differences can occur.

Bonmarin (1989) and Rapp and Melville (1990) have performed studies of there-entering of the plunging wave. Bonmarin (1990) concentrates on the splash-up phenomenon. Rapp and Melville (1990) report a very systematic work with measurements of surface motion, breaking-induced currents, turbulent fluctuations, surface mixing, momentum flux and

energy dissipation. See Figure in Banner and Peregrine (1993) for an example of the

measured mean velocity field at a number of time levels after the occurrence of a plunging

breaker. Numerical simulation of fluid motion after re-entrance of the plunging breaker

using a volume of fluid method has been reported by Lin et al. (1997). The paper describes

the use of a turbulence model and comparison of the numerical results with measurements

by Chang and Liu (1.996).

Spilling breakers

The traditional criterion for wave breaking is that horizontal water velocities in the crest must exceed the Speed of the crest For regular waves it was established by Stokes (184.7,

1 880)thatthis criterion is equivalent to the following criterion's: the crest of the wave attains a sharp point with an angel of 120°. the ratio of wave height to wavelength is approximately 1/7. the particle acceleration atthe crest of the wave equals to 0.5g.

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Phenomenology of brealdng waven

WI. deifthydraulia

H3466 February. 999

These criterion's indicate upper limits for whiòh a regular wave propagates stable. For regular waves these limits are never reached due to various instabilities. Refinements to these criterion's have been made by several authors, see Longuet-Higgins (1969, 1974,

1976), Cokelet (1977), and others. For irregular waves it was hypothesised by Snyder and Kennedy (1983), Sny4er et al. (1983) and Kennedy and Snyder (1983) that e.g. the vertical

acceleration controls stability. Longuet-Higgins (1985,1986) pointed out that careful distinction between Lagrangian and Eulerian açcelerations is necessary. See further the section about the statistics of breaking waves in Chapter 3. Although in the context of

plunging breakers for both deep and shallow water, we mention here the work of Griffiths

(1992) In this paper the flndmgs of a number of investigators are tabulated and it was

found that with one exception maximum velocities for deep and shallow plunging breakers were about 1.0 to 1.3 times the phase velocity.

A quite detailed description of the beginning of a (small-scale) spilling breaker is given by Longuet-Higgins (1994). From the introduction of thjs article we cite:

'Commonly it is assumed that a spilling breaker begins as a small-scale plunging breaker, but recent experimental studies, which we shall describe, show that tins is not always the case. Waves with lengths up to 2 m may break in a .quite different way. Parasitic capillary

waves tend to förm on the forward face of the wave [...] emerging at a point sQme way ahead of the crest. The flow beneath the capillaries then separates and the crest quickly becomes turbulent and "crumples" owing to loss of energy. Often the fluid in the crest advances down the forward face of the wave without any overturning of the free surface.

Air can however be entrained near the front edge of the breaker. All of this has been

observed to take place in the laboratory with mechanically generated waves, withOut the action of any wind; see Figures 4a tO 4d.' The figures to which is referred are taken from

Duncan et al. (1994).

The evolution of a spilling breaker after its initiation it more amenable to modelling since

steady examples can be generated. Banner and Perçgrine (1993) give an overview of models

based on the 'roller'-concept in which a region of turbulence rides passively on the rest of

the fluid. They refer to the work of Tuliñ and Comte (1986) änd Comte (1987) as the furthest development in the application of the roller-concept to practical modelling.

Laboratory expriments on spilling brakers have been reported by Lin and Rockwell

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3

Statistics of breaking waves

3.1

IntrodUction

The statistics of breaking waves is usually determined from a breaking criterion and a probability density function of a quantity related to the breaking criterion. In the eighties

relatively much work has been done to derive statistics based on a limiting steepness and

the joint probability density function of wave heights and wave periods. However, it was shown by e.g. Holthuijsen and Herbers (1986) and Mather et al. (1988) that the practical applicability of such an approach may be restricted since they found that for directionally

spread wave fields waves alteady break for small steepness. We only found a few recent

studies on the statistics of breaking waves in the above-described way but also noted that discussion about applicability is still ongoing. In this chapter we first summarise the most

relevant aspect of wave statistics m the next section and then give a bnef overview of

literature on the statistics of breaking waves.

3.2

Wave Statistics

Wave statistics is generally expressed in terms of probability density functions (p.dL's).of

some relevant parameters. These in turn are usually expressed in terms of spectral parameters. For Iatçr reference we therefore first summarise in this section the most important spectral parameters in view of this literaturó survey. For a more complete description of spectral description and spectral properties, see e.g. Massel (1986), Chapter:

3 We also bnefly discuss some definitions of wave parameters Several p d f 's are

discussed which are relevant for the description of the Statistics of breaking waves.

The random character of ocean waves is usually described in terms of the spectral density

function S(w), which represents a distributiOn of wave energy in the frequençy domain. Figure 2 shows an example of a typical wave spectrum.

2 3

frequéntië

Figure 2: Typical wave spectrum(JONS WAP)

6

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The spectral moments mr are defined as

rnr=JS(oi)dw.

The few first moments are of special importance for the spectral description of ocean waves. The first tro moments m0and m1 determine the. mean wave frequency aiid mean

wave period, i.e.

rn1

-

CO=-

andT=27t-m0

Two measures Of spectral width that are of importance later are i

rn

and

E2.JfOm4fl2

m0m4

-Note that in the latterparameter the fourth-order moment in4 occurs. This is a.rather ci-ucial

parameter Sin for practical applications, the vahi ofthe fourth moment ofthe spectrum is

vi)T sensitive to the noise in the data and the cut-off frequency of the spectrum. For a

theoretical JONSWAP or Pierson-Moskowitz spectrufli the fourth moment does notj even

exist It is noted that the parameter e is alsorelevant for cnteria for wave breaking because

it represents the variance of the vertical acceleration of the sea surface, see Srokosz (1986) Atiother parameter for spectral width (and wave groupiness)is ,c(r), defined as

2

()

d]

[ï S(w) sin(wr)

dT].

The first term between square brackets is the auto-covanance of the surface elevation, which is the Fourier transform of the spectriiiìì 5(w). The second term between square

brackets is the Hubert transform of the auto-covariance.Therefore ic(r) can be interpreted as the envelope of the auto-correlation of the- free surface e1evtion as a function of the time lag r - Usually one works with the parameter ic(T), i.e. the value at a time lag of one mean wave period. This -parameter is much more robust than thç previous two parameters V and

e, since it much less sensitive to high-frequency noise.

All three parameters -vaiy between zero and one. But while y and e increase when the width of the specfrùm increases, the parameter ic(T) decreases when the width of the

spectrum increases.

-For studying p d f 's of wave parameters, especiallywhen non-linearity is involved, it is of

cruciai importance to describe them in a unique way. In recent literature and in this

literature survey the recommendations are

followed proposed by PIANC and the

Intematipnal Association for Hydraulic Research (lAhR, 1989). For example, a wave height is defined as zero-dòwn-crossing wave height in which the wave trough occurs before the wave crest Among these parameters are typical non-linear parameters such as

crest front steepness atid vertical asymmetry factor.

7

Phenomenclogy et breaking waves

WI. defthydralilics

The most commonly used wave height p.d.f. is thè Rayleigh distribution

H

(H2

f (H) = ---i- exp

---

with = m0 the variance of the surface elevation. Although derived under the assumptions of Gaussian distribution of the surface elevation änd nanow-bandedness of the spectrum, the Rayleigh probability density functiOn seems to be a good approxiipation of

the short-term wave-height statistics, as shown by Longuet-Higgins (1980) and Tayfun

(1990).

Because there is a strong relation between breaking and the sea surface slope, it is also important to consider the jOint dIstribution of wave heights ad wave slopes. Using the dispersion relation for ocean surface waves (for imeansed free-surface conditions) this

distribution can be uniquely described in terms of the joint distribution of wave heights and

wave petiods Most of the developed theoryis written iii terms of the latter distribulion and therefore we describe it here in the same way. Later we describe some literature involving

j oint distributions of wave heights änd specially defined wave slopes. Many papers dealing

with radar observations of the sea surface use the joint distribution of wave heights and

wave slopes.

As with many theoretical papers oñ wave statistics, expressions for the joint distribution of

wave heights and periods have been derived from the pioneering papers by Rice (1944,1945) on Gaússian random noise for electromagnetic signais. Longuet-Higgins

(1975,1983) found using the non-dimensional variables =

HI.J;and z

= TI Tthe

p.d.f.

f2() =

ex{_Ç[i+_-(

12

_{= 4v[1+(1+v2Y2]}

To illustrate a typical pd.f., examples are shown in Figure 3.

6 - 6 v=0.2 H3466 February. 1999 a,

r

cl

Figure 3: Jóintprobability density function according to (6) for two values of the parameter V

8

0.5 1 1.5 0.5 1 1.5

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An alternative for this distribution is the distribution derived by Cavanié et ai. (1976) which involves the parameter E and therefore depends on the fourth moment m4 . In Ochi and Tsai (1983) a joint p.d.f. for wave heights and periods is derived using more specific definitions of wave height and period. This p.d.f. is then used to derive statistics of breaking waves.

Myrhaug and Kjeldsen (1984, 1987) have reported the use of joint p.d.f.'s of wave heights

and wave slopes. Among these joint distributions were crest front steepness-wave height and vertical asymmetry factor-wave height distributions. Their studies are nöt primarily directed to derive the statistics of breaking wavés but on the occurrence of steep and high

waves.

Finally we mention here studies on wave group statistics. Most studies on wave group statistics áre stimulated by the fact that waye groups often cause serious problems for the safety of marine systems. This is due to the successive attack of high individual waves in the group, especially when the periods of these waves are close to the marine system's natural motion period. With respect to the occurrence of breaking waves, wave group

statistics gives an indication of the successive occurrence of breaking waves.

Most of past efforts in determining the group statistics were empirical (see, for example,

Goda (1976), Kimura (1980), Nolte and Bsu (1979), Rye (1974) and Rye and Lervik

(1981)). The first analytic model for grÓup statistics was established by Longuet-Higgins (1957, 1984) Itis formulated in terms of the amplitude A of the wave envelope Under the

assumption of a Gaussian distributión it can be deduced that A is Rayleigh distributed. The

incorporation of non-linear effects has been stuied in Tayfun and Lo (1989) and Tayfun

(1994). We further méntion the paper by Myrhaug ànd Rue (1996) on the joint distribution of successive wave periods.

3.3

Statistics

of

breaking waves

Ochi and Tsai (1983) proposed a model for breaking statistics based on the joint wave

amplitude-frequency distribution., examining one-dimensional, non-narrow band deep-water

waves with various frequency spectra. This class of models was developed further in studies by Srokosz (1986), Yuan et al. (1986) and Huang (1986). The probability of wave

breaking in these models is expressed in terms of a probability function p(r)., which

expresses the probability that a wave of height T will break. These expressions contain

spectral parameters including the fourth-order moment m4.

In order to avoid the problems associate4 with the susceptibility of thç fourth-order moment m4 to high-frequency noise in the spectrum, Greenhow (1989) proposed to relate the

fourth-order moment rn4 to the significant wave height H and significant wave period 7's.

However, this was verified on the basis of one field experiment only and also a theoretical justification is lacking, see the discussion on the fourth-order momentrn4in Section 3 .2.

9

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The most commonly accepted limit for wave breaking in random seas in 2D is that

proposed by Ochi and Tsai (1983), based on the wave steepness (note that gT2 = 2rrL in

deep water),

H = 0.O2OgT2. (8)

Note that H and T are the wave height and period of an individual wave. The value of the coefficient s =0.020 is about 10% lower than the regular wave condition mentioned in Chapter 2 on the ratio of wave height and wave length of 1/7. This value corresponds with

a =0.4 in the vertical threshold criterion which states that waves break when the vertical

acceleration in the crest is larger than ag.

In 3D however; there is no strong correlation between wave breaki.g and steepness criteria.

Holthuijsen and Herbers (1986) in a field study found that the joint p.d.f's of wave heights and periods for breaking and non-breaking waves are quite similar, mdicatmg that waves also break for small steepness Mather et al (1988) camed out studies on waves generated

in a 3D-facility and found that equation (8) indeed is an upper limit for breaking waves but that waves also break for much smaller steepness, see Figure 3 in Easson (1997). In a study

to investigate purely the 3D-effects, withoút the random nature of the wave spectrum, She

et al. (1994) lookec at the focusing of a regular wave in a 3D-tank. Steepnesses up to

s =0.040 were found for which waves break. This indicates that freak waves may occur

having much larger steepness than breaking waves.

We did not find many recent studies employing a distribution function with a breaking criterion to derive statistics of breaking waves Masse! (1998) reports of a model using the

vertical acceleration threshold but only conclUdes that his results are in qualitative agi-eement with field and laboratory observations. Kapdasli et al. (1995) proposç a

probability distribution of random wave breaking basçd on a wave steepness criterium nd using the marginal probability densities of individual wave heights. However, they do not

give the steps involved in the derivation of their probability distributions, nor do they make

comparisons with experimental data Green (1994) m a discussion of the Holthuijsen and

Herbers (1986) observations question the relation between the observed whitecappmg and

the onset of breaking.

I0

4

The influence of environmental conditions

4.1

Introduction

In the light of the previous findings it may not be surprising that very little is known about

the effect of environmental conditions on the breaking of waves. In this chapter literature

related to this that has been found is mentioned only briefly.

4.2

Wave grouping

The presence of wave groups with respect to loads on ships is important because of the successive attack of waves that may cause damage. Su (1986) mentions wave grouping as one of four important features of huge anomalous waves which can cause damaging The

other three are large wave heights, large wave steepness and wave breaking The relation of wave grouping with wave breaking is not described in this paper but we refer to it because

of the many important aspects discussed related to sailing ships Holthuijsen and Herbers

(1986) have investigated the occurrence of wave breaking inside wave groups. They

observed that two-thirds of the breaking waves occurred in one-third of the wave groups and that breaking generally occurs in the centre of such a group Sutherland (1992) found

that waves in a shorter group brealç at a lower height.

The evolution of wave groups is often described in terms of extensions of cubic non-linear

Schrodmger equations (one-dimensional) for the wave envelope A In Li (1993) such an

equation is described and effects of wind forcmg and breaking are investigated Results are compared with Su (1986) and Hólthuijsen and Herbers (1986). Taylor and Haagsma (1994)

have described the tise of such a non-linear evolution equation for the modelling of

focusing of steep wae groups. Simulation of wave group evolution and waye breaking with ,a (boundary integral method) has been.reported by Wang et ai. (1993). In one part of this

sidy the flow of a plunging jet is simulated (see also Chapter 2) and in another part a

technique is used to suppress wave breaking in order to be able to simulate wave group

evolution over a large period.

4.3

Directional spreading

Experiments Qn the effect of directional spreading are described in She et al. (1994), Kolaini and Tulin (1993), Kjeldsen (1982) and Nepf et al. (1998).The latter suggest that a breaking criterion based on the evolution of high-frequency components may be a more robust indicator for field application than a criterion on steepness. However, Nepf et al. (1998) do not present suggestions for an actual criterion based on the evolution of

high-frequency components in their paper. Computations are described in Tsai et aI. (1994) for

the almost highest short-crested waves indicating levels for breaking. This paper only discusses non-random waves. We finally mention Prislin et al. (1997) who discuss the

importance of wave directionality. They refer to Kj eldsen (1990) when stating 'Sometimes

wt deift hydraulics

ship capsizings occur not because of extreme wve heights but because of sudden impacts

by waves from different directions.'

4.4

Wind and current

No specific references have been found regarding the influence of wind and current on

wave breaking at open sea. However, in coastal areas pronounced effects can be found.

The wind of coarse is important in the generation of the waves, but is not the primary cause

of the waves to break, which is in first instance due to a non-linear instability of the wave.

In case of very strong storm winds the wind is reported to be capable to blow water directly from the crests of the waves. A strong variation of the wind-driven mean horizontal velocity near the water surface can increase the wave length, which reduces the wave steepness and

the probability of wave breaking. In the laboratory wave length changes of 5 to 10% have

been observed for a strongly sheared current near the free surface.

In the surf zone near the coast it has been observed that an off-shore blowing wing increases

the probability of the waves to break, for waves with the same mean characteristics

(significant wve height, wave period and water depth).

The presence of currents does in most cases have no other effect than Doppler shifting the

waves. Since the wave steepness is the primary non-linearity parameter, the effect of current can in first instance be incorporated by taking the changes in wave length into account.

On a larger scale refraction and shoaling of the waves on the current can be important, such

as for instance in tidal inlets along the coast, or for largetidal or geophysical currents separating with big eddies or vortices from a coast (e.g. Norway). Experience and ship

observations show that very steep and very high breaking waves may occur in such

situations (Kjeldsen, 1982).

12

5

Conclusions and recommendations

In this literature survey on breaking waves we found that the understanding of breaking waves is growing but also that much knowledge still lacking, especially when judging

cönsistency between different results. Important

trends that can be observed are thç

development of more sophisticated field measurement techniques or laboratory

experiments and the development of numerical techniques such as the volume of fluid

method. These techniques help to understand what the mechanisms are behind wave

breaking Numerical models may become suitable to simulate the complete wave breaking process but for application there is still a large need to classify the breakingproblems one

wants to consider.

The survey on literatuxe on the statistics of breaking waves seems to indicate that the

development of statistical models has notprogressed much the last years due to the lack of

a proper breaking criterion Further study on the reasons why waves break may give new

impetus to this field.

The influence of envfronmçntal conditions on wave breaking is hardly reported of in

literature Most literature has been found on the influence of wave grouping Understanding öf the physics of breaking waves seems to be necessarily to progress in this field.

With respect to any future stu4ies on wave breaking for specific design or development

purposes, we recommend the following:

Idtificatinn of the importance of breaking waves in relation to these purposes in

comparison with the importance of high and steep waves.

Specification of the purpose of the use of models for the statistics of waves.

Identification of relevant measuring techniques including high spatial resolution and

identification (i.e. field measuring techniques) for such studies.

Identification of techniques for the controlled generation of wave sequences with

breaking waves at specified position and time in the laboratory, including non-linear

wave dispersion for adequate focusing of the waves at a certain point in spaceand time. Identification of relevant numerical models for such studies.

w. ddft hydra4lics

Rèferences

Banner, ML. and D.H. Peregrine, 1993: Wave breakihgin deep water. Annu. Rev.Fluid Mech., Vol. 25, p. 373-397.

Bonmarin, P., 1 989: Geometric properties of deep-water breaking waves, J. FluidMech.. VOl. 209, p. 405-433. Broeze, J., 1 993 : Numerical modelling ofnônlinear free surface waves with a3D panel method. PhD

disSertation. Twente University, the Netherlands,

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