Wave Breaking

Lessen Outcomes

To describe shallow-water & deepwater-water wave breaking. To estimate the properties of shallow-water breakers.

Wave Breaking in Deep Water

Also termed open-water whitecaps.

Induced by strong winds that increase wave heights rapidly.

The maximum height of a wave traveling in deep water is limited by a maximum wave steepness for which the waveform can remain stable.

Beyond the limiting steepness, the wave begins to break and dissipate a part of their energy.

Limiting Steepness in Deep Water

Michell (1893) found the limiting steepness to be given by

which occurs when the crest angle is 120o.

This limiting steepness occurs when the water particle velocity at the wave crest just equals the wave celerity (uc c).

A further increase in steepness would result in particle velocities at the wave crest greater than the wave celerity (uc > c) and, consequently, instability.

7

1142.0

o

o

L

H

Wave Breaking in Shoaling Water

The surf zone is the region extending from the seaward boundary of wave breaking to the limit of wave uprush.

Within the surf zone, wave breaking is the dominant hydrodynamic process.

Wave Breaking in Shoaling Water

When wave moves into shoaling water, the limiting steepness is a function of the relative depth d/L and the beach slope mperpendicular to the direction of wave advance.

Deepwater waves start to feel the bottom when d/L . The water particle motion reaches to bottom and disturbs sediments. Underwater friction and turbulence at bottom slows the wave and shortens wavelength.

When the wave steepness reaches a limiting steepness, the wave breaks, dissipating energy and inducing nearshore currents and an increase in mean water level.

Breakers disturb bottom, erode & transport sediments.

Wave Breaking in Shoaling Water

The depth that is shallow enough to initiate breaking is termed the breaking depth db.

The maximum limit of wave height above which the wave becomes instable and breaks is termed the breaker height Hb.

Properties of Breaker

SWL

ds

Hb

db

m1

Coastal structure

Breaker

Wave heights are a function of water depth.

Wave Breaking in Shoaling Water

Breaker Type

The breaker type is a function of the beach slope m and the wave steepness H/L.

Occur for high steepness waves on gently sloping beaches.

Portions of the wave crest appear to break gently (spill), creating foam as it spills down the face of the wave.

Several wave crests may be breaking simultaneously, giving the appearance of several rows of breaking waves throughout the breaking zone (dissipative beaches).

Spilling breakers generate less turbulence near the bottom and thus tend to be less effective in suspending sediment.

Spilling Breaker

Occur on steeper beaches and/or for flatter waves.

Wave curls over forming a tunnel until the wave breaks and plunges down the face of the wave in a violent tumbling action, resulting in high splash and scour into sea bottom.

Plunging breakers are more commonly associated with swell waves that approach the beach with much longer wavelengths.

Expert surfers love this type of wave!

Plunging Breaker

Describe breakers in the transition from plunging to surging.

Occur on steep beaches.

Wave fronts more or less explodes forwards.

May be found where swell breaks on steep beaches made up of course materials.

Beaches with collapsing and surging breakers are often called reflective beaches.

Collapsing Breaker

Occur on very steep beaches/man-made seawall or for long waves.

Wave crest remains unbroken and the front face of the wave advances up the steep beach with very little or no breaking. The entire face of the wave usually displays churning water and produces foam, but an actual curl never develops.

This type of breaker is often described as creating the appearance that the water level at the beach is suddenly rising and falling.

Surging Breaker

Breaker type may be correlated to the surf similarity parameter, b

Breaker Type

bb

bLH

m

/

Hb = Breaker heightLb = Breaker wavelengthm = beach slope = tan

Spilling Breaker: b < 0.4

Plunging Breaker: 0.4 < b < 2.0

Collapsing / Surging Breaker: b > 2.0

On a uniformly sloping beach, breaker type is estimated by (Battjes, 1974):

b

bb

d

H

Hb = Breaker heightdb = Depth at breaking

Breaker Index

A breaker index criterion is easier to use in many calculations:

b

b

b

b

L

d

L

H 2tanh14.0

Miches Limiting Wave Steepness

Miche (1944) describes wave breaking (regular wave) in surf zone when the limiting wave steepness is

3

1

'3.3

1

'

o

oo

b

L

HH

H

Munks Breaker Index

Munk (1949) derived several relationships from a modified Solitary Wave Theory:

28.1b

b

H

d

Breaker height index:

Breaker depth index:

Godas Breaker Index

Goda (1970) developed a breaker index (Hb/Ho) relating the beach slope (m)and the incident wave steepness (Ho/gT

2).

Godas Breaker Depth Index

Goda (1970) developed an empirical relationship between Hb/dband db/Lo for various beach slopes:

3

4

1515.1

117.0

mL

d

b

o

b

b o

b

ed

L

d

H

Weggels Breaker Depth Index

Weggel (1973) developed empirical relationships between db/Hband Hb/gT

2 for various beach slopes m:

221 gT

Hcc

d

H b

b

b

USACE Breaker Depth Index

USACE (1984) expressed the Weggels results in the following equations:

)1(75.43 191mec

)1(

56.15.192 me

c

where

bp

bbp

m

sbL

dLeH

2tanh095.0 4

Kamphuiss Breaker Index

Kamphuis (1991) proposed two criteria for irregular waves:

m

b

sb ed

H 5.356.0

1. Wave steepness criterion:

2. Depth limited criterion:

Problem

A wave in deep water has 3 m high and 10 s period moving

towards the shore with a slope of m = 0.02. Determine

a. breaker height

b. type of breaker

c. breaker depth

d. breaker length

e. wave celerity at breaking

f. distance of breaker line from the shore.

Problem