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Wave Breaking

The release of energy derived from the wind, along a narrow coastal zone - geomorphic work done by wind, really, translated through medium of water.

Wave Breaking

Wave breaking is responsible for the processes which control beach morphology: (1) nearshore current generation

(2) sediment transport

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Wave Breaking

Show videos of Wave Break

Vilano beach movie Steamer’s Lane movie

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As waves shoal into shallow water, wave height increases and wave length decreases:

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H = H012n

c0c

"

# $

%

& ' 1/ 2

= H0gT4π

1gh

"

# $

%

& '

1/ 2

L = T gh

Wave steepness:

€

HL

=

H0gT4π

1gh

#

$ %

&

' (

1/ 2

T gh~ h−

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Something has to give!

Condition for Wave Breaking

Wave Breaking – When it occurs?.

Common misconception – “breaking is a result of waves dragging on the bottom, then trip forward due to friction” – NO! Friction plays a very small role – computer simulations that completely neglect friction can still produce breaking waves. A wave breaks when it becomes overly steep, because the velocity of water particles in the wave crest exceed the velocity of the wave form!

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Style of Breaking

Schematic and traces of high-speed photos illustrating different types of wave breaking behavior. But what causes each one of the different breaking styles?

Style of Breaking - Illustrated

Plunging waves (moderate beaches)

Spilling waves (flat beaches)

Surging waves (steep beaches)

First observations recognized that beach slope and wave steepness had something to do with this...

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Breaker Types – Examples from Davidson-Arnott text

Iribarren Number

This ratio of beach steepness to wave steepness has a deep-water form and a nearshore form.

ξ∞ < 0.5

0.5 < ξ∞ < 3.3

ξ∞ > 3.3

ξb < 0.4

0.4 < ξb < 2.0

ξb > 2.0

From Battjes, 1974

ξ

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ξ∞ =S

H∞L∞

$ % & '

( ) 1/ 2

€

ξb =S

HbL∞

$ % & '

( ) 1/ 2

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Wave Break Style vs. Ir. #

Lab Results from a Wave Tank

Early Numerical Models

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Early Numerical Models

More Recent Numerical Models

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More Recent Numerical Models

Solitary Wave Runup on a beach

More Recent Numerical Models

3-D Weakly Plunging Breaking Wave on a Beach

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More Recent Numerical Models

3-D Weakly Plunging Breaking Wave on a Beach

Wave Breaking Condition – γ (gamma) - ratio of Hb to hb

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γ b =Hb

hb

Is this a constant? some disagreement = 0.73 --> 1.03, from lab studies of monochromatic waves

For a given wave steepness, the higher the beach slope, the greater the value of γb

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Breaker Height Prediction - various forms

€

Hb

H∞

=1

3.3(H∞ /L∞)1/ 3

€

Hb

H∞

=0.563

(H∞ /L∞)1/ 5

€

Hb

H∞

=0.46

(H∞ /L∞)0.28

Munk (1949) - based on Solitary Wave Theory

Komar and Gaughan (1972) - based on Airy Wave Theory

Kaminsky and Kraus (1993) - based on Lab Measurements

Breaker Height Prediction - reconfigured

€

Hb

H∞

=0.563

(H∞ /L∞)1/ 5

----->

€

Hb = 0.39g1/ 5(TH∞2 )2 / 5

Data span 3 orders of magnitude of breaker heights Remarkably well-behaved data

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Surf Zone Wave Decay and Energy Dissipation

Steep, reflective beaches - Wave breaking (and energy dissipation) is concentrated through plunging breakers. Broken wave surges up the beach as runup.

Low-slope, dissipative beaches - Extensive, wide surf zone over which spilling breakers dissipate energy. At any time, several broken wave bores, and smaller unbroken waves, are visible.

Villano Beach

Anastasia Island Wav

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Reasons for understanding surf zone wave decay

Understanding the patterns of wave decay in the surf zone is important for two significant reasons: 1. Wave energy dissipation is inversely related to the alongshore pattern of wave energy delivery -- so it can help identify relative vulnerability of coastal property. 2. Wave energy expenditure is partially transformed into nearshore currents, which are responsible for sediment transport and beach morphologic modification.

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Waves in the Surf Zone – Thornton & Guza (1982) - Torrey Pines Beach

Torrey Pines Beach – fine sand with minimal bars and troughs. Wave staffs and current meters - measurements from 10 m water depth to inner surf zone. Published the distributions of wave breaking within the surf zone on a natural beach

The Surface Roller vs. The “Main Part” of the Breaking Wave

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Wave Height in the Inner Surf Zone or The Height of Surf Bores

Broken wave height is controlled primarily by water depth

Surf wave heights after initial breaking

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Waves over a barred beach profile

Bar (induces breaking)

Trough (breaking ceases)

Beach (breaking resumes)

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∂ ECg( )∂x

= −ε f −εb

3

sinh2

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khHf

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π

πρε

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εb =3 π16

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γ 2h31− 1

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Beach Profile

Wave Heights

Energy Flux Profile

Energy Dissipation

Thornton and Guza (1982, JGR)

Dissipation Models - Depth-controlled Random Wave Breaking

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Move locus of wave break seaward

Modeling Wave Energy Dissipation - Homer, Alaska