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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:
€
H = H012n
c0c
"
# $
%
& ' 1/ 2
= H0gT4π
1gh
"
# $
%
& '
1/ 2
L = T gh
Wave steepness:
€
HL
=
H0gT4π
1gh
#
$ %
&
' (
1/ 2
T gh~ h−
34
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
€
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
----->
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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
e en
ergy
dis
sipa
tion
patte
rn d
epen
ds o
n m
orph
olog
y of
the
beac
h
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
161
!!"
#
$$%
&=
khHf
c rmsff
π
πρε
€
εb =3 π16
ρgB3 f Hrms5
γ 2h31− 1
1+ Hrms γh( )2( )5 2
'
(
) ) )
*
+
, , ,
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