1392 Suntoyo Oe Wave Hydrodynamics (S2)(1a)
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Transcript of 1392 Suntoyo Oe Wave Hydrodynamics (S2)(1a)
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Wave Hydrodynamics
.
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Beach Terminology
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The inner shelf is a friction-dominated realm where
surface and bottom boundary layers overlap.
(From Nitrouer, C.A. and Wright, L.D.,Rev. Geophys., 32, 85, 1994. With permission.)
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Conceptual diagram illustrating physical transport
processes on the inner shelf.
(From Nitrouer, C.A. and Wright, L.D.,Rev. Geophys., 32, 85, 1994. With permission.)
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Ocean WavesOcean waves may be classified by thegenerating force
(wind, seismic events, or gravitational pull of the moon),therestoring force, (surface tension, gravity, the earths
rotation), or thefrequency of the waves.
Idealized Ocean Wave Spectrum
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Wind WavesA wind wave is
generated by thefriction of the wind
over the waters
surface.
As the wind blows over the surface of the water, friction and pressure
differences create small ripples in the water surface.
The wind pushes on the back side of the wave and pulls on the front,
transferring energy and momentum to the water.
As the wind continues to transfer momentum to the water, the wave
becomes higher.
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Wave GrowthThe area where wind waves are form and grow
is called thegeneration area.
Higher wind speeds mean more momentum to transfer to the water,
resulting in higher waves.
Duration is the length of time the wind is blowing. The longer thewind blows, the higher the waves and more chaotic the seas.
The heights of the waves in the generation area are determined by three
factors: wind speed,duration, andfetch.
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Fetch
Fetch is the horizontal distance that the wind blows across
the water.
Fetch is important in the early stages of wave formation, and will
control how large the wave will be at a given time.
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SwellAs deep-water waves depart the generation area,
they disperse with the long waves travel faster.This sorting by wave speed creates long regular wave patterns
calledswell.
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Shoaling WavesAs a waveshoals (approaches the shoreline)the wave period
remains constant, causing the wavelength to decrease and thewave height to increase.
Friction slows the bottom of the wave to while the top continues
at the same speed, causing the wave to tip forward.
WhenH/L, theratio of the wave
height to
wavelength,
reaches thecritical value of
1/7, the wave
breaks.
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Waves under the influence of
winds in a generating area
Waves moved away from the
generating area and no longerinfluenced by winds
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SMALL AMPLITUDE/FIRST
ORDER/AIRY WAVE THEORY
1. Fluid is homogenous andincompressible, therefore, the density isa constant.
2. Surface tension is neglected.
3. Coriolis effect is neglected.
4. Pressure at the free surface is uniform
and constant.
5. Fluid is ideal (lacks viscosity).
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SMALL AMPLITUDE/FIRST
ORDER/AIRY WAVE THEORY
6. The wave does not interact with any otherwater motion.
7. The bed is a horizontal, fixed, impermeableboundary which implies that the verticalvelocity at the bed is zero.
8. The wave amplitude is small and the waveform is invariant in time and space.
9. Waves are plane or low crested (twodimensional).
Can accept 1, 2, and 3and relax assumptions 4-9
for most practical solutions.
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WAVE CHARACTERISTICS
T = WAVE PERIOD
Time taken for two successive crests to pass a given
point in space
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Definition of Terms
ELEMENTARY, SINUSOIDAL,
PROGRESSIVE WAVE
h=eta
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WAVE CELERITY, LENGTH,
AND PERIOD
PHASE VELOCITY/WAVE CELERITY:(C) speed at whicha waveform moves.
Relating wavelength and H2
O depth to celerity, then
Since C = L/T, then is
NOTE: L exists on
both sides of the
equation.
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DEEP WATER:
Since:
Then:
Here, Since:
Then:
When d/L >0.5 =DEEP WATER
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1. Longer waves travel faster than shorter waves.
2. Small increases in T are associated with large increases in L.
Long waves (swell) move fast and lose little energy.
Short wave moves slower and loses most energy
before reaching a distant coast.
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MOTION IN A SURFACE WAVE
Local Fluid Velocities and Accelerations
(VERTICAL)
(HORIZONTAL)
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Water particle displacements from mean position for
shallow-water and deepwater waves.
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A h h li th t h ll d th h
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As waves approach a shoreline the water shallows and they change
from deepwater to transitional waves.
As water shallows the waves steepen and finally break to form surf
which surges towards the shoreline.
Wh f h th b h it h th b h f h
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When surf reaches the beach it rushes up the beach face as swash
and then runs back down the slope as backwash.
Swash and backwash moves sediment up and down the beach face.
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SUMMARY OF LINEAR WAVES
C =Celerity= Length/Time
Relating L (Wavelength) and D (Water Depth)
Since C = L/T, then becomes:
Since C = L/T, then becomes:
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PROBLEMS
GIVEN: A wave
with a period T =10 secs. ispropagatedshoreward from a
depth d = 200m toa depth d = 3 m.
FIND: C and L atd = 200m and
d = 3m.
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WAVE ENERGY AND POWER
Kinetic + Potential = Total Energy of Wave System
Kinetic: due to H2O particle velocity
Potential: due to part of fluid mass being above trough.(i.e. wave crest)
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WAVE ENERGY FLUX
(Wave Power)
Rate at whichenergy istransmitted in thedirection ofprogradation.
Summary of
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Summary of
LINEAR (AIRY) WAVE THEORY:
WAVE CHARACTERISTICS
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Regions of validity for various wave theories.
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HIGHER ORDER THEORIES
1. Better agreement between theoretical and
observed wave behavior.
2. Useful in calculating mass transport.
HIGHER ORDER WAVES ARE:
More peaked at the crest.
Flatter at the trough. Distribution is skewed above SWL.
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Comparison of second-order Stokes profile with linear
profile.
USEFULNESS OF
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USEFULNESS OF
HIGHER ORDER THEORIES
MASS TRANSPORT VELOCITY = U(2)
The distancea particle isdisplacedduring onewave period.
NB: Mass transport in the direction of propagation.
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HIGHER ORDER WAVES
Stokes
Takes wave height to 2nd order (H ) and higher Useful in higher energy environments
2
2nd order approximate wave profile is:
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If H/L is small, then profile can be represented by linear wave theory
For deep H2O Eq. reduces to:
THIRD ORDER APPROX. (Wave Velocity)
NB. If (H/L) is small, use linear wave theory equation.
TERM: Peaks crests
Flattens troughs
Conforms to shallow H2O wave profile
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VELOCITY OF A WAVE GROUP
WAVE GROUP/WAVE TRAIN
Speed not equal to wave travel for individual waves
GROUP SPEED = GROUP VELOCITY (Cg).
INDIVIDUAL WAVE SPEED = Phase velocity or wave
celerity.
Waves in DEEP or TRANSITIONAL WATER
In SHALLOW WATER
K = .4085376 YT = 1.065959
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Keulegan and Patterson (1940) Cnoidal Wave Theory
SI Units (m) Wave Height = .25 Wave Period = 2 WaterDepth = 1.1
Deep Water Length = 6.24 Present Length = 3.757897 Elliptical Modulus = .4085376
Net Onshore Displacement Umass = Mass Transport Velocity
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Time U(T) UMassSediment
Transport
Airy Wave TheoryLO = 6.24 L = 5.783304
T = 2s
H = 0.25m
D = 1.5m
NB. Umass
Symmetry
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Deformasi Gelombang
Breaking
Refraction
Diffraction
Reflection
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Refraction
Waves travel more slowly in shallow water(shallower than the wave base).
This is called refraction
This causes the wave front to bend so it is more
parallel to shore.
It focuses wave energy on headlands.
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Wave Refraction
EuropeanCoast,1996
Orthogonal
Surf / Breaker
Zone
Beach
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Wave Refraction
Seabed contour
Wave Crest
Path of crests diverge
and minimize impact ofwaves on shore
Seabed contour
Wave crest
Path of crests converge and maximize
impact of waves on shore
Shallow
Deep
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Long shore Transport
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Wave Diffraction
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50Orthogonal Wave Crest
Orthogonal
Energy Transfer
Wave Diffraction
Breakwater
Hi
Hd
r
L
b
q
Shadow Zone
Wave Diffraction
DiffractionCoeficient
( K )
K = Hd / Hi
K = (r/L, b,
q)
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Refleksi Gelombang
Europe
anCoast,1996
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Refleksi Gelombang
Untuk dinding vertikal, kedap air, dgn elevasidiatas muka air, hampir seluruh energi akandipantulkan kembali ke laut.
Hanya sebagian saja energi yang dipantulkan
jika gelombang menjalar di pantai yang agaklandai
Refleksi tergantung pada kelandaian pantai,kekasaran dasar laut, porositas dinding, dan
Angka Irribarren (Ir) : tanr
i
o
I
H
L
Kr = Hr / Hi
Kr = fungsi (a,
n, P, Ir)
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Perbedaan Gelombang
WAVES BREAKING
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WAVESBREAKING
Dean and Dalrymple, 2002
o
o
LH
b
tan
5.0
3.35.0
3.3
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Suntoyo
Hp. 081230988146http://www.its.ac.id/personal/index.php?id=suntoyo-oe
http://www.suntoyo.esmartweb.com/index.htm
http://www.flickr.com/photos/21947353@N08/
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