Transcript
m.a. Oseanografi Umum (ITK 221) 23/11/2009
Gelombang Laut (Ocean Waves)
Oleh : M. Tri Hartanto
Kenapa perlu mempelajari gelombang?
Giant Kelp, Teluk California Abrasi Pantai di Carita, Anyer
Gelombang Lepas Pantai Kangean, Jawa Timur
Gelombang Pantai Pelabuhan Ratu, Jabar
Sumber Energi
orripples
orseas
• A A WaveWave is a is a rhythmicrhythmic movementmovement that carries that carries energyenergy through matter or space.through matter or space.
• In oceans, waves move through In oceans, waves move through seawaterseawater
Caused byCaused by::
• WindWind
• EarthquakesEarthquakes
• Gravitational force of the Moon and Sun.Gravitational force of the Moon and Sun.
• When a wave passes through the ocean, When a wave passes through the ocean, individual individual water molecules move up and down but they do not water molecules move up and down but they do not move forward or backward.move forward or backward.
• When a wave breaks against the shore, When a wave breaks against the shore, the crest the crest outruns the trough and the crest collapses.outruns the trough and the crest collapses.
• Called aCalled a breaker. breaker.
• In this case, water does move forward and backward.In this case, water does move forward and backward.
Waves Caused by WindWaves Caused by Wind
•When wind blows across a body of When wind blows across a body of water, water, frictionfriction causes the water to causes the water to move along with the wind.move along with the wind.
•Wave Height depends on – Wave Height depends on – – Wind speedWind speed– Distance over which the wind blowsDistance over which the wind blows– Length of time the wind blowsLength of time the wind blows
Basic Properties of Waves…all waves!
Note that these definitions work also for radio waves, gamma rays and light waves.
In this case the interface is between the ocean and the atmosphere or between layers of different densities
Period
Celerity = C = Wavelength/Period
T
H
T
T 2
Wave Frequency
2
Wave Number
C
Wave Celerity
H
L
A
A
L
HH
LSteepness of
the wave
Definitions:
number of peaks
lengthk
number of peaks
time
Wave number
Frequency
Ocean Surface Wave
H
L
A
A
21
8E gH
The energy of the wave
Other definitions:
Ocean Surface Wave
Ocean Surface Wave exist because of 2 restoring forces
gravity
surface tension
Progressive Wave if moves energy through
the water
1t
L
2t
2 1
L L
ct t T k
Wave Speed
Wave crest
Waves preserve their period
The wavelength is a function of the period
The celerity is a function of the wavelength
TC
Long waves travel faster than short waves
“Small Amplitude” Waves
Period
Celerity = C = Wavelength/Period
T
H
T
201H
In reality, wave steepness of small amplitude waves < 1 / 50
txAtT
xA
cos
22cos
xg
tu
tHxu
1
momentum balance
2
12
1
tanh2
tanh2
h
ghgC
Obtained from equations of motion assuming the wave is progressive, incompressible and irrotational
Effects of Wave Dispersion (in deep water)
SWELL
Orbits of water particles are not quite closed -- net displacement = STOKES DRIFT
Short Deep Water Waves
wind waves and swell offshore
Motion of the Wave Form
Circular Motion
txeTH
uz
cos2
txeTH
wz
sin2
txeH z
sin2
2
txeH z
cos2
2
Long Shallow Water Waves
Tides, Tsunamis, Seiches, waves in shallow water
Elliptical Motion
What about INTERMEDIATE WATER WAVES?
txhgH
u cos2
txhz
TH
w
sin1
txhgTH
sin
4
txhzH
cos1
2
2
1
tanh
hg
C
Deep water wave: λλ < 2hh ( hh is depth ) or Short wave
This means that λλ is small and κh is large
1tanh h
222
21
Tg
TCg
gg
gC
Shallow water wave: λλ > 20hh ( hh is depth ) or Long wave
This means that λλ is large and κh is small hh tanh
hghg
C
21
h
λλ
h
λλ
DEEP OCEAN
SHALLOW WATERS
1d
L
1d
L
Two limits in wave speed
2
gLc
c gd
Depends on wavelength
InDependent of wavelength
C
IntermediateWaves
Deep WaterWaves
Shallow WaterWaves
hgC
2gTC
2
1
tanh
hg
C
hg tanh2
Dispersion relation(relation between frequency and wave number)
Deep waves are dispersive
Shallow waves are non-dispersive
Waves in the area of the fetch
Group Velocity Cg = Velocity of the wave envelope
In deep waters:
Cg = 0.5 C
In shallow waters: Cg = C
hhC
Cg 2sinh2
12
(green wave – moving to the right; blue wave to the left)
Group Velocity = Velocity of the wave envelope
Motion of water particles beneath waves --
energy travels across the surface, not water particles
Four factors controlling height and shape of wind waves
• Wind Speed: Proportional
• Wind duration: e.g. synoptic vs. sea-breeze
• Fetch: Distance over which the wind blows.
• Original Sea State: begin from rough or smooth surface
Increased Wind Speed causes waves with increased height, wavelength and period
Fully developed sea --
waves can no longer grow
Average and Significant Wave Height
0
5
10
15
20
25
20 30 40 50 60 70 80 90
Wind Speed
Wav
e H
eig
ht
Ave. Hgt Sig. Hgt.
Significant Wave Height = average of highest 1/3 of the waves.
Significant Wave Height
Small amplitude waves: Steepness < 1/20 (1/50 in real ocean)η= A cos(κx - ωt); A=H/2, κ = 2π/λ, ω=2π/T
Phase speed or wave celerity C
wavelength
Group velocity Cg
Wave particle horizontal velocity u
vertical velocity w
Horizontal displacements
Vertical displacements
Subsurface pressure
gggT
C 2
2
1
tanh
hg
C 2
1hgC
2
2gT hgT
tanh2
2
TC
hhC
Cg 2sinh
21
2 15.0
h
CCg
1
h
CCg
tx
hzhgTH
u
cos2cosh
2cosh2
tx
hzhgTH
w
sin
2cosh2sinh
2
tx
hzhH
sin2cosh
2cosh2
tx
hzhH
cos
2cosh2sinh
2
gz
hzh
gp
2cosh
2cosh
txhgH
u cos2
txhz
TH
w
sin1
txhgTH
sin
4
txhzH
cos1
2
zgp
txeTH
uz
cos2
txeTH
wz
sin2
txeH z
sin2
2
txeH z
cos2
2
zgegpz
2
hg tanh2
deep waves (short)λ < 2h
intermediate waves2h < λ < 20h
shallow waves (long)λ > 20h
In shallow waters, waves refract, diffract, reflect and/or break
Refraction
Change of wave celerity (bending of rays) due to changes in bathymetry
Diffraction
Change of wave celerity (bending of rays) due to the presence of an obstacle
Waves Reflection
Breaking
Waves break when steepness (H / λ) < 1 / 7 or H / d ~ 0.8
Internal Waves
T = min to several hrs
Wave length = 1 - 300 m
Current shear on stratification
An INTERNAL WAVEcreate regions of
convergence and divergence in the layer between the surface and the internal wave
Convergences at troughs
They propagate roughly like a shallow water wave but the gravity restoring force is reduced by the difference in density.
m/sC
dgC
1100001.010
112
2
12
How about C of a surface (wind-induced) wave?Internal Waves in a closed basin
• Pulsa energi gelombang internal terjadi di lapisan interface misalnya: lapisan pycnocline di laut• Ditandai dengan adanya naik-turunnya lapisan air• Gelombang internal merambat lebih lambat bila dibandingkan dengan gelombang permukaan• Karakteristiknya menunjukkan periode dan panjang gelombang yang besar• Ordo tinggi gelombang internal dapat mencapai beberapa meter bahkan dapat mencapai 100 m
Beberapa hal berkaitan dengan gelombang internal:
Standing Waves
Natural standing wave (lake, harbor, estuary) ---- seiche
• Created by earthquakes, underwater landslides, meteorites -- cause a series of waves or wave train
• “Harbor wave” definitely not a “tidal wave”• T = 15 min to 1 hour• Wave length = 100s of km• Speed of shallow water surface wave
smdgC /200400010
Tsunami
Tsunami in Papua New Guinea
1960 Chile Tsunami
2004 Tsunami in the Indian Ocean
http://en.wikipedia.org/wiki/2004_Indian_Ocean_earthquake
http://www.digitalglobe.com/tsunami_gallery.html
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