Gelombang

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

txA cos

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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