Special Public Seminar on Special Public Seminar on Earthquakes and TsunamisEarthquakes and Tsunamis

Tsunami from the Perspective

of Ocean Waves

Professor K. W. Chow

Department of Mechanical Engineering

University of Hong Kong

GOAL: GOAL: Try to understand how tsunamis can Try to understand how tsunamis can

cause so much damage and destruction cause so much damage and destruction from the perspective of ocean waves:from the perspective of ocean waves:

(A) water waves in the open oceans, (A) water waves in the open oceans, (B) their dynamics near the seashore. (B) their dynamics near the seashore.

General ideas about wave motion General ideas about wave motion Very often, a ‘fluid’ (liquid or gas) Very often, a ‘fluid’ (liquid or gas)

transmits energy and information by small transmits energy and information by small disturbances or waves. disturbances or waves.

Sound waves – a sequence of Sound waves – a sequence of compressions and relaxations in a gas.compressions and relaxations in a gas.

How about waves in water?How about waves in water?Try to classify them through the periods of

wave motion:(1) We jump up and return to the ground in

a few seconds, due to gravity. The same principle applies to water particles.

Hence ordinary gravity waves on the sea surface have a period of a few seconds.

(2) Tides have periods of roughly 12 hours.(3) Anything in between?

In fact a whole spectrum of wave In fact a whole spectrum of wave motions is possible:motions is possible:

IMPLICATIONS:IMPLICATIONS:

What are tsunamis?What are tsunamis?Commonly asked questions:(1) How high do the waves need to be to

qualify as a ‘tsunami’?(2) Will we see a 10-meter high wall of

water in the open ocean?(3) Waves shown in television news

reports are not particularly huge, why are they so damaging?

(4) Will I see a 10-foot tsumami in Hong Kong?

These are not the most appropriate These are not the most appropriate questions. The proper question to ask, questions. The proper question to ask,

perhaps, is:perhaps, is:

How can Nature transfer a huge How can Nature transfer a huge amount of energy from the amount of energy from the

epicenter to the coast through epicenter to the coast through water waveswater waves??

The answer:The answer:Through ‘long oceanic waves’, Through ‘long oceanic waves’,

since such long waves are:since such long waves are: (1) moving very fast; (1) moving very fast;

(2) non-dispersive; and(2) non-dispersive; and (3) can excite motion through a large (3) can excite motion through a large

depth of water.depth of water.Results: most dissipation mechanisms Results: most dissipation mechanisms (geometry, friction, scattering…) do not (geometry, friction, scattering…) do not

have time to attenuate this flow of energy.have time to attenuate this flow of energy.

Moving Fast??Moving Fast??(1) Generally, any disturbance or pattern in (1) Generally, any disturbance or pattern in water consists of various components with water consists of various components with

different wavelengths.different wavelengths.(2) Water waves:(2) Water waves:

Long waves travel at a HIGH velocity.Long waves travel at a HIGH velocity.Short waves travel at a LOW velocity.Short waves travel at a LOW velocity.

Long waves are thus the first wave Long waves are thus the first wave group observed at the coast.group observed at the coast.

All long wave components travel at the speed All long wave components travel at the speed of of square root (g H)square root (g H), where, where

gg = acceleration due to gravity, 9.8 m s = acceleration due to gravity, 9.8 m s–2–2,,HH = water depth. = water depth.

For the Japan earthquake:For the Japan earthquake:(1) At a depth of around 1000 meters, the (1) At a depth of around 1000 meters, the

speed is around 100 m sspeed is around 100 m s–1–1. . Speed of a Boeing 747 at cruising altitude Speed of a Boeing 747 at cruising altitude

is approximately 150 – 250 m sis approximately 150 – 250 m s–1–1. . (2) At the shore, the depth is zero. Let us (2) At the shore, the depth is zero. Let us

simplify the dynamics by taking an ‘average simplify the dynamics by taking an ‘average depth’ of 500 meters, an average speed is depth’ of 500 meters, an average speed is

then 70 m sthen 70 m s–1–1. . (3) Time to travel 100 km ≈ 1400 seconds (3) Time to travel 100 km ≈ 1400 seconds

≈ 23 minutes!!≈ 23 minutes!!

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Non-dispersive??Non-dispersive??Dispersion of white light (sunlight) into Dispersion of white light (sunlight) into

components: as light rays of different colors components: as light rays of different colors have different refractive indices (or speeds) have different refractive indices (or speeds)

inside the glass prism.inside the glass prism.

DISPERSIONDISPERSION(1) Components of different wavelengths (1) Components of different wavelengths

move with different speeds.move with different speeds.

(2) Example: Many students are walking (2) Example: Many students are walking to the canteen. If they all walk at the to the canteen. If they all walk at the same speed, they arrive at the same same speed, they arrive at the same

time. If each student walks at a different time. If each student walks at a different speed, the group will ‘disperse’.speed, the group will ‘disperse’.

DispersionDispersionIf dispersion is present, the pulse

broadens.

Animation courtesy of Dr. Dan Russell, Kettering University

Long waves are nonLong waves are non––dispersivedispersive

In the case of water waves, all long waves In the case of water waves, all long waves travel at the same speed travel at the same speed

(= square root of ((= square root of (gg HH)), and are thus )), and are thus non–dispersive.non–dispersive.

The various long wave components do NOT The various long wave components do NOT separate from each other, and pound on the separate from each other, and pound on the

coast at the same time.coast at the same time.

Particle paths??Particle paths??As the wave form progresses, each particle oscillates in a circular or elliptic path, with

dimensions decreasing with depth.

IMPLICATIONS:IMPLICATIONS:

Dimensions of particle trajectories decrease exponentially as we go deeper into the fluid. Typically these paths will become very small at a water depth larger than a few wavelengths.

A water wave moving from left to right.Each particle moves in an elliptical path of

decreasing dimension.

For short waves of say 1 meter, water motion is negligible in water deeper than say 5 meters. Motions in such a small region are easily scattered or dissipated.

For long waves of say 10 km (which is greater than the ocean depth), this motion will persist throughout most of the ocean!!

Waves in the open ocean explained, Waves in the open ocean explained, how can we understand the dynamics how can we understand the dynamics

as the waves approach the shore?as the waves approach the shore?

Several Factors:Several Factors:(1) On approach to shore, the wavelength (1) On approach to shore, the wavelength must be compressed to a smaller value, must be compressed to a smaller value,

and this will ‘squeeze’ the wave to a and this will ‘squeeze’ the wave to a larger amplitude.larger amplitude.

(2) Geometric configuration: an ‘enclosed (2) Geometric configuration: an ‘enclosed harbour’ or ‘gulf’ might elevate the wave harbour’ or ‘gulf’ might elevate the wave

amplitude.amplitude.

Effect of a gulf

(3) ‘Piling up’ or ‘Nonlinear’ effects – (3) ‘Piling up’ or ‘Nonlinear’ effects – Faster moving waves from the back catch Faster moving waves from the back catch

up with the slower moving waves in the up with the slower moving waves in the front. front.

The speed of long waves is The speed of long waves is square root of (square root of (g Hg H))

gg = acceleration due to gravity, 9.8 m s = acceleration due to gravity, 9.8 m s–2–2

HH = water depth. = water depth.As the waves approach shore, As the waves approach shore, HH

decreases and hence the speed will decreases and hence the speed will decrease. Hence the waves start to pile up decrease. Hence the waves start to pile up

and the amplitude increases.and the amplitude increases.

How a Tsunami Increases in HeightHow a Tsunami Increases in Height

Large scale tsunamis: Can it Large scale tsunamis: Can it happen in Victoria Harbour?happen in Victoria Harbour?

My personal (emphasize ‘My’) opinion – My personal (emphasize ‘My’) opinion – should be unlikely (??):should be unlikely (??):

(1) Geography: Hong Kong, especially (1) Geography: Hong Kong, especially Victoria Harbour, is surrounded or shielded Victoria Harbour, is surrounded or shielded

by islands and peninsulas, unless the by islands and peninsulas, unless the epicenters are located very nearby and in epicenters are located very nearby and in

very special positions.very special positions.Waves seldom turn 90 degrees.Waves seldom turn 90 degrees.

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(2) ‘Geometric factors / configurations’: (2) ‘Geometric factors / configurations’: Many disturbances or vibrations, Many disturbances or vibrations,

including ‘tsunamis’ or shallow water including ‘tsunamis’ or shallow water waves, are governed by the ‘wave waves, are governed by the ‘wave

equation’.equation’.

● ● Propagation in one spatial dimension: Propagation in one spatial dimension: No attenuation.No attenuation.

● Propagation in two spatial dimensions: ● Propagation in two spatial dimensions: Amplitude decays like 1/(square root of the Amplitude decays like 1/(square root of the

distance from the epicenter).distance from the epicenter).

Unless the epicenter is really close to Unless the epicenter is really close to Hong Kong, Victoria Harbour would be Hong Kong, Victoria Harbour would be less vulnerable than say Banda Aceh less vulnerable than say Banda Aceh

(Indonesia, 2004) or Sendai (Japan 2011). (Indonesia, 2004) or Sendai (Japan 2011).

As a rough comparison:As a rough comparison:December 26, 2004: Banda Aceh, December 26, 2004: Banda Aceh,

Indonesia, about 200,000 (??) people Indonesia, about 200,000 (??) people perished. Time for tsunamis to reach perished. Time for tsunamis to reach

shore: roughly 30 minutes.shore: roughly 30 minutes.March 11, 2011: Sendai, Japan.March 11, 2011: Sendai, Japan.

Time for tsunamis to reach shore: Time for tsunamis to reach shore: roughly 30 minutes as well.roughly 30 minutes as well.

CONCLUSIONSCONCLUSIONS(1) Tsunamis propagate as small (1) Tsunamis propagate as small

amplitude, long surface waves in the open amplitude, long surface waves in the open ocean.ocean.

(2) On approach to shore, the geometry of (2) On approach to shore, the geometry of the coast line, the shape of the sea floor the coast line, the shape of the sea floor and other factors will distort, compress or and other factors will distort, compress or

amplify the wave amplitudes.amplify the wave amplitudes.

(3) Computer simulations take a couple of (3) Computer simulations take a couple of days, but the most damaging, killer waves days, but the most damaging, killer waves typically arrive in 30 minutes or so. Better typically arrive in 30 minutes or so. Better run to a higher ground immediately during run to a higher ground immediately during

an earthquake.an earthquake.(4) We have ‘oversimplified’ the situation. (4) We have ‘oversimplified’ the situation.

The ocean is a complex system. Many The ocean is a complex system. Many other factors, e.g. internal waves, thermal other factors, e.g. internal waves, thermal stratification, and the rotation of the earth, stratification, and the rotation of the earth,

have been ignored. have been ignored.

THANK YOUTHANK YOU

Scenes from Japan before and Scenes from Japan before and after the tsunamiafter the tsunami

Extracted form :http://www.pics-site.com/2011/03/15/japan-before-and-after-earthquake-and-tsunami/

Scenes from Japan before and Scenes from Japan before and after the tsunamiafter the tsunami

Extracted form :http://www.pics-site.com/2011/03/15/japan-before-and-after-earthquake-and-tsunami/

Scenes from Japan before and Scenes from Japan before and after the tsunamiafter the tsunami

Extracted form :http://www.pics-site.com/2011/03/15/japan-before-and-after-earthquake-and-tsunami/

The wave equation forThe wave equation for‘tsunamis’ and shallow water waves.‘tsunamis’ and shallow water waves.

Mathematics: Mathematics: ∂∂22uu/∂/∂xx22 + ∂ + ∂22uu/∂/∂yy22 + ∂ + ∂22uu/∂/∂zz22 = (∂ = (∂22uu/∂/∂tt22)/)/cc22

uu = displacement, = displacement, cc = velocity = velocity