Special Public Seminar on
Earthquakes and Tsunamis
Tsunami from the Perspective
of Ocean Waves
Professor K. W. Chow
Department of Mechanical Engineering
University of Hong Kong
GOAL:
Try to understand how tsunamis can
cause so much damage and destruction
from the perspective of ocean waves:
(A) water waves in the open oceans,
(B) their dynamics near the seashore.
General ideas about wave motion
Very often, a ‘fluid’ (liquid or gas) transmits
energy and information by small
disturbances or waves.
Sound waves – a sequence of
compressions and relaxations in a gas.
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
motions is possible:
IMPLICATIONS:
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
questions. The proper question to ask,
perhaps, is:
How can Nature transfer a huge
amount of energy from the epicenter
to the coast through water waves?
The answer:
Through ‘long oceanic waves’,
since such long waves are:
(1) moving very fast;
(2) non-dispersive; and
(3) can excite motion through a large
depth of water.
Results: most dissipation mechanisms
(geometry, friction, scattering…) do not
have time to attenuate this flow of energy.
Moving Fast??
(1) Generally, any disturbance or pattern in
water consists of various components with
different wavelengths.
(2) Water waves:
Long waves travel at a HIGH velocity.
Short waves travel at a LOW velocity.
Long waves are thus the first wave group
observed at the coast.
All long wave components travel at the speed
of square root (g H), where
g = acceleration due to gravity, 9.8 m s–2,
H = water depth.
For the Japan earthquake:
(1) At a depth of around 1000 meters, the
speed is around 100 m s–1.
Speed of a Boeing 747 at cruising altitude
is approximately 150 – 250 m s–1.
(2) At the shore, the depth is zero. Let us
simplify the dynamics by taking an ‘average
depth’ of 500 meters, an average speed is
then 70 m s–1.
(3) Time to travel 100 km ≈ 1400 seconds
≈ 23 minutes!!
THANK YOU
Non-dispersive??
Dispersion of white light (sunlight) into
components: as light rays of different colors
have different refractive indices (or speeds)
inside the glass prism.
DISPERSION
(1) Components of different wavelengths
move with different speeds.
(2) Example: Many students are walking
to the canteen. If they all walk at the
same speed, they arrive at the same
time. If each student walks at a different
speed, the group will ‘disperse’.
Dispersion

If dispersion is present, the pulse
broadens.
Animation courtesy of Dr. Dan Russell, Kettering University
Long waves are non–dispersive
In the case of water waves, all long waves
travel at the same speed
(= square root of (g H)), and are thus
non–dispersive.
The various long wave components do NOT
separate from each other, and pound on the
coast at the same time.
Particle paths??
As the wave form progresses, each particle
oscillates in a circular or elliptic path, with
dimensions decreasing with depth.
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,
how can we understand the dynamics
as the waves approach the shore?
Several Factors:
(1) On approach to shore, the wavelength
must be compressed to a smaller value,
and this will ‘squeeze’ the wave to a
larger amplitude.
(2) Geometric configuration: an ‘enclosed
harbour’ or ‘gulf’ might elevate the wave
amplitude.
Effect of a gulf
(3) ‘Piling up’ or ‘Nonlinear’ effects – Faster
moving waves from the back catch up with
the slower moving waves in the front.
The speed of long waves is
square root of (g H)
g = acceleration due to gravity, 9.8 m s–2
H = water depth.
As the waves approach shore, H
decreases and hence the speed will
decrease. Hence the waves start to pile up
and the amplitude increases.
How a Tsunami Increases in Height
Large scale tsunamis: Can it happen in
Victoria Harbour?
My personal (emphasize ‘My’) opinion –
should be unlikely (??):
(1) Geography: Hong Kong, especially
Victoria Harbour, is surrounded or shielded
by islands and peninsulas, unless the
epicenters are located very nearby and in
very special positions.
Waves seldom turn 90 degrees.
THANK YOU
(2) ‘Geometric factors / configurations’:
Many disturbances or vibrations,
including ‘tsunamis’ or shallow water
waves, are governed by the ‘wave
equation’.
● Propagation in one spatial dimension:
No attenuation.
● Propagation in two spatial dimensions:
Amplitude decays like 1/(square root of the
distance from the epicenter).
Unless the epicenter is really close to
Hong Kong, Victoria Harbour would be
less vulnerable than say Banda Aceh
(Indonesia, 2004) or Sendai (Japan 2011).
As a rough comparison:
December 26, 2004: Banda Aceh,
Indonesia, about 200,000 (??) people
perished. Time for tsunamis to reach shore:
roughly 30 minutes.
March 11, 2011: Sendai, Japan.
Time for tsunamis to reach shore:
roughly 30 minutes as well.
CONCLUSIONS
(1) Tsunamis propagate as small amplitude,
long surface waves in the open ocean.
(2) On approach to shore, the geometry of
the coast line, the shape of the sea floor
and other factors will distort, compress or
amplify the wave amplitudes.
(3) Computer simulations take a couple of
days, but the most damaging, killer waves
typically arrive in 30 minutes or so. Better
run to a higher ground immediately during
an earthquake.
(4) We have ‘oversimplified’ the situation.
The ocean is a complex system. Many
other factors, e.g. internal waves, thermal
stratification, and the rotation of the earth,
have been ignored.
THANK YOU
Scenes from Japan before and after the
tsunami
Extracted form :http://www.pics-site.com/2011/03/15/japan-before-and-after-earthquake-and-tsunami/
Scenes from Japan before and after the
tsunami
Extracted form :http://www.pics-site.com/2011/03/15/japan-before-and-after-earthquake-and-tsunami/
Scenes from Japan before and after the
tsunami
Extracted form :http://www.pics-site.com/2011/03/15/japan-before-and-after-earthquake-and-tsunami/
The wave equation for
‘tsunamis’ and shallow water waves.
Mathematics:
∂2u/∂x2 + ∂2u/∂y2 + ∂2u/∂z2 = (∂2u/∂t2)/c2
u = displacement, c = velocity