The Physics of Tsunamis: The Harbour Wave
By: Anthony Uy
UBC Physics 420: Demonstrations
Following the events of the
Boxing Day Tsunami in the year 2004 -- its death toll and the destruction it wrought,
a lot of energy was put into the study of this natural catastrophe. What are
the causes of tsunamis? And why are they so powerful? What happens during a
tsunami? These are some of the questions that are to be discussed in this
presentation.
Figure 0
The most important thing to
be learned about tsunamis is that they are waves. Specifically, they are water
waves that form in the ocean, where the depths of the water average 4 km.
Displacement of water following a huge release of energy from, say, an
earthquake or a cosmic body impact creates a wave or a series of waves that
have a wavelengths on the order of hundreds of kilometers long. Although
tsunamis usually have small amplitudes (on the order of 1 m), the volume of the
water that gets displaced and the speeds reached by these waves allow them to
carry enough energy to wipe out towns and cities.
Figure 1. http://www.digitalglobe.com/tsunami_gallery.html
Figure 2. http://www.digitalglobe.com/tsunami_gallery.html
Theory*:
Transverse waves
Figure 3: www.kettering.edu/~drussell/Demos/waves/wavemotion.html
Longitudinal waves
Figure 5: www.kettering.edu/~drussell/Demos/waves/wavemotion.html
These
2 animations courtesy of Dr. Dan Russell,
A water wave is a combination
of both transverse and longitudinal waves. As a result, the water
molecules move in an elliptical pattern (circular
in deep water waves). For example, if one observes the movement of a floating
object in water waves, say a piece of cork, one will notice that the cork will
move in a circular pattern.
Figure 6: http://faculty.gvsu.edu/videticp/waves.htm
According to the depth of the
water and the wavelength (see parts of a
wave), water waves can be classified into three categories: deep-water, intermediate, and shallow-water waves. Deep water waves
are characterized by the depth-wavelength ratio greater than 2:1 (depth at
least twice the wavelength). Examples of these are typical wind-driven waves at
sea, or a small pebble dropping into a pond. An important aspect of deep water
waves is that the wave speed depends solely on the wavelength of the wave.
This is called the dispersion
relation.
On the other hand, shallow
water waves have depth-wavelength ratios less than
This has an important
implication in the physics of tsunamis: as a 700 km / hr (typical) wave
approaches land where water depth is shallower, it slows down. In light of the
conservation of energy, the kinetic energy is transferred into potential
energy, and in this case as gravitational potential energy. Thus the 500 km
wavelength gets shorter as the tail of the tsunami catches up to a slower
front, while the wave amplitude builds up in height. As the bottom part of this
traveling wall of water slows down considerably, eventually the wave breaks and
floods the land, while pushing forward with much energy.
Click here to view deep and
shallow water waves and the orbits of the water molecules. Don’t let the
terminology trick you, shallow water waves don’t necessarily mean that the
water is shallow. A water wave in a deep ocean a few kilometers deep can be a
shallow water one as long as the wavelength is sufficiently long! Between these
two extremes is an intermediate state where 1 / 20 < depth / wavelength <
2.
A Tsunami is a water wave
caused by a huge displacement of water in the ocean. Common examples of causes
are earthquakes, landslides, and volcanic activity. The energy released into
the water by these natural phenomena travels through the water in the form of a
wave with exceedingly long wavelengths, on the order of hundreds of kilometers.
* Thanks to Dr. Ver of UBC Earth and Ocean Sciences Dept. for the information about tsunamis and shallow-water waves.
What makes Tsunamis so
dangerous?
Figure 7: Comparison of energies
Quiz:
If the wavelength of a
Tsunami is 500 km, and the depth of the ocean it travels on is 4 km, calculate
(a)
the speed of the
wave
(b)
*the energy carried
by a 1 m wide section of this Tsunami if its amplitude is 1 m. (This part
requires some integral calculus). For those who want to skip the calculus part,
click here for hints.
Figure
8: Tsunami heading to shore
This energy is ~1 / 60 of the
energy carried by a nuclear bomb*. Considering that a tsunami stretches over
hundreds of kilometers, we can see the energy released in such a quake is
capable to destroy whole towns in the surrounding coasts, and since a tsunami
can travel over long distances without losing much energy, it is capable of
bringing destruction to far away places as well.
* http://newton.nap.edu/html/oneuniverse/energy_solution_4.html
Setup:
The Tsunami experiment requires
the following essential components:
1) Wave tank (or trough) This is where the wave will propagate
2) Run-up (incline) This
is where the experiment simulates a shore (preferably adjustable)
3) Wave
generator Waves
would have to be generated, usually a rectangular plate that fits the inside of
the trough
4) Water Water
preferably has coloring so that the waves can be easily seen
Can you identify the parts?
Figure
9: Setup of experiment
The UBC Physics Department has
been generous to provide for the building of the wave tank that I used for the
demonstration. It is made of plexiglass and measures 11’ x 1’ x 1’. It is
necessary that the tank be long, since long wavelengths (with shallow water
depths) are the condition for having tsunamis.
Figure 10: Picture of wave tank
The run-up, if the experiment
is attempted, will be advantageous to be adjustable, so that the effects of the
different kinds of slopes might be observed. This is also the setup can be
adjusted to find the best position for a breaking wave (which is usually the
spectacular part in the demo).
The best wave generator would
be one that almost fits the section of the wave tank. The reason for this is
that the less water that can leak through the gap between the generator and the
tank, the more the energy that can be transported through the wave, since the
water doesn’t have anywhere else to go. In other words, a 12-inch generator
will push more water that a 6-inch one, and thus allow the wave to carry more
energy.
I used blue food coloring for
the water, in order that the waves might be seen more easily from the side, as
the plexiglass is transparent.
Figure 11: Short animation of breaking wave
Causes of Tsunamis:
The Boxing Day Tsunami was
caused by a slipping in a megathrust fault in the Indian Ocean. The quake off
the coast of
Over time, the plates in the
subduction zone lock up, and as one plate continues to be pushed under another,
the plate above is forced to fold like a springboard. Eventually, the stress on
the upper plate reaches the limit, and the fold springs back, causing a huge
displacement of water in a very brief period of time. This sudden release of
energy is what causes the hundreds-of-kilometers-long-wave that travels as fast
as a passenger jet plane. [Discovery Channel, ibid.].
Figure 12: These 3 images show approximately what
happened above the megathrust fault.
These images explain why the
waters first receded along the coast of
--In
Tsunami Video\MOV01.MPG (928 kB)
Tsunami Video\MOV02.MPG (864 kB)
--While a receding shoreline
is simulated by the next videos:
Tsunami Video\MOV03.MPG (1,055 kB)
Tsunami Video\MOV04.MPG (2,014 kB)
While the danger in the
breaking 100-ft high wave is obviously dangerous, the hidden danger in the
receding shoreline is that the waters will recede (as the trough reaches the
land first) laying the beach bare with fishes left in the sand. People were
then attracted to this curious phenomenon and go into the sand, while after
some time the waters come rushing back as the crest arrives. As can be seen in
the video, the water level increased dramatically (remember that a few
millimeters in the simulation may correspond to meters or hundreds of meters in
reality), engulfing not only to the previous water level but up to several
millimeters higher than it.
For a very informative video
on tsunamis, go to this link: http://www.seed.slb.com/en/scictr/watch/living_planet/tsunami.htm
Why the Interest?
So why the interest in all
these especially for North Americans? These tsunamis only happen in parts of
Figure 13 & 14: http://www.pgc.nrcan.gc.ca/seismo/hist/megafig.htm
Images courtesy of Natural Resources Canada
But how can there be preparation
for such an unpredictable phenomenon? The most important thing is being aware
that a megathrust earthquake can happen anytime. As for the safety measures,
when a warning sign of the tsunami occurs (say, an earthquake), going to higher
grounds is a very effective way to avoid the effects of a tsunami for
individuals. Since time is of the essence in these circumstances, it would be
wise to leave even homes to the raging waters instead of precious human life.
Other Wave Experiments:
Slinky
Circular motion of water
molecules
Sources:
Wikipedia. 2004
Discovery Channel. Unstoppable
Wave. Viewed December 2006.
Special Thanks to:
Dr. Leah May Ver of the Earth and Ocean Sciences Department
of UBC for allowing me to use many of her images and movies.
Mr. Matthew Sluyter and for constructing the tsunami trough
as well as the adjustable “beach” and the wave generator. Thanks to Mr. Csaba
too.
Dr. Andrej Kotlicki and to Dr. Chris Waltham for their
comments and suggestions.
My Phys 420 classmates who have contributed with ideas and
suggestions.
UBC for having such a great course! Physics 420
Demonstrations!