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.

Banda Aceh, Indonesia, June 28, 2004

Figure 1.    http://www.digitalglobe.com/tsunami_gallery.html

Banda Aceh, Indonesia, December 28, 2004

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, Kettering University

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 1:20 (wavelength at least twenty times the depth). In this case, the wave speed depends only on the depth of the water. This relationship is given by

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 Sumatra, Indonesia was estimated to be between magnitude 9.1 and 9.3 on the Richter scale, the second largest quake ever recorded on a seismograph [Wikipedia, “2004 Indian Ocean Earthquake”]. This particular earthquake is rare and occurs approximately every 300 years [Discovery Channel, “Unstoppable Wave”]. This is the situation when one plate subducts under another. Normally, when in an underwater ridge the plates are pushed apart, one plate slides under another in the subduction zone. This is where megathrust earthquakes occur.

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 Indonesia (east of the fault) while a wall of water arrived first at Thailand (west of the fault).

--In Thailand, a 30-meter high [Wikipedia, ibid.] wave was seen to break near along the shore:

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 Asia and Hawaii, right? Wrong. While in recent history tsunamis plagued mostly only Asia and Hawaii, it must be remembered that there is a megathrust fault similar to the one that caused the Indian Ocean Tsunami near the coast of North America. The Cascadia subduction zone runs from the northern end of California along Oregon, Washington, and up to Southern British Columbia. An earthquake of similar magnitude would cause great devastation to the shores of these states (luckily for us Vancouverites, Vancouver Island shields us significantly from any such occurrence). But part of the cause of the amount of casualties of the Indian Ocean Tsunami is that the people were unprepared for such a catastrophic event.

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:

Circular motion of water molecules

Sources:

Wikipedia.  2004 Indian Ocean Tsunami.  Accessed January 2006.  Website: http://en.wikipedia.org/wiki/2004_Indian_Ocean_earthquake

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!