The Physics of Tsunamis: The Harbour Wave
By: Anthony Uy
UBC Physics 420: Demonstrations
Following the events of theBoxing 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 arethe causes of tsunamis? And why are they so powerful? What happens during atsunami? These are some of the questions that are to be discussed in thispresentation.
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Figure 0
The most important thing tobe learned about tsunamis is that they are waves. Specifically, they are waterwaves 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, anearthquake or a cosmic body impact creates a wave or a series of waves thathave a wavelengths on the order of hundreds of kilometers long. Althoughtsunamis usually have small amplitudes (on the order of 1 m), the volume of thewater that gets displaced and the speeds reached by these waves allow them tocarry enough energy to wipe out towns and cities.
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Figure 1. http://www.digitalglobe.com/tsunami_gallery.html
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Figure 2. http://www.digitalglobe.com/tsunami_gallery.html
Theory*:
Transverse waves
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Figure 3: www.kettering.edu/~drussell/Demos/waves/wavemotion.html
Longitudinal waves
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Figure 5: www.kettering.edu/~drussell/Demos/waves/wavemotion.html
These2 animations courtesy of Dr. Dan Russell,
A water wave is a combinationof both transverse and longitudinal waves. As a result, the watermolecules move in an elliptical pattern (circularin deep water waves). For example, if one observes the movement of a floatingobject in water waves, say a piece of cork, one will notice that the cork willmove in a circular pattern.
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Figure 6: http://faculty.gvsu.edu/videticp/waves.htm
According to the depth of thewater and the wavelength (see parts of awave), water waves can be classified into three categories: deep-water, intermediate, and shallow-water waves. Deep water wavesare characterized by the depth-wavelength ratio greater than 2:1 (depth atleast twice the wavelength). Examples of these are typical wind-driven waves atsea, or a small pebble dropping into a pond. An important aspect of deep waterwaves is that the wave speed depends solely on the wavelength of the wave.
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This is called the dispersionrelation.
On the other hand, shallowwater waves have depth-wavelength ratios less than (wavelength at least twenty times the depth). In thiscase, the wave speed depends only onthe depth of the water. This relationship is given by
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This has an importantimplication in the physics of tsunamis: as a 700 km / hr (typical) waveapproaches land where water depth is shallower, it slows down. In light of theconservation of energy, the kinetic energy is transferred into potentialenergy, and in this case as gravitational potential energy. Thus the 500 kmwavelength gets shorter as the tail of the tsunami catches up to a slowerfront, while the wave amplitude builds up in height. As the bottom part of thistraveling wall of water slows down considerably, eventually the wave breaks andfloods the land, while pushing forward with much energy.
Click here to view deep andshallow water waves and the orbits of the water molecules. Don’t let theterminology trick you, shallow water waves don’t necessarily mean that thewater is shallow. A water wave in a deep ocean a few kilometers deep can be ashallow water one as long as the wavelength is sufficiently long! Between thesetwo extremes is an intermediate state where 1 / 20 < depth / wavelength <2.
A Tsunami is a water wavecaused by a huge displacement of water in the ocean. Common examples of causesare earthquakes, landslides, and volcanic activity. The energy released intothe water by these natural phenomena travels through the water in the form of awave with exceedingly long wavelengths, on the order of hundreds of kilometers.
* Thanks to Dr. Ver of UBC Earth and Ocean Sciences Dept. forthe information about tsunamis and shallow-water waves.
What makes Tsunamis sodangerous?
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Figure 7: Comparison of energies
Quiz:
If the wavelength of aTsunami is 500 km, and the depth of the ocean it travels on is 4 km, calculate
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<![if !supportLists]>(b)<![endif]>*the energy carriedby a 1 m wide section of this Tsunami if its amplitude is 1 m. (This partrequires some integral calculus). For those who want to skip the calculus part,click here for hints.
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Figure8: Tsunami heading to shore
This energy is ~1 / 60 of theenergy carried by a nuclear bomb*. Considering that a tsunami stretches overhundreds of kilometers, we can see the energy released in such a quake iscapable to destroy whole towns in the surrounding coasts, and since a tsunamican travel over long distances without losing much energy, it is capable ofbringing destruction to far away places as well.
* http://newton.nap.edu/html/oneuniverse/energy_solution_4.html
Setup:
The Tsunami experiment requiresthe following essential components:
<![if !supportLists]>1) <![endif]>Wave tank (or trough) This is where the wave will propagate
<![if !supportLists]>2) <![endif]>Run-up (incline) Thisis where the experiment simulates a shore (preferably adjustable)
<![if !supportLists]>3) <![endif]>Wavegenerator Waveswould have to be generated, usually a rectangular plate that fits the inside ofthe trough
<![if !supportLists]>4) <![endif]>Water Waterpreferably has coloring so that the waves can be easily seen
Can you identify the parts?
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Figure9: Setup of experiment
The UBC Physics Department hasbeen generous to provide for the building of the wave tank that I used for thedemonstration. It is made of plexiglass and measures 11’ x 1’ x 1’. It isnecessary that the tank be long, since long wavelengths (with shallow waterdepths) are the condition for having tsunamis.
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Figure 10: Picture of wave tank
The run-up, if the experimentis attempted, will be advantageous to be adjustable, so that the effects of thedifferent kinds of slopes might be observed. This is also the setup can beadjusted to find the best position for a breaking wave (which is usually thespectacular part in the demo).
The best wave generator wouldbe one that almost fits the section of the wave tank. The reason for this isthat the less water that can leak through the gap between the generator and thetank, the more the energy that can be transported through the wave, since thewater doesn’t have anywhere else to go. In other words, a 12-inch generatorwill push more water that a 6-inch one, and thus allow the wave to carry moreenergy.
I used blue food coloring forthe water, in order that the waves might be seen more easily from the side, asthe plexiglass is transparent.
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Figure 11: Short animation of breaking wave
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Causes of Tsunamis:
The Boxing Day Tsunami wascaused by a slipping in a megathrust fault in the Indian Ocean. The quake offthe coast of
Over time, the plates in thesubduction 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 onthe upper plate reaches the limit, and the fold springs back, causing a hugedisplacement of water in a very brief period of time. This sudden release ofenergy is what causes the hundreds-of-kilometers-long-wave that travels as fastas a passenger jet plane. [Discovery Channel, ibid.].
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Figure 12: These 3 images show approximately whathappened above the megathrust fault.
These images explain why thewaters first receded along the coast of
--In
Tsunami Video\MOV01.MPG (928 kB)
Tsunami Video\MOV02.MPG (864 kB)
--While a receding shorelineis simulated by the next videos:
Tsunami Video\MOV03.MPG (1,055 kB)
Tsunami Video\MOV04.MPG (2,014 kB)
While the danger in thebreaking 100-ft high wave is obviously dangerous, the hidden danger in thereceding shoreline is that the waters will recede (as the trough reaches theland first) laying the beach bare with fishes left in the sand. People werethen attracted to this curious phenomenon and go into the sand, while aftersome time the waters come rushing back as the crest arrives. As can be seen inthe video, the water level increased dramatically (remember that a fewmillimeters in the simulation may correspond to meters or hundreds of meters inreality), engulfing not only to the previous water level but up to severalmillimeters higher than it.
For a very informative videoon 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 allthese especially for North Americans? These tsunamis only happen in parts of
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Figure 13 & 14: http://www.pgc.nrcan.gc.ca/seismo/hist/megafig.htm
Images courtesy of Natural Resources Canada
But how can there be preparationfor such an unpredictable phenomenon? The most important thing is being awarethat a megathrust earthquake can happen anytime. As for the safety measures,when a warning sign of the tsunami occurs (say, an earthquake), going to highergrounds is a very effective way to avoid the effects of a tsunami forindividuals. Since time is of the essence in these circumstances, it would bewise to leave even homes to the raging waters instead of precious human life.
Other Wave Experiments:
Slinky
Circular motion of watermolecules
Sources:
Wikipedia. 2004
Discovery Channel. UnstoppableWave. Viewed December 2006.
Special Thanks to:
Dr. Leah May Ver of the Earth and Ocean Sciences Departmentof UBC for allowing me to use many of her images and movies.
Mr. Matthew Sluyter and for constructing the tsunami troughas well as the adjustable “beach” and the wave generator. Thanks to Mr. Csabatoo.
Dr. Andrej Kotlicki and to Dr. Chris Waltham for theircomments and suggestions.
My Phys 420 classmates who have contributed with ideas andsuggestions.
UBC for having such a great course! Physics 420Demonstrations!