FORMATION & SCIENCE
LIFE of a tsunami
Panel 1: Initiation
Panel 2: Split
Panel 3: Amplification
Panel 4: Run up
Panel 1 : initiation
Earthquakes are commonly associated with ground shaking that is a result of elastic waves traveling through the solid earth.
However, near the source of submarine earthquakes, the seafloor is "permanently" uplifted and down-dropped, pushing the entire water column up and down. The potential energy that results from pushing water above mean sea level is then transferred to horizontal propagation of the tsunami wave (kinetic energy). For the case shown above, the earthquake rupture occurred at the base of the continental slope in relatively deep water. Situations can also arise where the earthquake rupture occurs beneath the continental shelf in much shallower water.
Note: In the figure, the waves are greatly exaggerated compared to water depth. In the open ocean, the waves are at most several meters high spread over many tens to hundreds of kilometers in length.
Panel 3-1 : amplification
Several things happen as the local tsunami travels over the continental slope. Most obvious is that the amplitude increases. In addition, the wavelength decreases. This results in steepening of the leading wave--an important control of wave run up at the coast (next panel). Note that the first part of the wave reaching the local shore is a trough, which will appear as the sea receeding far from shore. This is a common natural warning sign for tsunamis. Note also that the deep ocean tsunami has traveled much farther than the local tsunami because of the higher propagation speed. As the deep ocean tsunami approaches a distant shore, amplification and shortening of the wave will occur, just as with the local tsunami shown above.
There are some formulas to prove this. Shallow-water waves move at a speed, c, that is dependent upon the water depth and is given by the formula:
where g is the acceleration due to gravity (= 9.8 m/s2) and H is the depth of water. According to this formula, the typical water depth is around 4000 m, so a tsunami will therefore travel at around 200 m/s, or more than 700 km/h.
Panel 2 : split
Within several minutes of the earthquake, the initial tsunami (Panel 1) is split into a tsunami that travels out to the deep ocean (distant tsunami), and another tsunami that travels towards the nearby coast (local tsunami).
The height above mean sea level of the two oppositely traveling tsunamis is approximately half that
of the original tsunami (Panel 1).
(This is somewhat modified in three dimensions, but the same idea holds.)
Panel 3-2 : amplification
A tsunami travels at a speed that is related to the water depth - hence, as the water depth decreases, the tsunami slows. However, the tsunami's energy flux, which is dependent on both its wave speed and wave height, remains nearly constant. Consequently, as the tsunami's speed diminishes, its height grows. This is called shoaling. Because of this shoaling effect, a tsunami that is unnoticeable at sea, may grow to be several metres or more in height near the coast.
The increase of the tsunami's waveheight as it enters shallow water is given by the formula:
where hs and hd are waveheights in shallow and deep water and Hs and Hd are the depths of the shallow and deep water. So a tsunami with a height of 1 m in the open ocean where the water depth is 4000m would have a waveheight of 4 to 5 m in water of depth 10 m.
Panel 4 : Run up
Tsunami run up occurs when a peak in the tsunami wave travels from the near-shore region onto shore. Run up is a measurement of the height of the water onshore observed above a reference sea level.
Except for the largest tsunamis, such as the 2004 Indian Ocean event, most tsunamis do not result in giant breaking waves (like normal surf waves at the beach that curl over as they approach shore). Rather, they come in much like very strong and fast-moving tides (i.e., strong surges and rapid changes in sea level). Much of the damage inflicted by tsunamis is caused by strong currents and floating debris. The small number of tsunamis that do break often form vertical walls of turbulent water called bores. Tsunamis will often travel much farther inland than normal waves.
Do tsunamis stop once on land? No! After run up, part of the tsunami energy is reflected back to the open ocean and scattered by sharp variations in the coastline. In addition, a tsunami can generate a particular type of coastal trapped wave called edge waves that travel back-and forth, parallel to shore. These effects result in many arrivals of the tsunami at a particular point on the coast rather than a single wave as suggested by Panel 3. Because of the complicated behavior of tsunami waves near the coast, the first runup of a tsunami is often not the largest, emphasizing the importance of not returning to a beach many hours after a tsunami first hits.