Wave Interaction with Small Islands:
--Algorithm describes the run up of the tsunami onto a small round island
--Algorithm keeps the velocity and total depth of zero over the shore
--The algorithm is approximated over the unit rectangle and the following matrices are produced
--The variables are defined, and then the equation is solved
h(x,y) = the depth of still water
H(x,y,t)=h(x,y)+n(x,y,t) = total depth of water in relation to time
n(x,y,t) = free surface elevation
g = gravitational constant
The result of this equation indicate as the wave approaches the island it becomes steeper in shallower, which is a common wave principal, but it also indicates that after the wave passes over, or goes around the small circular island then there is a backlash on the side of the island away from the wave. So essentially the entire coastline of the island is affected by the wave, and depending on the topography of the island, the entire thing could be submerged due to the initial wave and the way it wraps around the back of the island. This applies to Micronesia, because in case of a tsunami not only would the initial impact damage the front half of the island, but the back side of the island would be impacted as well. So, it is not only necessary to be concerned with the facing shore, which is necessary to plan for the risk of a tsunami. The end result, in terms of risk assessment, is that a gradient of elevations can be used to map inundation on all sides of the island, not just the front side that experiences the first onslaught of the wave.
Wave Interaction with Seafloor:
There are many different factors that either increases the amplitude, speed, and ferocity of the wave, or the opposite.
- Coral- coral reefs although they can be severely damaged or even destroyed when the wave pulls out from shore and bring debris with it, help to slightly decrease the effects of the tsunami. (Pennisi)
- Deep Trenches Parallel to Shore- although when a trench is angled in it increases the effect of a tsunami, when it suddenly arises parallel towards shore it takes some of the impact out due to a sudden loss of amplitude from the rising of the shoreline in general. (Yalciner)
- Berms- A berm underwater is a raised area similar to a shelf or embankment; when the tsunamis hit underwater berms they can sometimes have a premature smaller break that can lessen the initial impact on shore (Pennisi)
- Trenches- along the coast if there is a trench that is perpendicular to the shoreline the energy of the wave becomes funneled in towards where the trench opens up, the wave goes faster and therefore has a larger impact on the shore
- Shallow Water- as the depth gets shallower, the wave goes faster and can have greater run-up on the shoreline and cause damage further in
- Smooth Bottom- with nothing to deter the tsunami from continuing the tsunami can continue in an idealistic setting and has the most potential to cause damage to the largest area when there is nothing to deter it
There are various structures that can inhibit the path of the tsunami and help to shelter the shoreline so as not to create further damage:
- Mangroves: these tightly entwined trees help to hold down the soil so when the wave recedes the land stays in place, in addition they will take the initial impact of the wave as opposed to buildings and other manmade structures further inland
- Bluffs/Cliffs: these rock structures are common on the coast of Peru and can shelter the major cities that are more inland from the full force of the tsunami, although the most recent population growth has been on flat farming plains there is still a significant population that lives in the metropolitan areas
- Sea Walls: these man made structures will collapse under the full force of a large tsunami but they can help in providing at least an first buffer to the energy of the wave which will be at least be partly dissipated by destroying the wall
- Levees: although they will not provide permanent protection, as was seen in New Orleans, they are a practical and economical defense that is better than being absolutely completely unprepared for any large seismic wave
Overall Connection to Risk Assessment:
Although within our official risk assessment of Peru and Micronesia bathymetry and coastline topography were not officially included, they play an important role in the propagation of waves. Given further time, the algorithm that would be ultimately created would include the bathymetry of the areas between the source of the tsunami and the coastline that is to be affected. The bathymetry of the area would be either classified as detrimental towards the wave or enhancing the wave. In addition, within the area of the algorithm that assesses damage a data set that is influenced by the coastline topography could indicate whether the features of the coastline would help to protect the inhabitants or just leave them exposed to the full force of the wave. Bathymetry and coastline topography greatly impact the propagation of a tsunami wave although they are not officially included in our assessment of the risk of Peru and Micronesia due to time constraints. SOURCES:
Bascom, Willard. Waves and Beaches. New York City: Doubleday, 1964.
Lida, K, and T Iwasaki. Tsunamis: Their Science and Engineering. Boston: D. Reidel, 1983.
Pennisi, Elizabeth. "Powerful Tsunami's Impact on Coral Reefs Was Hit and Miss." Science 4 Feb. 2005: 657. MIT. 20 Sept. 2005.
Yalciner, Ahmet C., Efim N. Pelinovsky, Emile Okal, and Costas E. Synolakis. Submarien Landslides and Tsunamis. Boston: Kluwer Academic, 2003.