Result and Conclusion

Check the practicality of the formula:

Assume Tsunami at Offshore:
Local Depth (d) = 5000 m
Wave Period (T) = 800 sec
Using wave calculator, wave length (L) = 176312 m
Wave Speed (C) = L / T = 221 m/s = 793 km/hr
Wave Height (H) = 0.6 m

Assume Tsunami at Nearshore:
Local Depth (d) = 100 m
Wave Period (T) = 800 sec
Using wave calculator, wave length (L) = 25063.05 m
Wave Height (H) = 4.5 m

The wave run-up obtained:

From the actual data, the wave run-up in Aceh, Indonesia reaches about 24 m. Hence the energy conservation formula gives approximately reasonable result. However, this method is very simplified. Some assumptions used in this method:

1. Regular tsunami wave
2. Frictionless bottom
3. Constant shoreline slope
4. No breakwater

In the real tsunami, the wave propagation will be more random. All type of factors can affect the wave propagation. In the real coastline, the slope is also irregular. Therefore, this method can be used for approximation but it doesn’t guarantee exact solution to the problem. More accurate formula can be derived from “Numerical Shallow Water Model”.

The summary of the numerical method is:

where: u = horizontal velocity
η = surface elevation
H = value of depth
g = gravity acceleration

where: H(r) = wave run-up
r = right direction from initial wateredge point
ro = width of a shore area with varied inclination
C = curvature parameter of the slope

Conclusion:

• Wave run-up height depends highly on the shore profile.

• The increase of an angle of the shore slope results in a decrease of the wave run-up but an increase in the extent of tsunami

• Therefore, we need more warning system on the shores with vulnerable profile.