Write down the mathematical model of Tsunami
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Abstract
The processes of tsunami evolution during its generation in search for possible amplification mechanisms resulting from unilateral spreading of the sea floor uplift is investigated. We study the nature of the tsunami build up and propagation during and after realistic curvilinear source models represented by a slowly uplift faulting and a spreading slip-fault model. The models are used to study the tsunami amplitude amplification as a function of the spreading velocity and rise time. Tsunami waveforms within the frame of the linearized shallow-water theory for constant water depth are analyzed analytically by transform methods (Laplace in time and Fourier in space) for the movable source models. We analyzed the normalized peak amplitude as a function of the propagated uplift length, width and the average depth o
Answer:-
Waves at the surface of a liquid can be generated by various mechanisms: wind blowing
on the free surface, wavemaker, moving disturbance on the bottom or the surface, or even
inside the liquid, fall of an object into the liquid, liquid inside a moving container, etc. In
this chapter, we concentrate on the case where the waves are created by a given motion of
the bottom. One example is the generation of tsunamis by a sudden seafloor deformation.
There are different natural phenomena that can lead to a tsunami. For example, one
can mention submarine slumps, slides, volcanic explosions, etc. In this chapter we use a
submarine faulting generation mechanism as tsunami source. The resulting waves have
some well-known features. For example, characteristic wavelengths are large and wave
amplitudes are small compared with water depth.
Two factors are usually necessary for an accurate modelling of tsunamis: information
on the magnitude and distribution of the displacements caused by the earthquake, and
a model of surface gravity waves generation resulting from this motion of the seafloor.
Most studies of tsunami generation assume that the initial free-surface deformation is
equal to the vertical displacement of the ocean bottom. The details of wave motion are
neglected during the time that the source operates. While this is often justified because the
earthquake rupture occurs very rapidly, there are some specific cases where the time scale
of the bottom deformation may become an important factor. This was emphasized for
example by Trifunac and Todorovska [TT01], who considered the generation of tsunamis
by a slowly spreading uplift of the seafloor and were able to explain some observations.
During the 26 December 2004 Sumatra-Andaman event, there was in the northern extent
of the source a relatively slow faulting motion that led to significant vertical bottom motion
but left little record in the seismic data. It is interesting to point out that it is the inversion