abstract.tex (1334B)
1 \begin{abstract} 2 The aim of this project is to give a master student a general idea of 3 fluid mechanics \cite{johnson_1997}, to further combine this knowledge 4 into modeling a problem focusing on a tsunami, generated by an earthquake 5 in the Indian Ocean in 2004 (''On the propagation of tsunami waves, with 6 emphasis on the tsunami of 2004`` by Adrian Constantin 7 \cite{constantin_tsunami}). In this regard the project focuses on 8 inviscid water flow, where the mass density of water can be taken to be 9 constant and qualitatively shows how to derive Euler's Equations of 10 Motion using basic multivariable calculus. The whole problem of modeling 11 water waves comes around to determining the wave profile at the surface 12 $z = h(x,y,t)$, where the need to introduce boundary conditions on the 13 governing equations comes into play. To derive model hierarchies for 14 different regimes (e.g. shallow water, long-wave or small amplitude) 15 dimensional analysis and scaling of the parameters together with 16 asymptotic expansion becomes essential. Asymptotic analysis then gives a 17 model for the regime of the solitary wave and the KdV equation which is 18 the region $\varepsilon=O\left(\delta^2 \right)$, the key to modeling the 19 tsunami wave before approaching the shore. 20 \end{abstract}