Water Wave Equation Lab Report

Introduction:
As humans evolve and the world around us develops, technologies become more advanced in order to cope with our surroundings. But no matter how much we advance as humans, nature will always remain stronger. The evidence is seen throughout the centuries as natural disasters destroyed and even wiped out entire nations within days, minuets and even seconds. In recent news, the nation of Nepal was struck by an earthquake with magnitude of 7.8 killing almost 8000 and injuring thousand others .
Some of the most well-known natural disasters include: floods, hurricanes, volcanic eruptions, landslides, and many more. Floods can either occur over a period of time, if heavy rains continue, or they can occur suddenly as what is called “flash

The tension between the tectonic plates and their movement causes the sea or ocean bed to be displaced which, in turn, causes the water to also be displaced in a short period of time forming a tsunami which starts off in circular waves. The mathematical propagation of a wave is modeled by what is called a water wave equation. The wave equations are mainly expressed in three dimensional calculations and models, but for simplicity only one dimensional equation will be used. In order to derive these equations we use a calculus technique called partial differential equations where, an equation with two or more variables is differentiated, but with respect to a single variable with the other being considered as constants.
There are two types of water wave equations, linear and nonlinear. The linear equation is used to describe the tsunami at the beginning of its journey and can be modeled using linear water wave equation but as it approaches the coast it then increases in power and force which is why it is more accurate to use than nonlinear water wave