TSUNAMI SHOALING THEORY

Abstract

When a kilometers-long tsunami wave approaches the coast, the amplitude of the tsunami wave will increase according to Green’s law, depending on the depth of the seawater. Near the shoreline, the increasing tsunami wave sucks from the front seawater and it will withdraw. The sea bottom will open, creating a drawback phenomenon. The drawback flow and the propagating wave front will collide and will form a wave with a sharp drop downwards. The tsunami break wave starts flowing rapidly to the shoreline. To simulate the situation, we can imagine a virtual dam break (theory by Ritter). As a result, we can use the rules for tsunami wave break theory to calculate an emerging massive flow. The velocity of the break wave can be obtained according to the “dam wall break flow” theory. By these rules, the flow velocity, the parabolic form of flowing water surface, the depth of the sea water at shoreline, the duration, the level of the maximum run-up height onshore and flow loading for buildings can all be calculated. The whole aforementioned shoaling process is presented by easily understandable figures. A simplified calculation example is presented based on the Asian tsunami of 2004 in Xaaphuun in Somalia, from which we have a lot of input data from 0.25-degree-shallow shore. The third and strongest drawback of the tsunami was 1300 m long and 6 m deep. Knowing the shoreline velocity (11 m/s) and estimating the flow friction, we can calculate the depth of water at shoreline, the volume flow, the timing and the average run-up height onshore. The results were in accordance with real data. Also, an explanation will be formulated for the reason why the city of Faro was spared in the Lisbon earthquake and tsunami in 1755. The tsunami shoaling process includes shoreline approaching increasing tsunami wave, drawback, collision of flows, virtual dam break, massive flow to the shoreline and run-up onshore.