The second part of the lecture concerns recent long tsunami-like waves, especially waves where the leading part of the wave is depressed, which was a characteristic feature of the tsunamis that approached the coast-lines of SEAsia in 2004 and Japan in 2011. As such waves travel from the source region, a non-linear Kortweg-de Vries model of R. Grimshaw, K.W. Lam and J.C.R. Hunt (2014) shows how when a depression wave is followed by an elevation (a 'breather) there is a transition at a location which can be estimated when the peak elevation catches up with the peak depression and nearly doubles in height before it then decreases and travels in front of the depression. In situations where the depression reaches the beach, recent modelling and laboratory studies show how the depression deepens, leading to a back flow and drying out of the beach, before there is a transition when the following much amplified elevation (in which the total momentum of the wave is maintained) surges up the beach and moves some kilometres inland, which corresponds with recent and past observations (Klettner et al. 2012).
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