Tadayoshi Kano

(Kyoto, Japan)

Tunamis on a deep open sea and on a gentle sloping beach

Tunamis as shallow water waves:
(1) The shallow water wave equations show that tunamis propagate on a deep open sea by, at least, the sound speed. (2) On a gentle sloping beach, the shallow water wave equations show that the diminution of propagation speed caused by the diminution of the water-depth results the deformation and, eventually, the break down of tunamis. The shallow water wave equation have a corresponding conservation law on a sloping beach and shock formation corresponding tunamis breaking on the shore.
(3) A mathematical justification for tunamis as shallow water waves is given.