Colloquium on April 14th, 2008

Michael Berry
University of Bristol

Tsunami asymptotics

For most of their propagation distance, tsunamis are linear dispersive waves whose speed is limited by the depth of the ocean and which can be regarded as a diffraction-decorated caustic in spacetime. For constant depth, uniform asymptotics gives a very accurate compact description of the tsunami profile generated by an arbitrary initial disturbance. Variations in depth can focus tsunamis onto cusped caustics, and this 'singularity on a singularity' constitutes an unusual diffraction problem, whose solution indicates that focusing can amplify the tsunami energy by an order of magnitude.