Propagation of very long water waves, with vorticity, over variable depth, with applications to tsunamis
We present a theory of very long waves propagating on the surface of water. The waves evolve slowly, both on the scale e (weak nonlinearity), and on the scale, a, of the depth variation. In our model, dispersion does not affect the evolution of the wave even over the large distances that tsunamis may travel. We allow a distribution of vorticity, in addition to variable depth. Our solution is not v