Dwarf solitary waves and low tsunamis

Abstract

This work applies the regularized solitary wave theory to develop accurate computational method for evaluating the dwarf solitary waves, with amplitude-to-water depth ratio α ≤ 10⁻², as a useful model of one-dimensional tsunamis propagating in the open ocean. The algebraic branch singularities of these solitary waves magnifying with diminishing wave amplitude, making their computations insurmountable by existing methods, are removed by the regularized coordinates given by this new theory. Numerical examples show that this new method can produce accurate results even for α ≅ 10⁻³ or less.

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