Runup of Nonlinearly Deformed Waves on a Coast

摘要

The problem of runup of long nonbreaking waves on a plane slope is well developed from the mathematical point of view within the framework of nonlinear theory of shallow water, which allows for an analytical solution using the Carrier-Greenspan transform. Various examples of incident waves are considered in the literature. A review of old works is given in [2]. We also cite the latest publications. However, in all the papers cited, the incident wave was symmetric or antisymmetric with equal steepness of the leading and trailing slopes. As a result, the formulas for the runup height can be parameterized. Parameterization includes the height and length of the incident wave as well as the distance to the coast. At the same time, numerous observations during the 2004 tsunami in the Indian Ocean indicate that the wave approaching the coast was strongly deformed with notable steepness of the leading front. We shall show that a wave with increased steepness of the leading front penetrates inland over longer distances than a wave with a symmetric profile.