The run-up of long waves of different polarity on non-reflecting and flat cross-shore profiles

In this work the features of long wave run-up of different polarity on a flat and non-reflecting slopes are investigated. The depth of non-reflecting bottom configurations, in which, under the theory of shallow water there is no reflection from the bottom, is related to the distance from the edge by the dependence h ~ x ^4/3 (where h is the depth of the basin and x is the distance from the edge). Only along Estonian coasts at least on 14 locations the bottom profile may be approximated by the exponent close to 4/3. For these locations the scenarios with high wave run-up are most probable. A long wave on such a beach, in the framework of the linear theory of shallow water, runs up particularly strongly, and the height of the wave on the coast significantly exceeds the height of the wave on a flat slope. A numerical solution was obtained within the framework of the nonlinear shallow water equations and Boussinesq type equations with the help of the CLAWPACK Software package (www.clawpack.org). The research was supported within the framework of the grant of the President of Russian Federation for state support of young Russian scientists (MK-1127.2017.5).