Exponentially Reduced Reflection (ERR) versus Linear Wave Theory (Airy-Laplace)

Abstract

The linear wave theory according to Airy/Laplace (1842) is widely used by engineers however violates the law of conservation of mass and considers local ground inclination α = 0⁰ only.Both shortcomings can be avoided(a) by extending Schulejkin's mirror method to represent orbital kinematics over flat ground to inclinations 0⁰ ≤ α ≤ 90⁰ and(b) by referring to the phase shift Δϕ between incident and reflected waves according to the author´s definition of the complex reflection coefficient CRC.This contribution includes Exponentially Reduced Reflection (ERR) for the first time as a wave theory applicable to complex boundary conditions, considering a priori an important cause of wave deformation over inclined seafloor.For instance, the change of the total orbital kinematics (orbital paths, velocities and accelerations) related to the water surface is shown for decreasing water depths on a slope 1 : n = 1 : 2.In contrast to the Airy/Laplace theory, lower orbital velocities are obtained above the still water level, which is important with respect to the design of offshore structures.