WAVE RUN-UP HEIGHT AND REFLECTION COEFFICIENT DUE TO SLOPES BASED ON LINEAR WAVE THEORY

Abstract

 In this study, we present an overview of fundamental wave theories, including linear long-wave theory on horizontal beds, small-amplitude wave theory on horizontal beds incorporating evanescent waves, and linear long-wave theory on uniformly sloping beds, focusing on wave reflection, transmission, and run-up phenomena. We derive analytical solutions for wave propagation over slopes and steps using these theories. While reflection and transmission over slopes vary with wavelength, water depth, and slope steepness, our analysis reveals that these phenomena are governed by a single dimensionless parameter: the ratio of the distance to the shoreline in the extension of the slope to the wavelength at the point of interest. Furthermore, we demonstrate that when waves, such as tsunamis, runup slopes from certain water depths, the amplification factor increases inversely proportional to the square root of the wave period. Additionally, we illustrate how qualitative understanding of various phenomena using these linear theories aids in critically evaluating results obtained from numerical simulations and AI.