Solutions of Kinematic-Dynamic Elements For Edge Waves On Sloping Bottom

Zhang, Y. (Research Institute of Coastal and Ocean Engineering,Hohai University Nanjing, Jiangsu,China) | Hong, G.W. (Research Institute of Coastal and Ocean Engineering,Hohai University Nanjing, Jiangsu,China) | Feng, W.B. (Research Institute of Coastal and Ocean Engineering,Hohai University Nanjing, Jiangsu,China)

OnePetro 

By using perturbation method, second-order analytical solutions of short edge-wave interactions were introduced. In this paper, the analytic expressions and numerical calculations of the main kinematicdynamic elements such as free surface elevation, velocity and energy of regular edge waves, spectrum and its characteristics of irregular edge waves were given. The calculation results had shown that significant distinctions on these kinematic-dynamic elements could appear due to different values of slope angle, the mode number and nonlinear interactions of edge waves.



INTRODUCTION

Edge waves are the trapped-waves propagating alongshore, which may occur near coastal region. They play an important role in the deformation of beach morphology, long-shore currents and wave runup etc. Linear analytic solutions of edge waves of 0-mode on a constant sloping beach were derived by Stokes (1846), which exponentially decay offshore and their energy is concentrated near shore region. Using the linear shallow water equations, Eckart (1951) obtained an approximation solutions of edge waves of infinite number modes to the same problem. Based on full water wave equations, Ursell (1952) presented the full linear solutions of finite mode edge waves. According to Ursell’s solutions, as the full mode number N becomes larger, the edge wave surface elevation, which has nodes N, become more complicated. The comparisons of the above mentioned Eckart’s and Ursell’s solutions were made by Yeh (1986) etc. It is shown that the error of the shallow water approximation is larger as the beach slope gets steeper and the distance is farther from the shoreline. Recently, several excitation mechanisms of edge waves were proposed by Gallagher (1971),Guza & Davis(1974),Bowen & Guza (1978), Foda & Mei (1981), Lippman& Holman (1997), Lin (2005) etc. based on nonlinear resonant interactions of three waves, four waves, wavebreaking in the surf zone. Most of them were based on nonlinear shallow water equation of long waves on gentle slope.