Modeling Ocean Swell and Overtopping Waves: Understanding Wave Shoaling with Varying Seafloor Topographies

Abstract

One risk posed by hurricanes and typhoons is local inundation as ocean swell and storm surge bring a tremendous amount of energy and water flux to the shore. Numerical wave tanks are developed to understand the dynamics computationally. The three-dimensional equations of motion are solved by the software ‘Open Field Operation And Manipulation’ v2206. The ‘Large Eddy Simulation’ scheme is adopted as the turbulence model. A fifth-order Stokes wave is taken as the inlet condition. Breaking, ‘run-up’, and overtopping waves are studied for concave, convex, and straight-line seafloors for a fixed ocean depth. For small angles of inclination (<10°), a convex seafloor displays wave breaking sooner than a straight-line one and thus actually delivers a smaller volume flux to the shore. Physically, a convex floor exhibits a greater rate of depth reduction (on first encounter with the sloping seafloor) than a straight-line one. Long waves with a speed proportional to the square root of the depth thus experience a larger deceleration. Nonlinear (or ‘piling up’) effects occur earlier than in the straight-line case. All these scenarios and reasoning are reversed for a concave seafloor. For large angles of inclination (>30°), impingement, reflection, and deflection are the relevant processes. Empirical dependence for the setup and swash values for a convex seafloor is established. The reflection coefficient for waves reflected from the seafloor is explored through Fourier analysis, and a set of empirical formulas is developed for various seafloor topographies. Understanding these dynamical factors will help facilitate the more efficient designing and construction of coastal defense mechanisms against severe weather.