The dynamics of oceanic waves running up an inclined slope : theoretical approach and coastal engineering applications

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. Understanding wave shoaling and its nonlinear behaviour in the coastal region is critical for developing effective coastal defence systems. This thesis endeavours to scrutinise the evolution of ocean swells in various bathymetries through theoretical formulation and numerical simulations of the behaviour of waves approaching the shore. The first study utilized numerical wave tanks to understand wave dynamics computationally. The three-dimensional equations of motion are solved by the software OpenFOAM. The ‘volume of fluid’ method and the phase fraction parameter are employed at the free surface. The large eddy simulation scheme is used as the turbulence model. Relaxation zones are deployed to filter the unwanted reflection. 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. Grid independence and sensitivity tests are performed to ensure accuracy. For small angles of inclination (<10⸰), 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 than a straight-line one. Long waves with speed proportional to the square root of the depth thus experience a larger deceleration. Nonlinear (or ‘piling up’) effects occur earlier than 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. In the second study, a model based on the variable coefficient nonlinear Schrödinger equation which involves a gain/loss term arising from waves running up a sloping beach. This study concentrated on investigating how weakly nonlinear, narrow-banded wave packets evolve in an inhomogeneous medium, which can be representative of the context of coastal engineering. The choice of a 'forcing' boundary condition distinguishes this study from previous works in the literature. It allows energy to enter the computational domain. Waves approaching shore under storm surges can be modelled by these dynamics. The amplification process is determined by the competition between gain, dispersion, and nonlinearity. When waves move up a sloping beach, the concave seafloor has the least steepening effect, followed by a straight line, and then the convex seafloor., agreeing well with the first study.