Modeling Wave-Wave Interactions and 3-D Wave-Induced Circulation in the Presence of Reflection-Diffraction

Abstract

Accurate prediction of wave environment is critical to the design of ports, harbors and coastal structures. In this dissertation, two advancements for existing phase-resolving models based on elliptic mild-slope equation (EMSE) are proposed. First, an approach is developed to simulate wave-wave interactions using nonlinear elliptic mild-slope equation in domains where wave reflection, refraction, diffraction and breaking effects must also be considered. This involves the construction of an efficient solution procedure involving effective boundary treatment, modification of the nonlinear equation to resolve convergence issues, and validation of the overall approach. For solving the second-order boundary-value problem using finite difference method, the Alternating Direction Implicit (ADI) scheme is employed, and the use of approximate boundary conditions is supplemented, for improved accuracy, with internal wave generation method and dissipative sponge layers. The performance of the nonlinear model is investigated for a range of practical wave conditions involving reflection, diffraction and shoaling in the presence of nonlinear wave-wave interactions. In addition, the transformation of wave spectrum due to nonlinear shoaling and breaking, and nonlinear harbor resonance inside a rectangular harbor are simulated. Numerical calculations are compared with the results from other relevant nonlinear models and experimental data available in literature. Based on these results, a methodology is then developed which can be used to advance the existing finite element models to include wave-wave interaction effects. The finite element model developed in this study is applied to simulate nonlinear wave transformation inside Ponce de Leon Inlet, FL. Results show that the methodology developed here performs reasonably well, and has thus improved the applicability of this class of wave transformation models.

Second, a generalized expression for the three-dimensional radiation stress tensor (RST) is derived from first principles. Computation of vertically-dependent RS using this expression requires prior knowledge of the complex velocity potential obtained from phase-resolving wave models based on linear wave theory. As such, this represents a generalization of the vertically-integrated (2-D) RST proposed by Bettess and Bettess (1982) and is applicable to arbitrary linear wave fields. It can therefore be used to simulate 3-D wave-induced flow fields in harbors and coastal regions where the presence of structures and bathymetric irregularities may cause reflection, diffraction, breaking and focusing (caustics). To investigate the performance of the generalized formulation, a 3-D coupled current-wave system is developed which involves a wave prediction model (based on elliptic mild-slope equation) and a 3-D circulation model that uses the generalized RST. The coupled system is then applied to three different cases involving wave propagation over a sloping beach, a standing-wave case, and wave interaction with a shore-parallel breakwater. Numerical calculations of the wave-induced set-up/down and the 3-D current fields are compared with analytical results and experimental data available in literature. Results show that the approach developed here performs reasonably well and has a wide range of applicability. In addition, the existing (2-D and 3-D) radiation stress formulations are shown to be the special cases of this generalized form, which is further used to develop an analytical expression of 3-D RST for full/partial standing waves over flat bottom.