Numerical and theoretical investigation of coupled wind–wave–current environment

Abstract

Understanding the interaction mechanisms among ocean surface waves, turbulent air, and ocean currents is beneficial to many environmental applications. This thesis focuses on fundamental questions of ocean surface wave dynamics and free surface flows. We first study the wind-wave generation process in a combined numerical and theoretical approach. We perform wave-surface-fitted direct numerical simulation of turbulent wind over initially calm water to capture the multistage generation of water waves using a wave-surface-fitted grid. Detailed analyses are conducted to evaluate the initial stage and principal stage of the Phillips theory in both physical space and wavenumber space. We further propose a random sweeping turbulence pressure–wave interaction model by introducing the random sweeping hypothesis of air pressure fluctuations to the Phillips theory and obtain an asymptotic solution of the mean square of surface wave elevations over time. In the physical space, we use the random sweeping turbulence pressure–wave interaction model to obtain a quantitative prediction of the growth rate of surface elevation variance in the principal stage, which is found to agree with the direct numerical results better than the Phillips theory. We next investigate nonlinear interactions between ocean wavefield and subsurface currents using high-fidelity numerical simulations. Several typical wake patterns are simulated using the velocity-based boundary integral method, and the influence of complex currents on the surface waves is analyzed quantitatively using theoretical solutions of wave–current interactions. We also present a method for solving the inverse problem of deducing the current field based on surface-wave data using machine-learning techniques. A deep neural network is designed for processing spatial-temporal surface wave data. The proposed neural network can effectively deduce the current field, and we analyze the distributions of regression errors and the training dataset dependency. In the final part, we focus on interfacial scalar transport in free-surface flows. We analyze a nonlinear integral equation for calculating free surface divergence based on surface thermal information. We theoretically prove the local linear convergence of the corresponding Picard iteration method for solving the integral equation when the surface heat flux is a real-analytic function of time. The rate of convergence can be determined explicitly based on our theoretical analysis. Numerical examples are provided to test the convergence performance, which shows good agreement on the rate of convergence with the theoretical predictions.