Ocean wave dynamics with high fidelity numerical simulations

Abstract

Wind waves are ubiquitous on the ocean surface and play an active role in air-sea interactions. Wind waves grow due to wind forcing and dissipate most of their energy through wave breaking. There are still many open questions regarding these two physical processes. The former involves coupling with the atmospheric boundary layer; the latter is a fully nonlinear process that classical weakly nonlinear wave theories fail to account for.This thesis applies novel numerical methods to the long-standing wind wave problems, which results in new perspectives on both processes. Two tailored numerical frameworks are introduced. The two-phase Volume-of-Fluid framework solves the Navier-Stokes equations for both water and air and resolves waves’ response to realistic wind forcing together with their feedback to the wind with high fidelity. The multi-layer framework focuses solely on the water side and solves the free-surface Navier-Stokes equations with a gradient-limiter that models breaking without surface overturning. It greatly reduces the computational cost, which enables the implementation of phase-resolved simulations of broadband random wave fields. In the mechanical study of wind wave growth, we verify that growth can be attributed to pressure variation at the interface. We systematically report the pressure variation’s amplitude and phase shift with different wave slopes and wave ages, which feeds back to the continuous discussion on growth mechanisms. We observe rich phenomena such as steep wave shape, airflow separation, and micro-breaking. The wave form drag depends on the specific wave status, not only on the (global) wave slope. The growth rate parameterization is discussed as a scaling law independent of any particular growth mechanism. In the statistical study of breaking waves, we observed a power-law scaling of the breaking distribution in the numerically resolved range, and the breaking frequency is within the scattering of field observations. We proposed a wave-slope-based scaling law that collapses the numerical data, which can be explained by the physical argument that breaking is foremost a process controlled by the wave slope. In addition to studying two specific problems regarding wind waves, the current thesis serves as a proof of concept for the two numerical frameworks we propose.