Numerical simulation of water waves using Navier-Stokes equations

The main purpose of this thesis is to use state of the art computational fluid dynamics techniques to solve the problem of water-wind waves which are related to air-sea interaction. In general, air-sea interaction is studied in a de-coupled manner where both air and water phases are separate and the water phase is either considered as a smooth or rough wall which is stationary or moving. However, in real ocean waves the air and water are coupled. Mass, momentum, heat and energy exchange takes place mostly on the surface waves and this process is culminated when the waves break. Numerical modelling to study these processes requires the solution of the full Navier-Stokes equations along with capturing the interface boundary of the wave with high accuracy, thereby helping us to understand the physical processes taking place on the air-water interface and improve current wave modelling techniques. Our primary motivation is two fold: (1) to investigate the accuracy and reliability of the state of the art numerical techniques available for simulating free surface flows and model air-water wave interaction and (2) to study various near surface physical processes taking place at the transient, viscous, rotational and nonlinear air-water wave interface and understand its effects on the momentum and energy exchange in wind waves. The work presented in this thesis investigates a numerical model to solve the full Navier Stokes equations required to model transient, viscous, rotational and nonlinear water waves. The first step in the process is to model the water waves when the average wind speed is zero. Various other physical aspects related to wave dynamics are discussed for intermediate depth and deep water waves with different steepnesses. They are compared with earlier experimental and theoretical works available in order to verify the accuracy of the model . The second step is to model these water waves in the presence of wind blowing at different speeds and analyze its effects on various near surface physical properties and its effect on the motions in the air and underlying water. The other purpose of this thesis is to investigate some very interesting aspects related to wave dynamics such as vorticity and shear stress which are little studied due to complexities surrounding near surface flow measurements and the lack of an accurate analytical solution. The current work provides a tool for the application of CFD techniques to reliably predict wind-wave interaction by using numerical modelling techniques used in multi-phase flow environments. The accuracy and convergence of the numerical technique used in this thesis is illustrated by comparing the numerical results with analytical and theoretical results available. The technique is demonstrated to be accurate in the simulation of twodimensional flows where turbulent effects are negligible. At higher wind speeds, the use of suitable turbulence closure models is recommended. The main conclusions drawn from the study are: (1) accurate simulation of two and three dimensional, unsteady, viscous and nonlinear water waves is possible with current CFD techniques; (2) The role played by shear stress and vorticity in the wind wave interaction is important and cannot be ignored; (3) the vertical velocity gradients observed inside the water in intermediate depth water waves are found to be stronger than deep water waves; and (4) the effect of the bottom boundary on the magnitude of free surface vorticity is not found to be high.