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.