Numerical Simulations of Laminar Air–Water Flow of a Non-linear Progressive Wave at Low Wind Speed

A numerical simulation for two-dimensional laminar air–water flow of a non-linear progressive water wave with large steepness is performed when the background wind speed varies from zero to the wave phase speed. It is revealed that in the water the difference between the analytical solution of potential flow and numerical solution of viscous flow is very small, indicating that both solutions of the potential flow and viscous flow describe the water wave very accurately. In the air the solutions of potential and viscous flows are very different due to the effects of viscosity. The velocity distribution in the airflow is strongly influenced by the background wind speed and it is found that three wind speeds, \(U=0\), \(U=u_m\) (the maximum orbital velocity of a water wave), and \(U=c\) (the wave phase speed), are important in distinguishing different features of the flow patterns.