Numerical simulation of viscous, nonlinear and progressive water waves

Abstract

A numerical simulation is performed to study the velocity, streamlines, vorticity and shear stress distributions in viscous water waves with different wave steepness in intermediate and deep water depth when the average wind velocity is zero. The numerical results present evidence of ‘clockwise’ and ‘anticlockwise’ rotation of the fluid at the trough and crest of the water waves. These results show thicker vorticity layers near the surface of water wave than that predicted by the theories of inviscid rotational flow and the low Reynolds number viscous flow. Moreover, the magnitude of vorticity near the free surface is much larger than that predicted by these theories. The analysis of the shear stress under water waves show a thick shear layer near the water surface where large shear stress exists. Negative and positive shear stresses are observed near the surface below the crest and trough of the waves, while the maximum positive shear stress is inside the water and below the crest of the water wave. Comparison of wave energy decay rate in intermediate depth and deep water waves with laboratory and theoretical results are also presented.