Mechanisms And Modelling of Wind Driven Waves

Abstract

This paper reviews (in qualitative and order of magnitude terms) the main mechanisms determining wind driven waves and their quantitative modelling for the different stages as the wind speed and the Reynolds number both increase, initially through coupling the instability ‘waves’ in the laminar boundary layers above and below the water surface, secondarily through initiation of eddy structures in turbulent boundary flow over flat water surface (’cats paws’) and thirdly as distorted airflow passes over the undulating water surface with different kinds of dynamics, wave shapes (ranging from sinusoidal to pointed forms), amplitude H, wavelength L, travelling at speed c_r and growth rate c_i/U_*, coupled with the flow below the water surface. Significant flow features are the turbulent thin shear layers on the surface and detached ‘critical’ layers above the surface, which are also affected by the variation of surface roughness near the crests of the waves, by recirculating, separated flows near the surface and by high gradients of turbulence structure in the detached critical layers. Two phase flows in the recirculation zones on the lee side of waves leads to spray in the air above the water surface which also amplifies the boundary layer turbulence. Two phase bubbly flows below the surface generate near surface bubbles and may increases the surface drag downstream of the wave crests. The topology of node and saddle singular points in these mean recirculating flows provides a kinematic description of these flows. Idealised dynamical studies are presented of the variation of the wave amplitude through wind forces on waves moving in groups of waves, and thence physical models are proposed for the transfer of wave energy between large and small frequencies and length scales of wave spectra.