The Effects of Variable Parameters on the Behavior of Initial Wind Waves

The generation mechanism of short wind waves is generally thought to be a viscous instability at the air-sea interface. The short, regular waves arising from a sudden wind on a still water surface have a dispersion relation which is characteristic of gravity-capillary waves. The effects of variable surface tension, viscosity and shear flow parameters on the behavior of these waves were studied. A numerical hydrodynamic stability analysis of a coupled laminar shear flow was accomplished by integrating a transformed version of the Orr-Sommerfeld equation, subject to the boundary conditions at a two-fluid interface. Unbounded growth problems usually encountered in a direct numerical integration of the Orr-Sommerfeld equation were avoided by the use of the compound matrix method, an efficient numerical technique based on a Riccati transformation. Phase speeds and growth rates of the waves generated by the instability mechanism were obtained for various surface tension and viscosity values as well as for different shear flow characteristics. The conjectured maximum growth rate/minimum phase speed relationship is shown to be valid only for specific values of surface tension. Changes in the viscosity of water are shown to have a large effect on the behavior of the waves, while changes in the viscosity of air do not. The role of the air velocity profile characteristics are shown to be subordinate to those of water-side parameters in the generation and subsequent growth of the initially appearing short waves. The disturbance is confined to a narrow region on either side of the interface which is of much smaller scale than free wave motion