The effects of surfactants on the formation and evolution of capillary waves

Abstract

The effects of surface-active agents on the formation and evolution of small capillary ripples developing in the forward front of short water waves is investigated numerically. The capillary waves, believed to have a significant relevance in the process of wave breaking and the onset of turbulence, accompany the initial development of spilling breakers. A novel hybrid numerical methodology is introduced to couple the full two-fluid Navier–Stokes equations with the free boundary motion and with the surfactant dynamics. The hybrid method uses dynamically adaptive front-tracking to accurately represent interfacial quantities and forces and to aid in treating the numerical difficulties associated with surface tension. At the same time the method employs the level set approach to efficiently update the material properties of the flow. It is found that the capillaries are dramatically affected by the presence of surfactants. The capillary region is invariably marked by accumulation of surfactants that reduces locally the interfacial tension. The size of the wave roller (bulge) diminishes and both the amplitude and wavelength of the capillary ripples also decrease as interfacial tension gradients increase. When surface convection dominates over diffusion, the accumulation of surfactants in the capillary region intensifies and the roller gets smaller and flatter. Large concentration gradients can be produced and these lead to a spread of vorticity along the spilling breakers as a result of the tangential Marangoni stress. In addition to the full two-phase viscous flow simulations, boundary integral computations of the corresponding potential inviscid flow are also performed to compare and contrast the two models in the case of uniform interfacial tension. Differences between the potential and the viscous flows are observed as soon as the wave steepens and develops high-curvature regions.