Interactions among waves, surfactants and currents.

Abstract

Interactions among capillary-gravity waves, surfactants and currents in deep water are discussed in this thesis. The problem of wave reflection and refraction in the presence of surface contaminant (surfactant) with a sudden spatial concentration variation is investigated and a closed form solution for potential function is found using complex integration. The energy of the reflected wave is small except at grazing angles. Linear capillary-gravity waves with slowly spreading surfactant are studied using matched asymptotic expansions and multiple scales. The wave bending and wave damping are calculated when the surfactant has a slowly spatial variation. The damping ratio is larger than that without surfactant but the value is still of the same order in Reynolds number if the surfactant concentration gradient is of the order of magnitude chosen here. The nonlinearity of the capillary-gravity waves and its effects on the surfactant spreading are discussed and it is found that a secondary boundary layer of Stuart type is required for the mean flow. Finally the effects of a vortex pair on the distribution of the surfactant concentration are investigated numerically. The results show how the surfactant is pushed away by the vortex pair and how the change of surface tension due to the change of surfactant concentration affects the path of the vortex pair and the generation of the secondary vortex.