Abstract
In this study, we develop a theoretical model with which we can predict spatial and temporal spectra of the surface divergence at a contaminated turbulent air-water interface. In the present model, the flow field close to a contaminated interface is approximated as superposition of a free-surface flow at a clean interface and a surfactant-induced flow. As a result, the damping factor, which represents the ratio between the intensity of the surface divergence at a contaminated interface and that at a clean interface, is analytically derived as a function of spatial wavenumber k, frequency ω and Marangoni number Ma. The present predictions agree well with the results of direct numerical simulation at a wide range of Marangoni number.
