The Effect of Contaminant Drag Reduction on the Onset and Evolution of Langmuir Circulations

A new mechanism of instability leading to development of Langmuir circulations is proposed and studied based on the hypothesis that the turbulence and, correspondingly, the eddy viscosity are reduced in regions of higher than average contaminant concentration. Here, bubbles are considered as the contaminant, although it is known that surfactants and some particles also are capable of turbulence reduction. The analysis shows that only a very small local decrease in eddy viscosity is needed to initiate the instability. Simplifications to the momentum and bubble turbulence models, as well as neglect of vertical advection, make it possible to analytically solve the perturbation equations and determine the characteristic scale with the maximum growth rate. The scale of the fastest-growing Langmuir circulations is found to be a function of the concentration of bubbles in the near-surface layer, the surface current shear (wind shear), the Stokes drift created by the surface waves, and the eddy viscosity. In contrast to the results of earlier models, the analysis predicts that the maximum change in the current velocity along the direction of the wind (the so-called jets and wakes) is at the surface, not below it. The ratio of perturbation of along-wind surface current and vertical velocity generated by circulations (the pitch) and the aspect ratio of the Langmuir rolls are in reasonable agreement with the experimental data.