Transient convective structures in a cooled water layer in the presence of a drift flow and a surfactant

Abstract

The paper is concerned with three-dimensional convective structures arising in a water layer cooled from above and covered by an adsorbed insoluble surfactant. The water is subjected to a laminar drift flow produced by tangential stresses on a free surface. The surface diffusion of the surfactant are taken into account within the approximation of a nondeformable flat surface. After appropriate reformulation of standard equations governing gravity-capillary convection and surfactant concentration, the problem is solved numerically using a pseudospectral method employed in our previous work. Development of the convective structures with increasing Reynolds number, surfactant film elasticity, and layer thickness is studied. The minimal layer thickness is chosen taking into account the results of relevant laboratory experiments. The cell-to-roll transition is revealed in the thin layer with increasing Reynolds number. The role of dissipation due to the surfactant film is elucidated by comparison with purely gravitational convection. The turbulent convection arising in a thicker layer subjected to a laminar shear flow is examined. Disordered streets containing elongated cells and swirl-like motions are revealed. Images of the surface temperature and the perturbed surfactant concentration are compared.