TOPOLOGICAL FLUID-DYNAMICS OF INTERFACIAL FLOWS

The topological description of flows in the vicinity of a solid bounda ry, that is familiar from the aerodynamics literature, has recently be en extended to the case of flow at a liquid-gas interface or a free su rface by Lugt [Phys. Fluids 30, 3647 (1987)]. Lugt's work is revisited in a more general setting, including nonconstant curvature of the int erface and gradients of surface tension, using tools of modern nonline ar dynamics. Bifurcations of the flow pattern occur at degenerate conf igurations. Using the theory of unfolding, this paper gives a complete description of the bifurcations that depend on terms up to the second order. The general theory of this paper is applied to the topology of streamlines during the breaking of a wave and to the flow below a sta gnant surface film.