2-DIMENSIONAL PATTERNS IN RAYLEIGH-TAYLOR INSTABILITY OF A THIN-LAYER

We study experimentally and theoretically the evolution of two-dimensi onal patterns in the Rayleigh-Taylor instability of a thin layer of vi scous fluid spread on a solid surface. Various kinds of patterns of di fferent symmetries are observed, with possible transition between patt erns, the preferred symmetries being the axial and hexagonal ones. Sta rting from the lubrication hypothesis, we derive the nonlinear evoluti on equation of the interface, and the amplitude equation of its Fourie r components. The evolution laws of the different patterns are calcula ted at order two or three, the preferred symmetries being related to t he non-invariance of the system by amplitude reflection. We also discu ss qualitatively the dripping at final stage of the instability.