Evolution of unsteady jets in the Rayleigh-Taylor instability

The paper concerns the temporal evolution of the Rayleigh-Taylor instability of two superimposed fluids in a vertical channel. At large times the instability results in the formation of a wide nearly-steady bubble of the lighter fluid rising through the channel, and thin long unsteady jets of the heavier fluid flowing down the channel walls. The jet flow appears to be tractable asymptotically by the method of matched asymptotic expansions. The solution has been obtained with the planar tips of jets characterized by the jump of the interface slope.