Evolution of unsteady jets in the Rayleigh-Taylor instability
- 1Institute for Industrial Mathematics, Ben-Gurion University of the Negev, Beer-Sheva, Israel
- 2School of Mathematical Sciences, Tel-Aviv University, Ramat-Aviv, Israel and The Levich Institute for Physico-Chemical Hydrodynamics, The City College of New York, NY-10031, USA
- 3Institute of Oceanology of Russian Academy of Sciences, 117851 Moscow, Russia
Abstract. 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 expansions. The solution has been obtained with the planar tips of jets characterized by the jump of the interface slope.