Abstract
The temporal development of a single mode Rayleigh-Taylor instability consists of three stages: the linear, free fall and terminal velocity regimens. The purpose of this paper is to report on new phenomena observed in the approach to terminal velocity. Our numerical study shows an unexpected nonuniform approach to terminal velocity. The nonuniformity applies especially to the spikes, which are fingers of heavy fluid falling into the light fluid, but it also applies to the rising bubblesof light fluid. For spikes especially, our results call into question the meaningfulness of a terminal velocity for moderate values of the Atwood number A. After a short time period of pseudo-terminal plateau, the spike velocity increases to a significantly higher maximum, followed by a decrease. This phenomena appears to be due to a slow evolution in the shape of the spike and bubble. We find a relation between the spike (bubble) acceleartion and the tip curvature. In correlation with an increase in the spike velocity, the main body of the spike becomes narrower and the tip curvature increases. Our numerical results are by the Front Tracking method. The very late time simulations considered here required stabilization by a small value for the viscosity, so that the compressible Navier-Stokes equations govern the dynamics.
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Supported by the MICS program of the U.S. Department of Energy DE-FG02-90ER25084, DE-AC02-98CH10886, the Department of Energy Office of Inertial Fusion, the Army Research Office, grant DAAL-03-91-0027 and the National Science Foundation, grant DMS-0102480.
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Glimm, J., Li, Xl. & Lin, AD. Nonuniform Approach to Terminal Velocity for Single Mode Rayleigh-Taylor Instability. Acta Mathematicae Applicatae Sinica, English Series 18, 1–8 (2002). https://doi.org/10.1007/s102550200001
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DOI: https://doi.org/10.1007/s102550200001