J. Korean Math. Soc. 2017; 54(2): 663-673
Online first article December 27, 2016 Printed March 1, 2017
https://doi.org/10.4134/JKMS.j160219
Copyright © The Korean Mathematical Society.
Sujin Choi and Sung-Ik Sohn
Gangneung-Wonju National University, Gangneung-Wonju National University
We consider the multi-harmonic model for the bubble evolution in the Rayleigh-Taylor instability in two and three dimensions. We extend the multi-harmonic model in two dimensions to a high-order and present a new class of steady-state solutions of the bubble motion. The growth rate of the bubble is expressed by a continuous family of two free parameters. The critical point in the family of solutions is identified as a saddle point and is chosen as the physically significant solution. We also present the multi-harmonic model in the cylindrical geometry and find the steady-state solution of the axisymmetric bubble. Validity and limitation of the model are also discussed.
Keywords: Rayleigh-Taylor instability, multi-harmonic model, bubble, steady-state solution
MSC numbers: Primary 76E17, 76E30
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