Multiple eigenmodes of the Rayleigh-Taylor instability observed for a fluid interface with smoothly varying density

C. X. Yu, C. Xue, J. Liu, X. Y. Hu, Y. Y. Liu, W. H. Ye, L. F. Wang, J. F. Wu, and Z. F. Fan
Phys. Rev. E 97, 013102 – Published 4 January 2018
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Abstract

In this article, multiple eigen-systems including linear growth rates and eigen-functions have been discovered for the Rayleigh-Taylor instability (RTI) by numerically solving the Sturm-Liouville eigen-value problem in the case of two-dimensional plane geometry. The system called the first mode has the maximal linear growth rate and is just extensively studied in literature. Higher modes have smaller eigen-values, but possess multi-peak eigen-functions which bring on multiple pairs of vortices in the vorticity field. A general fitting expression for the first four eigen-modes is presented. Direct numerical simulations show that high modes lead to appearances of multi-layered spike-bubble pairs, and lots of secondary spikes and bubbles are also generated due to the interactions between internal spikes and bubbles. The present work has potential applications in many research and engineering areas, e.g., in reducing the RTI growth during capsule implosions in inertial confinement fusion.

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  • Received 4 May 2017
  • Revised 24 November 2017

DOI:https://doi.org/10.1103/PhysRevE.97.013102

©2018 American Physical Society

Physics Subject Headings (PhySH)

Fluid Dynamics

Authors & Affiliations

C. X. Yu1, C. Xue1, J. Liu1,2, X. Y. Hu1, Y. Y. Liu1, W. H. Ye1, L. F. Wang1, J. F. Wu1, and Z. F. Fan1,*

  • 1Institute of Applied Physics and Computational Mathematics, Beijing 100088, China
  • 2Center for Applied Physics and Technology, Peking University, Beijing 100871, China

  • *fan_zhengfeng@iapcm.ac.cn

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Vol. 97, Iss. 1 — January 2018

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