Nonlinear oscillations in three-armed tubes

Alexander Duncan Davidson Craik, K Hirata

Research output: Contribution to journalArticlepeer-review

8 Citations (Scopus)

Abstract

We consider nonlinear gravitational oscillations of inviscid liquid in arrangements of three tubes joined at their bases, for which the dynamical system is four-dimensional and conservative. Though the problem of two joined tubes was solved in 1738, that of three tubes appears to have remained unstudied. We consider both weakly-nonlinear theory, which gives rise to coupled amplitude evolution equations; and also full numerical solutions. In this way, an understanding is reached of the strengths and limitations of the weakly-nonlinear approximation. Both the weakly-nonlinear approximation and the full system display amplitude modulations on a slow timescale; but only the full system captures a narrow region of chaos. (C) 2002 tditions scientifiques et medicales Elsevier SAS. All rights reserved.

Original languageEnglish
Pages (from-to)3-26
Number of pages24
JournalEuropean Journal of Mechanics - B/Fluids
Volume22
DOIs
Publication statusPublished - Jan 2003

Keywords

  • FORCED SURFACE-WAVES
  • FARADAY RESONANCE
  • EXCITATION
  • DYNAMICS

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