Stability of waves on fluid of infinite depth with constant vorticity

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Abstract

The stability of periodic travelling waves on fluid of infinite depth is examined in the presence of a constant background shear field. The effects of gravity and surface tension are ignored. The base waves are described by an exact solution that was discovered recently by Hur and Wheeler (J. Fluid Mech., vol. 896, 2020). Linear growth rates are calculated using both an asymptotic approach valid for small-amplitude waves and a numerical approach based on a collocation method. Both superharmonic and subharmonic perturbations are considered. Instability is shown to occur for any non-zero amplitude wave.

Original languageEnglish
Article numberA46
JournalJournal of Fluid Mechanics
Volume936
Early online date17 Feb 2022
DOIs
Publication statusPublished - 10 Apr 2022

Keywords

  • waves/free-surface flows

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