A note on the Stokes phenomenon in flow under an elastic sheet

Christopher J. Lustri*, Lyndon Koens, Ravindra Pethiyagoda

*Corresponding author for this work

Research output: Contribution to journalArticle

Abstract

The Stokes phenomenon is a class of asymptotic behaviour that was first discovered by Stokes in his study of the Airy function. It has since been shown that the Stokes phenomenon plays a significant role in the behaviour of surface waves on flows past submerged obstacles. A detailed review of recent research in this area is presented, which outlines the role that the Stokes phenomenon plays in a wide range of free surface flow geometries. The problem of inviscid, irrotational, incompressible flow past a submerged step under a thin elastic sheet is then considered. It is shown that the method for computing this wave behaviour is extremely similar to previous work on computing the behaviour of capillary waves. Exponential asymptotics are used to show that free-surface waves appear on the surface of the flow, caused by singular fluid behaviour in the neighbourhood of the base and top of the step. The amplitude of these waves is computed and compared to numerical simulations, showing excellent agreements between the asymptotic theory and computational solutions. This article is part of the theme issue 'Stokes at 200 (part 2)'.

Original languageEnglish
Article number20190530
Pages (from-to)1-16
Number of pages16
JournalPhilosophical Transactions of the Royal Society A: Mathematical, Physical and Engineering Sciences
Volume378
Issue number2179
DOIs
Publication statusPublished - 4 Sep 2020

Keywords

  • free surface flow
  • elastic sheet
  • Stokes phenomenon

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