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

Lustri, Christopher J; Koens, Lyndon; Pethiyagoda, Ravindra

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)'.

Citation

Lustri, C. J., Koens, L., & Pethiyagoda, R. (2020). A note on the Stokes phenomenon in flow under an elastic sheet: Stokes Phenomenon in flow under a sheet. Philosophical transactions. Series A, Mathematical, physical, and engineering sciences, 378(2179), Article 20190530. https://doi.org/10.1098/rsta.2019.0530

• Journal Article Type: Article
• Acceptance Date: May 12, 2020
• Online Publication Date: Aug 3, 2020
• Publication Date: Sep 4, 2020
• Deposit Date: Jan 25, 2022
• Publicly Available Date: Feb 16, 2022
• Journal: Philosophical Transactions of the Royal Society A: Mathematical, Physical and Engineering Sciences
• Print ISSN: 1364-503X
• Publisher: The Royal Society
• Peer Reviewed: Peer Reviewed
• Volume: 378
• Issue: 2179
• Article Number: 20190530
• DOI: https://doi.org/10.1098/rsta.2019.0530
• Public URL: https://hull-repository.worktribe.com/output/3916633