Related Experiment Video
Updated: Dec 12, 2025

Visualization of Flow Field Around a Vibrating Pipeline Within an Equilibrium Scour Hole
Published on: August 26, 2019
A note on the Stokes phenomenon in flow under an elastic sheet
Christopher J Lustri1, Lyndon Koens1, Ravindra Pethiyagoda2
1Department of Mathematics and Statistics, Macquarie University, 12 Wally's Walk, Sydney, New South Wales 2109, Australia.
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)'.
Related Concept Videos
Stokes' Law
The expression for the force on a solid spherical object in a fluid is called Stokes' law. Stokes' law is valid only...
Navier–Stokes Equations
Steady, Laminar Flow Between Parallel Plates
Couette Flow
Steady, Laminar Flow in Circular Tubes
Newtonian Fluid: Problem Solving
A velocity gradient forms within the fluid when a Newtonian fluid is placed between two parallel plates, with...

