High-frequency instabilities of Stokes waves. (25th April 2022)

• Record Type: Journal Article
• Authors: Creedon, Ryan P.; Deconinck, Bernard; Trichtchenko, Olga
• Is Part Of: Journal of fluid mechanics. Volume 937(2022)
• Publication Date: 2022-04-25
• Subjects: surface gravity waves; Fluid mechanics -- Periodicals; 532.005
• DOI: 10.1017/jfm.2021.1119
• Languages: English
• ISSNs: 0022-1120

Abstract

Abstract: Abstract : Euler's equations govern the behaviour of gravity waves on the surface of an incompressible, inviscid and irrotational fluid of arbitrary depth. We investigate the spectral stability of sufficiently small-amplitude, one-dimensional Stokes waves, i.e. periodic gravity waves of permanent form and constant velocity, in both finite and infinite depth. We develop a perturbation method to describe the first few high-frequency instabilities away from the origin, present in the spectrum of the linearization about the small-amplitude Stokes waves. Asymptotic and numerical computations of these instabilities are compared for the first time, with excellent agreement.