2021/07/24 by Ryan Creedon, Bernard Deconinck, Olga Trichtchenko · 2 citations
Earth and Planetary Sciences · Mathematics · Physics and Astronomy · #Amplitude #Classical mechanics #Coastal and Marine Dynamics #Compressibility #Computation #Conservative vector field #Euler equations #Euler's formula #Gravity wave #Inviscid flow #Linearization #Mathematical analysis #Mathematics #Mechanics #Nonlinear system #Ocean Waves and Remote Sensing #Oceanographic and Atmospheric Processes #Optics #Perturbation (astronomy) #Physics #Wave propagation #math.AP #physics.flu-dyn
paper · pdf · doi:10.1017/jfm.2021.1119
published in Journal of Fluid Mechanics 937 (Cambridge University Press) · 29 pages, 13 figures
arxiv created 2021/07/24 · openalex publication_date 2022/02/28 · arxiv updated 2022/03/14 · openalex created_date 2025/10/10 · openalex updated_date 2026/08/05
Euler's equations govern the behavior 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. Using a nonlocal formulation of Euler's equations developed by Ablowitz et al. (2006), 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 to excellent agreement.