A new application of Crapper's exact solution to waves in constant\n vorticity flows

2020/03/02 by Vera Mikyoung Hur, Jean‐Marc Vanden‐Broeck, Hur, Vera Mikyoung +1 · 1 citation
Earth and Planetary Sciences · #Coastal and Marine Dynamics #FOS: Physical sciences #Fluid Dynamics (physics.flu-dyn) #Ocean Waves and Remote Sensing #Oceanographic and Atmospheric Processes

paper · pdf · doi:10.48550/arxiv.2003.00950

openalex publication_date 2020/03/02 · openalex created_date 2022/09/28 · openalex updated_date 2026/07/28

Abstract

In 1957 Crapper found an exact solution for capillary waves propagating at\nthe surface of an irrotational flow of infinite depth. Here we provide\nconclusive analytical and numerical evidence that a Crapper wave makes the\nprofile of a periodic traveling wave propagating, in the absence of the effects\nof gravity and surface tension, in a constant vorticity flow. This is achieved\nby constructing a Stokes expansion up to the third order in a small amplitude\nparameter and by numerically computing large amplitude waves.\n

Cited by

• Gravity water waves over constant vorticity flows: From laminar flows to touching waves

Related

• Existence of capillary-gravity waves that are perturbations of Crapper's waves
• Existence of gravity-capillary Crapper waves with concentrated vorticity
• Stokes waves in a constant vorticity flow
• Stokes waves with constant vorticity: I. numerical computation
• Overhanging and touching waves in constant vorticity flows