Work

Stokes waves in rotational flows: internal stagnation and overhanging profiles

Year: 2025

Type: article

Abstract: Periodic travelling waves at the free surface of an incompressible inviscid fluid in two dimensions under gravity are numerically computed for an arbitrary vorticity distribution. The fluid domain over one period is conformally mapped from a fixed rectangular one, where the governing equations along with the conformal mapping are solved using a finite-difference scheme. This approach accommodates internal stagnation points, critical layers and overhanging profiles, thereby overcoming limitations of previous studies. The numerical method is validated through comparisons with known solutions for zero and constant vorticity. Novel solutions are presented for affine vorticity functions and a two-layer constant-vorticity scenario.

Source: Journal of Fluid Mechanics

DOI: 10.1017/jfm.2025.10373

Authors: Alex George Doak, Vera Mikyoung Hur, Jean-Marc Vanden-Broeck

Institutions: University of Bath, University of Illinois Urbana-Champaign, University College London

Language: English

Topic: Nonlinear Waves and Solitons

Subfield: Statistical and Nonlinear Physics

Field: Physics and Astronomy

Domain: Physical Sciences

Open Access status: hybrid

Estimated APC paid: $3,550

Funders: National Science Foundation, Engineering and Physical Sciences Research Council, Division of Mathematical Sciences