Work

Symmetric Water Waves with Surface Tension: Traveling Wave Behavior and Maximal Horizontal Velocity

Year: 2025

Type: article

Abstract: We study spatially periodic solutions to the two-dimensional water wave problem with surface tension. Assuming symmetry of the wave profile and of the horizontal velocity component at the free surface, we show that the solution necessarily corresponds to a traveling wave. This result relies on maximum principles for subharmonic functions and the structural properties of the governing equations. As a further consequence, in the case of positive constant vorticity, we establish that the maximum of the horizontal velocity remains invariant in time.

Source: Water Waves

DOI: 10.1007/s42286-025-00125-6

Author: Andrei Stan

Institutions: Babeș-Bolyai University, Tiberiu Popoviciu Institute of Numerical Analysis

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: $3,490

Funder: European Commission