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We study theoretically the capillary-gravity waves created at the water-air interface by a small two-dimensional perturbation when a depth-dependent current is initially present in the fluid. Assuming linear wave theory, we derive a general…

Soft Condensed Matter · Physics 2015-05-28 Michael Benzaquen , Elie Raphael

This paper considers two-dimensional steady solitary waves with constant vorticity propagating under the influence of gravity over an impermeable flat bed. Unlike in previous works on solitary waves, we allow for both internal stagnation…

Analysis of PDEs · Mathematics 2021-10-12 Susanna V. Haziot , Miles. H. Wheeler

This paper studies periodic traveling gravity waves at the free surface of water in a flow of constant vorticity over a flat bed. Using conformal mappings the free-boundary problem is transformed into a quasilinear pseudodifferential…

Analysis of PDEs · Mathematics 2015-05-14 Adrian Constantin , Eugen Varvaruca

We study stationary capillary-gravity waves in a two-dimensional body of water that rests above a flat ocean bed and below vacuum. This system is described by the Euler equations with a free surface. Our main result states that there exist…

Analysis of PDEs · Mathematics 2020-06-18 Mats Ehrnström , Samuel Walsh , Chongchun Zeng

We consider two-dimensional steady periodic gravity waves on water of finite depth with a prescribed but arbitrary vorticity distribution. The water surface is allowed to be overhanging and no assumptions regarding the absence of stagnation…

Analysis of PDEs · Mathematics 2024-08-27 Erik Wahlén , Jörg Weber

In this experimental study, we investigate the interaction of gravity-capillary solitary waves generated by two surface pressure sources moving side by side at constant speed. The nonlinear response of a water surface to a single source…

Fluid Dynamics · Physics 2017-02-13 Naeem Masnadi , James H. Duncan

In this paper, we study the three-dimensional gravity-capillary water wave problem involving an irrotational, perfect fluid with gravity and surface tension. We focus on steady waves propagating uniformly in one direction. Assuming constant…

Analysis of PDEs · Mathematics 2025-09-09 Changfeng Gui , Shanfa Lai , Yong Liu , Juncheng Wei , Wen Yang

We study the onset of the wave-resistance due to the generation of capillary-gravity waves by a partially immersed moving object in the case where the object is hold at a fixed immersion depth. We show that, in this case, the wave…

Soft Condensed Matter · Physics 2009-11-07 F. Chevy , E. Raphael

We present a numerical study of spatially quasi-periodic gravity-capillary waves of finite depth in both the initial value problem and traveling wave settings. We adopt a quasi-periodic conformal mapping formulation of the Euler equations,…

Fluid Dynamics · Physics 2023-05-09 Jon Wilkening , Xinyu Zhao

In this paper we present a characterization of the symmetric rotational periodic gravity water waves of finite depth and without stagnation points in terms of the underlying flow. Namely, we show that such a wave is symmetric and has a…

Analysis of PDEs · Mathematics 2014-01-24 Bogdan-Vasile Matioc

In this article we consider irrotational gravity water waves with finite bottom. Our goal is two-fold. First, we represent the equations in holomorphic coordinates and discuss the local well-posedness of the problem in this context. Second,…

Analysis of PDEs · Mathematics 2016-07-12 Benjamin Harrop-Griffiths , Mihaela Ifrim , Daniel Tataru

By a bifurcation argument we prove that the capillary-gravity Whitham equation features asymmetrical periodic travelling wave solution of arbitrarily small amplitude. Such waves exist only in the weak surface tension regime…

Analysis of PDEs · Mathematics 2024-01-23 Ola Mæhlen , Douglas Svensson Seth

We consider the two-dimensional capillary water waves with nonzero constant vorticity in infinite depth. We first derive the Babenko equation that describes the profile of the solitary wave. When the velocity $c$ is close to a critical…

Analysis of PDEs · Mathematics 2024-08-08 James Rowan , Lizhe Wan

We study periodic, two-dimensional, gravity-capillary traveling wave solutions to a viscous shallow water system posed on an inclined plane. While thinking of the Reynolds and Bond numbers as fixed and finite, we vary the speed of the…

Analysis of PDEs · Mathematics 2024-11-22 Noah Stevenson

The last decade has seen a significant increase in the number of studies devoted to wave turbulence. Many deal with water waves, as modeling of ocean waves has historically motivated the development of weak turbulence theory, which adresses…

Fluid Dynamics · Physics 2021-07-09 Eric Falcon , Nicolas Mordant

In this paper we consider the steady water wave problem for waves that possess a merely $L_r-$integrable vorticity, with $r\in(1,\infty)$ being arbitrary. We first establish the equivalence of the three formulations--the velocity…

Analysis of PDEs · Mathematics 2013-11-28 Calin Iulian Martin , Bogdan-Vasile Matioc

We study theoretically the capillary-gravity waves created at the water-air interface by a small object during a sudden accelerated or decelerated rectilinear motion. We analyze the wave resistance corresponding to the transient wave…

Fluid Dynamics · Physics 2015-05-18 Fabien Closa , Alexei Chepelianskii , Elie Raphael

The classical irrotational capillary-gravity water wave problem described by the Euler equations with a nonlinear free surface boundary condition over a flat bed is considered. A modified flow force has been defined and a new formulation of…

Analysis of PDEs · Mathematics 2020-10-20 Biswajit Basu , Calin Iulian Martin

In this Letter we consider long capillary-gravity waves described by a fully nonlinear weakly dispersive model. First, using the phase space analysis methods we describe all possible types of localized travelling waves. Then, we especially…

Classical Physics · Physics 2020-02-20 Dimitrios Mitsotakis , Denys Dutykh , Aydar Assylbekuly , Dauren Zhakebayev

We study two-dimensional periodic capillary-gravity water waves propagating at the free surface of water in a flow with arbitrary, prescribed vorticity over a flat bed. Using conformal mappings and a new Babenko-type reformulation of…

Analysis of PDEs · Mathematics 2023-06-14 Erik Wahlén , Jörg Weber