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The present study describes, first, an efficient algorithm for computing capillary-gravity solitary waves solutions of the irrotational Euler equations with a free surface and, second, provides numerical evidences of the existence of an…

Fluid Dynamics · Physics 2020-02-20 Didier Clamond , Denys Dutykh , Angel Duran

In this paper, we investigate the spectral stability of periodic traveling waves in the two dimensional gravity-capillary water wave problem. We derive a stability criterion based on an index function, whose sign determines the spectral…

Analysis of PDEs · Mathematics 2026-02-10 Changzhen Sun , Erik Wahlén

We investigate theoretically and experimentally the capillary-gravity waves created by a small object moving steadily at the water-air interface along a circular trajectory. It is well established that, for straight uniform motion, no…

Classical Physics · Physics 2009-11-13 Alexei Chepelianskii , Frédéric Chevy , Elie Raphael

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

In this paper we construct periodic capillarity-gravity water waves with a piecewise constant vorticity distribution. They describe water waves traveling on superposed linearly sheared currents that have different vorticities. This is…

Analysis of PDEs · Mathematics 2013-02-25 Calin Iulian Martin , Bogdan--Vasile Matioc

In this paper, we examine the formation of small capillary waves (parasitic ripples) on the surface of steep steadily-travelling gravity waves. Previously, authors have developed ad-hoc analytical procedures for describing the formation of…

Fluid Dynamics · Physics 2021-07-28 Josh Shelton , Paul Milewski , Philippe H. Trinh

Processes of propagation and interaction of nonlinear gravity-capillary waves on the free surface of a deep non-conducting liquid with high dielectric constant under the action of a tangential electric field are numerically simulated. The…

Fluid Dynamics · Physics 2018-10-10 Evgeny A. Kochurin , Nikolay M. Zubarev

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

When traditional linearised theory is used to study gravity-capillary waves produced by flow past an obstruction, the geometry of the object is assumed to be small in one or several of its dimensions. In order to preserve the nonlinear…

Mathematical Physics · Physics 2015-10-16 Philippe H. Trinh , S. Jonathan Chapman

In this paper we construct small amplitude periodic internal waves traveling at the boundary region between two rotational and homogeneous fluids with different densities. Within a period, the waves we obtain have the property that the…

Analysis of PDEs · Mathematics 2012-02-15 Anca-Voichita Matioc

In geophysical environments, wave motions that are shaped by the action of gravity and global rotation bear the name of gravito-inertial waves. We present a geometrical description of gravito-inertial surface waves, which are low-frequency…

Analysis of PDEs · Mathematics 2026-04-21 Yves Colin de Verdière , Jérémie Vidal

We consider the gravity-capillary water waves equations of a 2D fluid with constant vorticity. By employing variational methods we prove the bifurcation of periodic traveling water waves -- which are steady in a moving frame -- for {\it…

Analysis of PDEs · Mathematics 2025-09-12 T. Barbieri , M. Berti , A. Maspero , M. Mazzucchelli

We are interested in the system of gravity water waves equations without surface tension. Our purpose is to study the optimal regularity thresholds for the initial conditions. In terms of Sobolev embeddings, the initial surfaces we consider…

Analysis of PDEs · Mathematics 2014-04-17 Thomas Alazard , Nicolas Burq , Claude Zuily

We present an existence and stability theory for gravity-capillary solitary waves with constant vorticity on the surface of a body of water of finite depth. Exploiting a rotational version of the classical variational principle, we prove…

Analysis of PDEs · Mathematics 2015-09-25 M. D. Groves , E. Wahlén

The dynamics of solitary gravity-capillary water waves propagating on the surface of a three-dimensional fluid domain is studied numerically. In order to accurately compute complex time dependent solutions, we simplify the full potential…

Fluid Dynamics · Physics 2015-06-05 Zhan Wang , Paul A Milewski

We study theoretically the capillary-gravity waves created at the water-air interface by an external surface pressure distribution symmetrical about a point and moving at constant velocity along a linear trajectory. Within the framework of…

Fluid Dynamics · Physics 2012-12-07 Michael Benzaquen , Frédéric Chevy , Elie Raphaël

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 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

We study the existence of traveling wave solutions to a unidirectional shallow water model which incorporates the full linear dispersion relation for both gravitational and capillary restoring forces. Using functional analytic techniques,…

Analysis of PDEs · Mathematics 2018-07-31 Mathew A. Johnson , J. Douglas Wright

The Sommerfeld boundary conditions, applied to an asymptotically weak gravitational field, are shown to imply that the 1/r part of the curvature tensor of a space-time, satisfying the Einstein equations, is of type null in the Petrov…

General Relativity and Quantum Cosmology · Physics 2016-04-13 Andrzej Trautman