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Related papers: Steep sharp-crested gravity waves on deep water

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A fundamental question in the study of water waves is the existence and stability of solitary waves. Solitary waves have been proved to exist and have been studied in many interesting situations, and often arise from the balance of…

Analysis of PDEs · Mathematics 2019-09-10 Mihaela Ifrim , Daniel Tataru

Although internal gravity waves are generally recognized as an important mechanism to distribute energy through the atmosphere, their dynamics near the instability is only partially understood to date. Many types of instabilities, notably…

Fluid Dynamics · Physics 2023-10-02 Georg Sebastian Voelker , Mark Schlutow

We consider the two-dimensional deep gravity-capillary water waves with point vortices. We first formulate the question in the holomorphic coordinates. Then, we derive an a priori energy estimate for water waves, and show that the water…

Analysis of PDEs · Mathematics 2025-04-28 Lizhe Wan

We establish novel existence results of $3d$ gravity-capillary periodic traveling waves. In particular we prove the bifurcation of multiple, geometrically distinct truly $3d$ Stokes waves having the same momentum of any non-resonant $2d$…

Analysis of PDEs · Mathematics 2026-04-15 Tommaso Barbieri , Massimiliano Berti , Marco Mazzucchelli

Numerically computed with high accuracy are periodic traveling waves at the free surface of a two dimensional, infinitely deep, and constant vorticity flow of an incompressible inviscid fluid, under gravity, without the effects of surface…

Fluid Dynamics · Physics 2023-01-25 Sergey A. Dyachenko , Vera Mikyoung Hur , Denis A. Silantyev

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 investigate the existence of solitary gravity waves traversing a two-dimensional body of water that is bounded below by a flat impenetrable ocean bed and above by a free surface of constant pressure. Our main interest is constructing…

Analysis of PDEs · Mathematics 2021-03-02 Adelaide Akers , Samuel Walsh

We consider the spectra of the 2-dim gravity waves of finite depth linearized at a uniform monotonic shear flow $U(x_2)$, $x_2 \in (-h, 0)$, where the wave numbers $k$ of the horizontal variable $x_1$ is treated as a parameter. Our main…

Analysis of PDEs · Mathematics 2023-06-01 Xiao Liu , Chongchun Zeng

We revisit the classical but as yet unresolved problem of predicting the breaking onset of 2D and 3D irrotational gravity water waves. This study focuses on domains with flat bottom topography and conditions ranging from deep to…

Atmospheric and Oceanic Physics · Physics 2017-04-04 X. Barthelemy , M. L. Banner , W. L. Peirson , F. Fedele , M. Allis , F. Dias

We perform experiments to study the inverse cascade regime of gravity wave turbulence on the surface of a fluid. Surface waves are forced at an intermediate scale corresponding to the gravity-capillary wavelength. In response to this…

Fluid Dynamics · Physics 2011-10-27 Luc Deike , Claude Laroche , Eric Falcon

In this paper we consider two-dimensional, stratified, steady water waves propagating over an impermeable flat bed and with a free surface. The motion is assumed to be driven by capillarity (that is, surface tension) on the surface and a…

Analysis of PDEs · Mathematics 2009-11-10 Samuel Walsh

This is the second paper in a series of papers analyzing angled crested type water waves with surface tension. We consider the 2D capillary gravity water wave equation and assume that the fluid is inviscid, incompressible, irrotational and…

Analysis of PDEs · Mathematics 2020-12-25 Siddhant Agrawal

This paper is concerned with two-dimensional, steady, periodic water waves propagating at the free surface of water either in a flow of finite depth and constant vorticity over an impermeable flat bed or in an irrotational flow of great…

Analysis of PDEs · Mathematics 2014-04-25 Peter de Boeck

Observations show that maximally-steep breaking water wave crest speeds are much slower than expected. We report a wave-crest slowdown mechanism generic to unsteady propagating deep water wave groups. Our fully nonlinear computations show…

Atmospheric and Oceanic Physics · Physics 2015-06-16 Michael Banner , Xavier Barthelemy , Francesco Fedele , Michael Allis , Alvise Benetazzo , Frederic Dias , William Peirson

Stokes perturbative solution of the nonlinear (boundary value dependent) surface gravity wave problem is known to provide results of reasonable accuracy to engineers in estimating the phase speed and amplitudes of such nonlinear waves. The…

Fluid Dynamics · Physics 2016-02-10 Megan Davies , Amit K Chattopadhyay

Gerstner or trochoidal wave is the only known exact solution of the Euler equations for periodic surface gravity waves on deep water. In this Letter we utilize Zakharov's variational formulation of weakly nonlinear surface waves and,…

Fluid Dynamics · Physics 2019-03-29 Nail S. Ussembayev

It is suggested that gravity waves could, in several cases, be detected by means of already (or shortly to be) available technology, independently of current efforts of detection. The present is a follow-up on a recently suggested detection…

General Relativity and Quantum Cosmology · Physics 2009-10-22 Redouane Fakir

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…

Fluid Dynamics · Physics 2025-02-26 Alex Doak , Vera Mikyoung Hur , Jean-Marc Vanden-Broeck

This paper considers two-dimensional steady continuous stratified periodic water waves. Firstly, we prove that each streamline must be symmetric about the crest line when it is strictly monotonous between troughs and crests by exploiting…

Analysis of PDEs · Mathematics 2021-09-01 Fei Xu , Yong Zhang , Fengquan Li

We generalize the periodic Evans function approach recently used to study the spectral stability of Stokes wave and gravity-capillary (including Wilton ripples) in water of finite depth to study spectral stability of Stokes waves in water…

Analysis of PDEs · Mathematics 2021-09-28 Zhao Yang