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The flow structures beneath waves have received significant attention from both theoretical and numerical perspectives. Most studies on this topic assume a flat bottom, leading to questions about the effects of variable bottom topography.…

Fluid Dynamics · Physics 2025-01-30 L. G. Martins , M. V. Flamarion , R. Ribeiro-Jr

We study surface gravity waves for viscous fluid flows governed by Darcy's law. The free boundary is acted upon by an external pressure posited to be in traveling wave form with a periodic profile. It has been proven that for any given…

Analysis of PDEs · Mathematics 2023-12-13 John Brownfield , Huy Q. Nguyen

This paper investigates solitary water waves propagating along the surface of a two-dimensional dielectric fluid with constant vorticity in the presence of an external electric field. We formulate the system as a nonlinear free boundary…

Analysis of PDEs · Mathematics 2026-04-28 Tingting Feng , Yong Zhang , Zhitao Zhang

In this paper we develop an existence theory for small amplitude, steady, two-dimensional water waves in the presence of wind in the air above. The presence of the wind is modeled by a Kelvin--Helmholtz type discontinuity across the…

Analysis of PDEs · Mathematics 2012-11-15 Samuel Walsh , Oliver Bühler , Jalal Shatah

This paper considers two-dimensional stably stratified steady periodic gravity water waves with surface profiles monotonic between crests and troughs. We provide sufficient conditions under which such waves are necessarily symmetric. This…

Mathematical Physics · Physics 2009-03-06 Samuel Walsh

We report experimental measurements of inertial waves generated by an oscillating cylinder in a rotating fluid. The two-dimensional wave takes place in a stationary cross-shaped wavepacket. Velocity and vorticity fields in a vertical plane…

Fluid Dynamics · Physics 2015-03-13 Pierre-Philippe Cortet , Cyril Lamriben , Frederic Moisy

Internal gravity waves play a primary role in geophysical fluids: they contribute significantly to mixing in the ocean and they redistribute energy and momentum in the middle atmosphere. Until recently, most studies were focused on plane…

Fluid Dynamics · Physics 2021-02-10 Thierry Dauxois , Sylvain Joubaud , Philippe Odier , Antoine Venaille

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

Variable-coefficient Korteweg - de Vries equation is applied to describe the interfacial wave transformation in two-layer fluid of variable depth. The soliton dynamics in this fluid is studied. The solitary wave breaks in two transient…

Atmospheric and Oceanic Physics · Physics 2012-10-08 I. Didenkulova , T. Talipova , E. Pelinovsky , O. Kurkina , A. Rodin , A. Pankratov , A. Naumov , A. Giniyatullin

Spiral waves arise in many biological, chemical, and physiological systems. The kinematical model can be used to describe the motion of the spiral arms approximated as curves in the plane. For this model, there appeared some results in the…

Dynamical Systems · Mathematics 2007-05-23 Chu-Pin Lo , Nedialko S. Nedialkov , Juan-Ming Yuan

Solitary-like surface waves that originate from the spatio-temporal evolution of falling liquid films have been the subject of theoretical and experimental research due to their unique properties that are not readily observed in the…

Fluid Dynamics · Physics 2023-01-10 Ivan S. Maksymov , Andrey Pototsky

Following a recent demonstration of stable trapping of floating particles by stationary (monochromatic) structured water waves [Nature 638, 394 (2025)], we report dynamic water-wave tweezers that enable controllable transport of trapped…

We study experimentally the onset of Faraday waves near the endwalls of rectangular vessel containing two stably-stratified fluid layers, subject to horizontal oscillations. These subharmonic waves (SWs) are excited, because the horizontal…

Fluid Dynamics · Physics 2025-01-01 Linfeng Piao , Anne Juel

We study wave-current interactions in two-dimensional water flows of constant vorticity over a flat bed. For large-amplitude periodic traveling waves that propagate at the water surface in the same direction as the underlying current…

Analysis of PDEs · Mathematics 2018-11-27 Adrian Constantin , Walter Strauss , Eugen Varvaruca

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

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 describe the effect of vibration on a confined volume of fluid which is density stratified due to its compressibility. We show that internal gravity-acoustic waves can be parametrically destabilized by the vibration. The resulting…

Fluid Dynamics · Physics 2009-10-27 Kausik S. Das , Stephen W. Morris , A. Bhattacharyay

We prove the nonexistence of two-dimensional solitary gravity water waves with subcritical wave speeds and an arbitrary distribution of vorticity. This is a longstanding open problem, and even in the irrotational case there are only partial…

Analysis of PDEs · Mathematics 2021-09-22 Vladimir Kozlov , Evgeniy Lokharu , Miles H. Wheeler

Coupled mixed convective and stratified systems are common in natural flows. To study experimentally the associated dynamics, we use a singular property of water: its non-linear equation of state is characterised by a maximum density close…

Fluid Dynamics · Physics 2020-11-10 Pierre Léard , Benjamin Favier , Patrice Le Gal , Michael Le Bars

In this paper a rotating two-fluid model for the propagation of internal waves is introduced. The model can be derived from a rotating-fluid problem by including gravity effects or from a nonrotating one by adding rotational forces in the…

Analysis of PDEs · Mathematics 2019-02-27 A. Durán