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The Euler's equations describe the motion of inviscid fluid. In the case of shallow water, when a perturbative asymtotic expansion of the Euler's equations is taken (to a certain order of smallness of the scale parameters), relations to…

Exactly Solvable and Integrable Systems · Physics 2007-09-02 Rossen I. Ivanov

A two-dimensional water wave system is examined consisting of two discrete incompressible fluid domains separated by a free common interface. In a geophysical context this is a model of an internal wave, formed at a pycnocline or…

Fluid Dynamics · Physics 2018-11-09 Alan Compelli , Rossen Ivanov

We investigate the properties of small-amplitude inertial waves propagating in a differentially rotating incompressible fluid contained in a spherical shell. For cylindrical and shellular rotation profiles and in the inviscid limit,…

Solar and Stellar Astrophysics · Physics 2015-06-04 C. Baruteau , M. Rieutord

We investigate the occurrence of topologically protected waves in classical fluids confined on curved surfaces. Using a combination of topological band theory and real space analysis, we demonstrate the existence of a system-independent…

Soft Condensed Matter · Physics 2020-11-25 Richard Green , Jay Armas , Jan de Boer , Luca Giomi

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

By "surface waves" one means a special kind of waves that propagate at the interface between two different media. There exists a large variety of such waves, which are interesting on their own, and sometimes have also practical importance…

Classical Physics · Physics 2021-07-12 M. I. Dyakonov

A model for internal interfacial waves between two layers of fluid in the presence of current and variable bottom is studied in the flat-surface approximation. Fluids are assumed to be incompressible and inviscid. Another assumption is that…

Pattern Formation and Solitons · Physics 2025-07-08 Rossen Ivanov , Lyudmila Ivanova

Spiral wave solutions are found in linear and weakly nonlinear irrotational water wave equations. These unsteady spiral waves evolve from suitable initial conditions; they are not induced by external forcing. In the linear case, a long-time…

Fluid Dynamics · Physics 2025-10-27 Mark J. Ablowitz , Justin T. Cole , Sean D. Nixon

We consider the stability of periodic gravity free-surface water waves traveling downstream at a constant speed over a shear flow of finite depth. In case the free surface is flat, a sharp criterion of linear instability is established for…

Analysis of PDEs · Mathematics 2007-11-28 Vera Mikyoung Hur , Zhiwu Lin

In this paper, we consider a problem inspired by the real-world need to identify the topographical features of ocean basins. Specifically we consider the problem of estimating the bottom impermeable boundary to an inviscid, incompressible,…

Analysis of PDEs · Mathematics 2023-08-22 Vishal Vasan , Manisha , Didier Auroux

The far field asymptotic of internal waves is constructed for the case when a point source of mass moves in a layer of arbitrarily stratified fluid with slowly varying bottom. The solutions obtained describe the far field both near the wave…

Fluid Dynamics · Physics 2007-05-23 Vitaly V. Bulatov , Yuriy V. Vladimirov , Vasily A. Vakorin

Consider the two-dimensional inverse elastic wave scattering by an infinite rough surface with a Dirichlet boundary condition. A non-interative sampling technique is proposed for detecting the rough surface by taking elastic wave…

Analysis of PDEs · Mathematics 2020-12-15 Tielei Zhu , Jiaqing Yang

We investigate steady symmetric gravity water waves on finite depth. For non-positive vorticity it is shown that the particles display a mean forward drift, and for a class of waves we prove that the size of this drift is strictly…

Mathematical Physics · Physics 2007-12-05 Mats Ehrnstrom

The problem about a body in a three dimensional infinite channel is considered in the framework of the theory of linear water-waves. The body has a rough surface characterized by a small parameter $\epsilon>0$ while the distance of the body…

Spectral Theory · Mathematics 2012-01-11 G. Cardone , T. Durante , S. A. Nazarov

We develop a weakly nonlinear model to study the spatiotemporal manifestation and the dynamical behavior of surface waves in the presence of an underlying interfacial solitary wave in a two-layer fluid system. We show that interfacial…

Pattern Formation and Solitons · Physics 2019-07-29 Shixiao W. Jiang , Gregor Kovačič , Douglas Zhou

We study the waves at the interface between two thin horizontal layers of immiscible liquids subject to high-frequency tangential vibrations. Nonlinear governing equations are derived for the cases of two- and three-dimensional flows and…

Fluid Dynamics · Physics 2018-10-30 Anastasiya V. Dolmatova , Denis S. Goldobin , Tatyana P. Lyubimova

This paper presents the second-order perturbation theory of the Navier-Stokes equations for free surface flows, with the wave amplitude considered as the perturbation parameter. Gravity-capillary surface waves in incompressible viscous…

Fluid Dynamics · Physics 2023-03-28 Arash Ghahraman , Gyula Bene

We investigate the particle trajectories in an irrotational shallow water flow over a flat bed as periodic waves propagate on the water's free surface. Within the linear water wave theory, we show that there are no closed orbits for the…

Mathematical Physics · Physics 2015-05-28 Delia Ionescu-Kruse

Here we consider the problem of small oscillations of a rotating inviscid incompressible fluid. From a mathematical point of view, new exact solutions to the two-dimensional Poincar\'e-Sobolev equation in a class of domains including…

Fluid Dynamics · Physics 2016-10-24 S. D. Troitskaya

This is a study of two-dimensional steady periodic travelling waves on the surface of an infinitely deep irrotational ocean, when the top streamline is in contact with a membrane which has a nonlinear response to stretching and bending, and…

Analysis of PDEs · Mathematics 2008-05-06 Pietro Baldi , John F. Toland