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We study propagation of high-frequency wave packets along a large-scale background wave which evolves according to dispersionless hydrodynamic equations for two variables (fluid density and flow velocity). Influence of the wave packet on…

Pattern Formation and Solitons · Physics 2023-06-08 D. V. Shaykin , A. M. Kamchatnov

A one-dimensional long-wave model of an unsteady three-layer flow of a stratified fluid under a lid is proposed, taking into account turbulent mixing in the intermediate layer. In the Boussinesq approximation, the equations of motion are…

Fluid Dynamics · Physics 2021-12-10 Alexander Chesnokov , Sergey Gavrilyuk , Valery Liapidevskii

The majority of coastal flows are characterized by turbulence, rendering the application of shallow water equations an inadequate approach for their accurate description. This paper presents a theory for characterizing accelerated coastal…

Fluid Dynamics · Physics 2024-09-19 Arno Roland Ndengna Ngatcha

We establish that solitary stationary waves in three dimensional viscous incompressible fluids are a generic phenomenon and that every such solution is a vanishing wave-speed limit along a one parameter family of traveling waves. The…

Analysis of PDEs · Mathematics 2023-09-13 Noah Stevenson , Ian Tice

We consider a layer of an inviscid fluid with free surface which is subject to vertical high-frequency vibrations. We derive three asymptotic systems of equations that describe slowly evolving (in comparison with the vibration frequency)…

Fluid Dynamics · Physics 2017-11-22 Konstantin Ilin

We report laboratory experiments on surface waves generated in a uniform fluid layer whose bottom undergoes a sudden upward motion. Simultaneous measurements of the free-surface deformation and the fluid velocity field are focused on the…

This article is concerned with an oceanographic model describing the asymptotic behaviour of a rapidly rotating and incompressible fluid with an inhomogeneous rotation vector; the motion takes place in a thin layer. We first exhibit a…

Analysis of PDEs · Mathematics 2012-07-03 Anne-Laure Dalibard , Laure Saint-Raymond

This paper aims at investigating the existence of localized stationary waves in the shallow subsurface whose constitutive behaviour is governed by the hyperbolic model, implying non-polynomial nonlinearity and strain-dependent shear…

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

In this paper we focus on the water waves problem for uneven bottoms on a two-dimensionnal domain. Starting from the symmetric Boussinesq systems derived in [Chazel, Influence of topography on long water waves, 2007], we recover the…

Analysis of PDEs · Mathematics 2009-02-02 Florent Chazel

By numerical simulation of exact equations of motion (in terms of conformal variables) for planar non-stationary potential flows of an ideal fluid with a free surface over a strongly non-uniform bottom profile, the effect of nonlinear…

Fluid Dynamics · Physics 2026-02-10 Victor P. Ruban

We consider the two-dimensional water-wave problem with a general non-zero vorticity field in a fluid volume with a flat bed and a free surface. The nonlinear equations of motion for the chosen surface and volume variables are expressed…

Analysis of PDEs · Mathematics 2024-09-04 Delia Ionescu-Kruse , Rossen Ivanov

We study here the water-waves problem for uneven bottoms in a highly nonlinear regime where the small amplitude assumption of the Korteweg-de Vries (KdV) equation is enforced. It is known, that for such regimes, a generalization of the KdV…

Analysis of PDEs · Mathematics 2009-01-22 Samer Israwi

We adapt the microcanonical framework of equilibrium statistical mechanics to predict the statistics of short waves in inhomogeneous moving media. For steady inhomogeneities and background flow, we compute the wave spectrum at any location…

Fluid Dynamics · Physics 2026-02-18 Alexandre Tlili , Basile Gallet

We investigate here the interactions of waves governed by a Boussinesq system with a partially immersed body allowed to move freely in the vertical direction. We show that the whole system of equations can be reduced to a transmission…

Analysis of PDEs · Mathematics 2021-02-16 Geoffrey Beck , David Lannes

Inertia-gravity waves are scattered by background flows as a result of Doppler shift by a non-uniform velocity. In the WKB regime, the scattering process reduces to a diffusion in spectral space. Other inhomogeneities the waves encounter,…

Fluid Dynamics · Physics 2025-03-19 Michael R. Cox , Hossein A. Kafiabad , Jacques Vanneste

We analyze a homogenization limit for the linear wave equation of second order. The spatial operator is assumed to be of divergence form with an oscillatory coefficient matrix $a^\varepsilon$ that is periodic with characteristic length…

Analysis of PDEs · Mathematics 2014-01-31 Tomas Dohnal , Agnes Lamacz , Ben Schweizer

In this paper, we want to understand the Proudman resonance. It is a resonant respond in shallow waters of a water body on a traveling atmospheric disturbance when the speed of the disturbance is close to the typical water wave velocity. We…

Analysis of PDEs · Mathematics 2016-09-28 Benjamin Melinand

We consider propagation of high-frequency wave packets along a smooth evolving background flow whose evolution is described by a simple-wave type of solutions of hydrodynamic equations. In geometrical optics approximation, the motion of the…

Pattern Formation and Solitons · Physics 2021-06-16 A. M. Kamchatnov , D. V. Shaykin

A series of laboratory experiments has been carried out in a thermally driven rotating annulus to study the onset of baroclinic instability, using horizontal and uniformly sloping bottom topographies. Different wave flow regimes have been…

Fluid Dynamics · Physics 2015-06-17 Miklos Vincze , Uwe Harlander , Thomas von Larcher , Christoph Egbers