English
Related papers

Related papers: Surface and internal gravity waves on a viscous li…

200 papers

This study analyzes steady periodic hydroelastic waves propagating on the water surface of finite depth beneath nonlinear elastic membranes. Unlike previous work \cite{BaldiT,BaldiT1,Toland,Toland1}, our formulation accommodates rotational…

Analysis of PDEs · Mathematics 2025-08-07 Yong Zhang

In the present note, we solved numerically the viscous vorticity equation of the initial-boundary value problem describing the classic Helmholtz phenomena of vortex interaction. In the leapfrogging of vortex pairs, we demonstrate the fact…

Fluid Dynamics · Physics 2018-07-24 F. Lam

A localised overpressure translating at a uniform speed greater than a critical value acts at the interface between two deep fluid layers with different densities. We analyse the resulting wave patterns using an initial-value problem…

Fluid Dynamics · Physics 2026-05-13 Vinod Kumar Kadari , Nikhil Yewale , Palas Kumar Farsoiya , Y. S. Mayya , Ratul Dasgupta

Internal waves propagate obliquely through a stratified fluid with an angle that is fixed with respect to gravity. Upon reflection on a sloping bed, striking phenomena are expected to occur close to the slope. We present here laboratory…

Pattern Formation and Solitons · Physics 2009-11-11 Louis Gostiaux , Thierry Dauxois , Henri Didelle , Joel Sommeria , Samuel Viboud

Internal gravity waves are an essential feature of stratified media, such as oceans and atmospheres. To investigate their dynamics, we perform simulations of the forced-dissipated kinetic equation describing the evolution of the energy…

Fluid Dynamics · Physics 2025-06-09 Vincent Labarre , Giorgio Krstulovic , Sergey Nazarenko

We introduce a numerical strategy to study the evolution of 2D water waves in the presence of a plunging jet. The free-surface Navier-Stokes solution is obtained with a finite but small viscosity. We observe the formation of a surface…

Fluid Dynamics · Physics 2024-05-01 Alan Riquier , Emmanuel Dormy

Theoretical results on water waves almost always start by assuming irrotationality of the flow in order to simplify the formulation. In this work, we investigate the well-foundedness of this hypothesis via numerical simulations of the…

Fluid Dynamics · Physics 2025-11-21 Alan Riquier , Emmanuel Dormy

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

We consider Euler's equations for free surface waves traveling on a body of density stratified water in the scenario when gravity and surface tension act as restoring forces. The flow is continuously stratified, and the water layer is…

Analysis of PDEs · Mathematics 2019-12-02 Joachim Escher , Patrik Knopf , Christina Lienstromberg , Bogdan-Vasile Matioc

We consider a two-dimensional, two-layer, incompressible, steady flow, with vorticity which is constant in each layer, in an infinite channel with rigid walls. The velocity is continuous across the interface, there is no surface tension or…

Analysis of PDEs · Mathematics 2023-10-18 Karsten Matthies , Jonathan Sewell , Miles H. Wheeler

The classical Kapitza instability of a gravity-driven falling film requires finite inertia to operate. We show that a surface-mode instability can arise in the complete absence of inertia when the film possesses a continuous viscosity…

Fluid Dynamics · Physics 2026-04-10 Shravya Gundavarapu , Darish Jeswin Dhas , Anubhab Roy

This paper concerns the construction of traveling wave solutions to the free boundary incompressible Navier-Stokes system. We study a single layer of viscous fluid in a strip-like domain that is bounded below by a flat rigid surface and…

Analysis of PDEs · Mathematics 2022-09-13 Junichi Koganemaru , Ian Tice

This paper studies periodic traveling gravity waves at the free surface of water in a flow of constant vorticity over a flat bed. Using conformal mappings the free-boundary problem is transformed into a quasilinear pseudodifferential…

Analysis of PDEs · Mathematics 2015-05-14 Adrian Constantin , Eugen Varvaruca

We consider the free boundary problem for a layer of compressible viscous barotropic fluid lying above a fixed rigid bottom and below the atmosphere of positive constant pressure. The fluid dynamics is governed by the compressible…

Analysis of PDEs · Mathematics 2024-11-01 Ting Sun , Yanjin Wang

Viscous flow past a finite flat plate moving in direction normal to itself is studied numerically.The plate moves with velocity $at^p$, where $p=0,0.5,1,2$. We present the evolution of vorticity profiles, streaklines and streamlines, and…

Fluid Dynamics · Physics 2015-06-19 Ling Xu , Monika Nitsche

A fundamental open problem in the theory of the multidimensional compressible Navier-Stokes equations is whether smooth solutions can develop singularities in finite time. For constant viscosity coefficients, recent remarkable results show…

Analysis of PDEs · Mathematics 2026-03-25 Gui-Qiang G. Chen , Lihui Liu , Shengguo Zhu

A detailed solution of an initial value problem of a vertically localized initial perturbation in rotating magnetized vertically stratified disk is presented. The appropriate linearized MHD equations are solved by employing the WKB…

Astrophysics · Physics 2009-01-07 Edward Liverts , Michael Mond

It is shown how to model weakly dissipative free-surface flows using the classical potential flow approach. The Helmholtz-Leray decomposition is applied to the linearized 3D Navier-Stokes equations. The governing equations are treated using…

Atmospheric and Oceanic Physics · Physics 2020-02-20 Denys Dutykh , Frederic Dias

We are concerned with a model describing the motion of two compressible, immiscible fluids with density-dependent viscosity in the whole $\mathbb R^3$. The phases of the flow may have different pressure and viscosity laws and are separated…

Analysis of PDEs · Mathematics 2025-10-14 Marcel Zodji

The viscosity of water induces a vorticity near the free surface boundary. The resulting rotational component of the fluid velocity vector greatly complicates the water wave system. Several approaches to close this system have been…

Fluid Dynamics · Physics 2020-06-16 D. Eeltink , A. Armaroli , M. Brunetti , J. Kasparian