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The dynamical response of edge waves under the influence of self-gravity is examined in an idealized two-dimensional model of a proto-stellar disc, characterized in steady state as a rotating vertically infinite cylinder of fluid with…

Solar and Stellar Astrophysics · Physics 2016-04-27 Ron Yellin-Bergovoy , Eyal Heifetz , Orkan M. Umurhan

Frequently encountered in nature, internal solitary waves in stratified fluids are well-observed and well-studied from the experimental, the theoretical, and the numerical perspective. From the mathematical point of view, these waves are…

Analysis of PDEs · Mathematics 2014-11-03 Andreas Klaiber

We prove that symmetric, doubly periodic, capillary-gravity water waves in finite depth bifurcating from non-uniform non-stagnant shear flows are necessarily two-dimensional to leading order. This is in stark contrast to the case of uniform…

Analysis of PDEs · Mathematics 2025-04-30 Douglas Svensson Seth , Kristoffer Varholm , Erik Wahlén , Jörg Weber

The structure of boundary currents formed from intermediately dense water introduced into a rotating, stably stratified, two-layer environment is investigated in a series of laboratory experiments, performed for Froude numbers ranging from…

Fluid Dynamics · Physics 2009-10-30 P. A. Yecko , S. P. Meacham

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

We study two-dimensional periodic capillary-gravity water waves propagating at the free surface of water in a flow with arbitrary, prescribed vorticity over a flat bed. Using conformal mappings and a new Babenko-type reformulation of…

Analysis of PDEs · Mathematics 2023-06-14 Erik Wahlén , Jörg Weber

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

A nonlinear Schr\"odinger equation for the envelope of two-dimensional gravity-capillary waves propagating at the free surface of a vertically sheared current of constant vorticity is derived. In this paper we extend to gravity-capillary…

Fluid Dynamics · Physics 2018-10-17 H. -C. Hsu , C. Kharif , M. Abid , Y. -Y. Chen

The problem of a travelling wave over an arbitrary quasi-flat bathymetry in a semi infinite channel is studied in the shallow-water formulation. It is shown how the streamfunction can be cast, in the vicinity of an elliptic equilibrium for…

Dynamical Systems · Mathematics 2018-02-12 Alessandro Fortunati

This paper studies the classical water wave problem with vorticity described by the Euler equations with a free surface under the influence of gravity over a flat bottom. Based on fundamental work \cite{ConstantinStrauss}, we first obtain…

Analysis of PDEs · Mathematics 2022-07-12 Guowei Dai , Yong Zhang

Vibrations can dynamically stabilize otherwise unstable liquid interfaces and produce new dynamic equilibria, called vibro-equilibria. Typically, the vibrations are homogeneous in the liquid and the liquid interface remains approximately…

Fluid Dynamics · Physics 2022-05-04 Benjamin Apffel , Christian Wilkinson , Emmanuel Fort

The dynamics of phase-separated interfaces shape the behavior of both passive and active condensates. While surface tension in equilibrium systems minimizes interface length, non-equilibrium fluxes can destabilize flat or constantly curved…

Soft Condensed Matter · Physics 2025-05-27 Florian Raßhofer , Simon Bauer , Alexander Ziepke , Ivan Maryshev , Erwin Frey

Slow flows of an ideal compressible fluid (gas) in the gravity field in the presence of two isentropic layers are considered, with a small difference of specific entropy between them. Assuming irrotational flows in each layer [that is ${\bf…

Atmospheric and Oceanic Physics · Physics 2010-12-30 V. P. Ruban

Internal waves describe the (linear) response of an incompressible stably stratified fluid to small perturbations. The inclination of their group velocity with respect to the vertical is completely determined by their frequency. Therefore…

Analysis of PDEs · Mathematics 2021-02-24 Roberta Bianchini , Anne-Laure Dalibard , Laure Saint-Raymond

We report the observation of gravity-capillary waves on a torus of fluid. By means of an original technique, a stable torus is achieved by depositing water on a superhydrophobic groove with a shallow wedge-shaped channel running along its…

Pattern Formation and Solitons · Physics 2021-10-13 Filip Novkoski , Eric Falcon , Chi-Tuong Pham

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 consider the free boundary problem for a 3-dimensional, incompressible, irrotational liquid drop of nearly spherical shape with capillarity. We study the problem from the beginning, extending some classical results from the flat case…

Analysis of PDEs · Mathematics 2026-03-31 Pietro Baldi , Vesa Julin , Domenico Angelo La Manna

The present research is devoted to the problem of stability of the fluid flow moving in a channel with flexible walls and interacting with the walls, which are subject to traveling waves. Experimental data shows that the energy of the…

Fluid Dynamics · Physics 2021-01-01 Marianna A. Shubov , Madeline M. Edwards

Pattern formation of a thin layer of vertically agitated wet granular matter is investigated experimentally. Due to the strong cohesion arising from the capillary bridges formed between adjacent particles, agitated wet granular matter…

Soft Condensed Matter · Physics 2013-01-24 Kai Huang Lorenz Butzhammer , Ingo Rehberg

We consider the gravity water waves system with a periodic one-dimensional interface in infinite depth and we establish the existence and the linear stability of small amplitude, quasi-periodic in time, traveling waves. This provides the…

Analysis of PDEs · Mathematics 2021-11-01 Roberto Feola , Filippo Giuliani