Related papers: Capillary-Gravity Water Waves: Modified Flow Force…

This paper considers steady surface waves `riding' a Beltrami flow (a three-dimensional flow with parallel velocity and vorticity fields). It is demonstrated that the hydrodynamic problem can be formulated as two equations for two scalar…

The nonlinear theory of acoustic-gravity waves (AGWs) in the atmosphere is revisited with the effects of the Coriolis force. Previous theory in the literature [Phys. Scr. \textbf{90} (2015) 055001] is advanced. Starting from a set of fluid…

The problem of interest in this article are waves on a layer of finite depth governed by the Euler equations in the presence of gravity, surface tension, and vertical electric fields. Perturbation theory is used to identify canonical…

In the field of differential equations, particularly fluid dynamics, many researchers have shown an interest in the behavior of time periodic solutions. In this paper, we study isentropic gas flow in a bounded interval and apply a time…

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…

We consider a two-dimensional, pure capillary drop of nearly-circular shape, having constant vorticity. We write the Craig-Sulem equations on the unit circle, then on the flat torus. We show their Hamiltonian structure and we then observe…

In this work, we solve the Euler's equations for periodic waves travelling under a sheet of ice using a reformulation introduced in Ablowitz et al. (2006). These waves are referred to as flexural-gravity waves. We compare and contrast two…

By proving a weighted contraction estimate in uniformly local Sobolev spaces for the flow of gravity water waves, we show that this nonlocal system is in fact pseudo-local in the following sense: locally in time, the dynamic far away from a…

By dispersive models of fluid mechanics we are referring to the Euler-Lagrange equations for the constrained Hamilton action functional where the internal energy depends on high order derivatives of unknowns. The mass conservation law is…

The Buckley-Leverett equation for two phase flow in a porous medium is modified by including a dependence of capillary pressure on the rate of change of saturation. This model, due to Gray and Hassanizadeh, results in a nonlinear…

This paper considers two-dimensional stratified water waves propagating under the force of gravity over an impermeable flat bed and with a free surface. We prove the existence of a global continuum of classical solutions that are periodic…

This paper considers two-dimensional steady solitary waves with constant vorticity propagating under the influence of gravity over an impermeable flat bed. Unlike in previous works on solitary waves, we allow for both internal stagnation…

In a recent work [1] the authors studied the dynamics of the interface separating a vacuum from an inviscid incompressible fluid, subject to the self-gravitational force and neglecting surface tension, in two space dimensions. The fluid is…

We are interested in the system of gravity water waves equations without surface tension. Our purpose is to study the optimal regularity thresholds for the initial conditions. In terms of Sobolev embeddings, the initial surfaces we consider…

When a solid body floats at the interface of a vibrating liquid bath, the relative motion between the object and interface generates outwardly propagating surface waves. It has recently been demonstrated that millimetric objects with…

A reduced dynamical model is derived which describes the interaction of weak inertia-gravity waves with nonlinear vortical motion in the context of rotating shallow-water flow. The formal scaling assumptions are (i) that there is a…

In this paper, we examine the formation of small capillary waves (parasitic ripples) on the surface of steep steadily-travelling gravity waves. Previously, authors have developed ad-hoc analytical procedures for describing the formation of…

Contact of a fluid with a solid or an elastic wall is investigated. The wall exerts molecular forces on the fluid which is locally strongly nonhomogeneous. The problem is approached with a fluid energy of the second gradient form and a wall…

The dynamical equations describing the evolution of a self-gravitating fluid can be rewritten in the form of a Schrodinger equation coupled to a Poisson equation determining the gravitational potential. This wave-mechanical representation…

We consider the nonlinear problem of steady gravity-driven waves on the free surface of a two-dimensional flow of an incompressible fluid (say, water). The flow is assumed to be unidirectional of finite depth and the water motion is…