Related papers: A Priori Estimates for Two-Dimensional Water Waves…
Motivated by numerically modeling surface waves for inviscid Euler equations, we analyze linear models for damped water waves and establish decay properties for the energy for sufficiently regular initial configurations. Our findings give…
We consider the full irrotational water waves system with surface tension and no gravity in dimension two (the capillary waves system), and prove global regularity and modified scattering for suitably small and localized perturbations of a…
The equations for waves on the surface of an irrotational incompressible fluid are derived in the coordinates of the velocity potential/stream function. The low frequency shallow water approximation for these waves is derived for a varying…
We consider two-layers of immiscible liquids confined between an upper and a lower rigid plate. The dynamics of the free liquid-liquid interface is described for arbitrary amplitudes by a single evolution equation derived from the basic…
In this paper we discuss a theoretical model for the interfacial profiles of progressive non-linear waves which result from introducing a triangular obstacle, of finite height, attached to the bottom below the flow of a stratified, ideal,…
We perform the stability analysis for a free surface fluid current modeled as two finite layers of constant vorticity, under the action of gravity and absence of surface tension. In the same spirit as Taylor ["Effect of variation in density…
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…
Numerically computed with high accuracy are periodic traveling waves at the free surface of a two dimensional, infinitely deep, and constant vorticity flow of an incompressible inviscid fluid, under gravity, without the effects of surface…
Quasi-two-dimensional fluids can be generated by confining a fluid between two parallel walls with narrow separation. Such fluids exhibit an inhomogeneous structure perpendicular to the walls due to the loss of translational symmetry.…
By revisiting the century-old problem of water bridge, we demonstrate that it is in fact dynamic and comprises of two coaxial water currents that carry different charges and flow in opposite directions. This spontaneous separation is…
In the study of ocean wave impact on structures, one often uses Froude scaling since the dominant force is gravity. However the presence of trapped or entrained air in the water can significantly modify wave impacts. When air is entrained…
Nonlinear dynamics of the free surface of finite depth non-conducting fluid with high dielectric constant subjected to a strong horizontal electric field is considered. Using the conformal transformation of the region occupied by the fluid…
We show that the water waves system is locally wellposed in weighted Sobolev spaces which allow for interfaces with corners. No symmetry assumptions are required. These singular points are not rigid: if the initial interface exhibits a…
We construct small-amplitude periodic water waves with multiple critical layers. In addition to waves with arbitrarily many critical layers and a single crest in each period, two-dimensional sets of waves with several crests and troughs in…
Vertical convection is the fluid motion that is induced by the heating and cooling of two opposed vertical boundaries of a rectangular cavity (see e.g. Wang et al. 2021). We consider the linear stability of the steady two-dimensional flow…
Nonlinear initial-boundary value problem on deep-water gravity waves of finite amplitude is solved approximately (up to small terms of higher order) assuming that the waves are generated by an initial disturbance to the water and the…
This Note determines the unsteady non-circulatory forces on an arbitrarily deforming panel with a Holder-continuous porosity distribution. An analytical expression for the non-circulatory pressure distribution is presented and evaluated for…
A fluid in contact with a flat structureless wall constitutes the simplest interface system, but the fluid-wall interfacial tension cannot be trivially and even unequivocally determined due to the ambiguity in identifying the precise…
We present a construction of a (d+2)-dimensional Ricci-flat metric corresponding to a (d+1)-dimensional relativistic fluid, representing holographically the hydrodynamic regime of a (putative) dual theory. We show how to obtain the metric…
We consider a control system describing the interaction of water waves with a partially immersed rigid body constraint to move only in the vertical direction. The fluid is modeled by the shallow water equations. The control signal is a…