相关论文: Dispersion equation for water waves with vorticity…

We consider the two-dimensional problem for steady water waves with vorticity on water of finite depth. While neglecting the effects of surface tension we construct connected families of large amplitude periodic waves approaching the…

In this paper, we establish the existence of Stokes waves with piecewise smooth vorticity in a two-dimensional, infinitely deep fluid domain. These waves represent traveling water waves propagating over sheared currents in a semi-infinite…

The existence of periodic waves propagating downstream on the surface of a two-dimensional infinitely deep water under gravity is established for a general class of vorticities. When reformulated as an elliptic boundary value problem in a…

We consider the gravity-capillary water waves equations of a 2D fluid with constant vorticity. By employing variational methods we prove the bifurcation of periodic traveling water waves -- which are steady in a moving frame -- for {\it…

For the problem describing steady, gravity waves with vorticity on a two-dimensional, unidirectional flow of finite depth the following results are obtained. (i) Bounds for the free-surface profile and for Bernoulli's constant. (ii) If only…

This paper presents a comprehensive analysis of two-dimensional water waves characterized by a significant adverse constant vorticity over flows without stagnation points. Surprisingly, we discover qualitative distinctions between this…

Periodic travelling waves at the free surface of an incompressible inviscid fluid in two dimensions under gravity are numerically computed for an arbitrary vorticity distribution. The fluid domain over one period is conformally mapped from…

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…

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…

We consider Stokes water waves on the vorticity flow in a two-dimensional channel of finite depth. In the paper "V.Kozlov, On first subharmonic bifurcations in a branch of Stokes waves, JDE, 2024," it was proved existence of subharmonic…

We consider traveling waves on a surface of an ideal fluid of finite depth. The equation describing Stokes waves in conformal variables formulation are referred to as the Babenko equation. We use a Newton-Conjugate-Gradient method to…

The two-dimensional free-boundary problem describing steady gravity waves with vorticity on water of finite depth is considered. It is proved that no small-amplitude waves are supported by a horizontal shear flow whose free surface is still…

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…

The two-dimensional free-boundary problem describing steady gravity waves with vorticity on water of finite depth is considered. Bounds for stream functions as well as free-surface profiles and the total head are obtained under the…

We study two-crested traveling Stokes waves on the surface of an ideal fluid with infinite depth. Following Chen and Saffman (1980), we refer to these waves as class $\mathrm{II}$ Stokes waves. The class $\mathrm{II}$ waves are found from…

The problem for two-dimensional steady gravity driven water waves with vorticity is investigated. Using a multidimensional bifurcation argument, we prove the existence of small-amplitude periodic steady waves with an arbitrary number of…

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…

In this article we apply local bifurcation theory to prove the existence of small-amplitude steady periodic water waves, which propagate over a flat bed with a specified fixed mean-depth, and where the underlying flow has a discontinuous…

In this study, a new set of fifth-order Stokes wave solutions, incorporating the effects of a linear shear current, is derived by utilizing the perturbation method originally proposed for pure waves that was recently published. The present…

We study steady axisymmetric water waves with general vorticity and swirl, subject to the influence of surface tension. This can be formulated as an elliptic free boundary problem in terms of Stokes' stream function. A change of variables…