Related papers: A geometric approach to generalized Stokes conject…
The two-dimensional free-boundary problem of steady periodic waves with vorticity is considered for water of finite depth. We investigate how flows with small-amplitude Stokes waves on the free surface bifurcate from a horizontal parallel…
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…
The original investigation of Lamb (1932, {\S}349) for the effect of viscosity on monochromatic surface waves is extended to account for second-order Stokes surface waves on deep water in the presence of surface tension. This extension is…
The direct detection of gravitational waves has provided new opportunities for studying the universe, but also new challenges, such as the detection and characterization of stochastic gravitational-wave backgrounds at different…
Euler's equations govern the behavior of gravity waves on the surface of an incompressible, inviscid, and irrotational fluid of arbitrary depth. We investigate the spectral stability of sufficiently small-amplitude, one-dimensional Stokes…
Babenko's equation describes traveling water waves in holomorphic coordinates. It has been used in the past to obtain properties of Stokes waves with smooth profiles analytically and numerically. We show in the deep-water limit that…
We provide a new method to recover the profile of Stokes waves, and more generally of waves with smooth vorticity, from measurements of the horizontal velocity component on a vertical axis of symmetry of the wave surface. Although we…
In this paper, we study the nonlinear modulational instability of two-dimensional hydroelastic Stokes waves in infinite depth. We first justify a focusing cubic nonlinear Schr\"odinger (NLS) approximation result for 2D deep hydroelastic…
The coupled motion is investigated for a mechanical system consisting of water and a body freely floating in it. Water occupies either a half-space or a layer of constant depth into which an infinitely long surface-piercing cylinder is…
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…
We develop a rigorous asymptotic derivation for two mathematical models of water waves that capture the full nonlinearity of the Euler equations up to quadratic and cubic interactions, respectively. Specifically, letting epsilon denote an…
In this article, we mainly investigate the properties of vertical velocity v for two dimensional steady water waves over a flat bed. Firstly we prove the existence of the inflection point for each streamline, then we find the behavior of v…
Two-dimensional potential flow of the ideal incompressible fluid with free surface and infinite depth can be described by a conformal map of the fluid domain into the complex lower half-plane. Stokes wave is the fully nonlinear gravity wave…
In 1880, Stokes famously demonstrated that the singularity that occurs at the crest of the steepest possible water wave in infinite depth must correspond to a corner of $120^\circ$. Here, the complex velocity scales like $f^{1/3}$ where $f$…
Two-dimensional free-surface potential flows of an ideal fluid over a strongly inhomogeneous bottom are investigated with the help of conformal mappings. Weakly-nonlinear and exact nonlinear equations of motion are derived by the…
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…
In this paper we investigate the dispersive properties of the solutions of the two dimensional water-waves system. First we prove Strichartz type estimates with loss of derivatives at the same low level of regularity we were able to…
We propose a Stokes expansion ansatz for finite-depth standing water waves in two dimensions and devise a recursive algorithm to compute the expansion coefficients. We implement the algorithm on a supercomputer using arbitrary-precision…
As mentioned by Schwartz (1974) and Cokelet (1977), it was failed to gain convergent results of limiting Stokes' waves in extremely shallow water by means of perturbation methods even with the aid of extrapolation techniques such as…
In this paper we investigate the qualitative behaviour of the pressure function beneath an extreme Stokes wave over infinite depth. The presence of a stagnation point at the wave-crest of an extreme Stokes wave introduces a number of…