Related papers: On the vorticity threshold for steady water waves
The flow structures beneath waves have received significant attention from both theoretical and numerical perspectives. Most studies on this topic assume a flat bottom, leading to questions about the effects of variable bottom topography.…
Steady surface waves in a two-dimensional channel are considered. We study bifurcations, which occur on a branch of Stokes water waves starting from a uniform stream solution. Two types of bifurcations are considered: bifurcations in the…
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…
A classical and central problem in the theory of water waves is to classify parameter regimes for which non-trivial solitary waves exist. In the two-dimensional, irrotational, pure gravity case, the Froude number $Fr$ (a non-dimensional…
The Stokes wave problem in a constant vorticity flow is formulated via a conformal mapping as a modified Babenko equation. The associated linearized operator is self-adjoint, whereby efficiently solved by the Newton-conjugate gradient…
The Stokes wave problem in a constant vorticity flow is formulated, by virtue of conformal mapping techniques, as a nonlinear pseudodifferential equation, involving the periodic Hilbert transform, which becomes the Babenko equation in the…
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…
In a recent research on degenerate points of steady axisymmetric gravity flows with general vorticity, it has been shown that the possible asymptotics near any stagnation point must be the "Stokes corner", the "horizontal cusp", or the…
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 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…
We study the modulational stability problem for the traveling periodic waves (called Stokes waves) in an infinitely deep fluid by using pseudo-differential operators in conformal variables. We derive the criteria and the normal forms for…
A Stokes wave is a traveling free-surface periodic water wave that is constant in the direction transverse to the direction of propagation. In 1981 McLean discovered via numerical methods that Stokes waves are unstable with respect to…
We investigate steady symmetric gravity water waves on finite depth. For non-positive vorticity it is shown that the particles display a mean forward drift, and for a class of waves we prove that the size of this drift is strictly…
We introduce a numerical strategy to study the evolution of 2D water waves in the presence of a plunging jet. The free-surface Navier-Stokes solution is obtained with a finite but small viscosity. We observe the formation of a surface…
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…
We consider classical steady water waves with a free surface, a flat bottom and constant vorticity $\gamma$. In the adverse case $\gamma>0$ we prove that there is an absolute upper bound on the amplitude, independent of the physical…
We consider stratified steady water waves in a two dimensional channel. Our main subject is spectral properties of the Frechet derivatives of steady water Stokes waves. One of main results is the absence of subharmonic water waves in a…
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 $f$…
We prove that for a large class of vorticity functions the crest of a corresponding travelling water wave is necessarily a point of maximal horizontal velocity. We also show that for waves with nonpositive vorticity the pressure in the flow…
We give a quite simple approach how to prove the absence of loops in bifurcation branches of water waves in rotational case with arbitrary vorticity distribution. The supporting flow may contain stagnation points and critical layers and…