Periodic Traveling Water Waves with Isobaric Streamlines
نویسندگان
چکیده
It is shown that in water of finite depth, there are no periodic traveling waves with the property that the pressure in the underlying fluid flow is constant along streamlines. In the case of infinite depth, there is only one such solution, which is due to Gerstner.
منابع مشابه
Regularity of Traveling Free Surface Water Waves with Vorticity
Abstract. We prove real analyticity of all the streamlines, including the free surface, of a gravityor capillary-gravity-driven steady flow of water over a flat bed, with a Hölder continuous vorticity function, provided that the propagating speed of the wave on the free surface exceeds the horizontal fluid velocity throughout the flow. Furthermore, if the vorticity possesses some Gevrey regular...
متن کاملAnalyticity of the Streamlines for Periodic Travelling Free Surface Capillary-Gravity Water Waves with Vorticity
For capillary-gravity water waves with vorticity we prove that all streamlines beneath the surface are real analytic.
متن کاملTraveling Waves for the Whitham Equation
The existence of traveling waves for the original Whitham equation is investigated. This equation combines a generic nonlinear quadratic term with the exact linear dispersion relation of surface water waves of finite depth. It is found that there exist small-amplitude periodic traveling waves with sub-critical speeds. As the period of these traveling waves tends to infinity, their velocities ap...
متن کاملGlobal Well-Posedness and Non-linear Stability of Periodic Traveling Waves for a Schrödinger-Benjamin-Ono System
The objective of this paper is two-fold: firstly, we develop a local and global (in time) wellposedness theory for a system describing the motion of two fluids with different densities under capillary-gravity waves in a deep water flow (namely, a Schrödinger-Benjamin-Ono system) for lowregularity initial data in both periodic and continuous cases; secondly, a family of new periodic traveling wa...
متن کاملRegularity for steady periodic capillary water waves with vorticity.
In the following, we prove new regularity results for two-dimensional steady periodic capillary water waves with vorticity, in the absence of stagnation points. Firstly, we prove that if the vorticity function has a Hölder-continuous first derivative, then the free surface is a smooth curve and the streamlines beneath the surface will be real analytic. Furthermore, once we assume that the vor...
متن کامل