相关论文: Approximations of steady periodic water waves in f…

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…

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…

Waves with constant vorticity and electrohydrodynamics flows are two topics in fluid dynamics that have attracted much attention from scientists for both the mathematical challenge and their industrial applications. The coupling of electric…

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…

While some works have investigated the particle trajectories and stagnation points beneath solitary waves with constant vorticity, little is known about the pressure beneath such waves. To address this gap, we investigate numerically the…

We investigate the particle trajectories in a constant vorticity shallow water flow over a flat bed as periodic waves propagate on the water's free surface. Within the framework of small amplitude waves, we find the solutions of the…

We numerically investigate the flow structure of periodic steady water waves of fixed relative mass flux propagating on rotational flows with piece-wise constant vorticity. We show that for wave solutions along the global bifurcation…

We modify the approach of Burton and Toland [Comm. Pure Appl. Math. (2011)] to show the existence of periodic surface water waves with vorticity in order that it becomes suited to a stability analysis. This is achieved by enlarging the…

We prove that the streamlines and the profile of periodic gravity water waves traveling over a flat bed with wavespeed which exceeds the horizontal velocity of all fluid particles are real-analytic graphs if the vorticity function is merely…

We investigate within the framework of linear theory the behaviour of the total (hydrodynamic) pressure and of the dynamic pressure in a regular wave train which propagates at the surface of water with a flat bed in a flow with constant…

We propose higher-order approximation formulae recovering the surface elevation from the pressure at the bed and the background shear flow for small-amplitude Stokes and solitary water waves. They offer improvements over the pressure…

We consider three-dimensional geophysical flows at arbitrary latitude and with constant vorticity beneath a wave train and above a flat bed in the $\beta$-plane approximation with centripetal forces. We consider the $f$-plane approximation…

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.…

Governing equations for two-dimensional inviscid free-surface flows with constant vorticity over arbitrary non-uniform bottom profile are presented in exact and compact form using conformal variables. An efficient and very accurate…

We derive equations relating the pressure at a flat seabed and the free-surface profile for steady gravity waves with constant vorticity. The resulting set of nonlinear equations enables the recovery of the free surface from pressure…

This paper studies the structural implications of constant vorticity for steady three-dimensional internal water waves. It is known that in many physical regimes, water waves beneath vacuum that have constant vorticity are necessarily two…

The motion of an interface separating two fluids under the effect of electric fields is a subject that has picked the attention of researchers from different areas. While there is an abundance of studies investigating the free surface wave…

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 wave-current interactions in two-dimensional water flows of constant vorticity over a flat bed. For large-amplitude periodic traveling waves that propagate at the water surface in the same direction as the underlying current…

We construct small-amplitude steady periodic gravity water waves arising as the free surface of water flows that contain stagnation points and possess a discontinuous distribution of vorticity in the sense that the flows consist of two…