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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…
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…
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 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…
While several articles have been written on water waves on flows with constant vorticity, little is known about the extent to which a nonconstant vorticity affects the flow structure, such as the appearance of stagnation points. In order to…
Flow structures beneath a moving disturbance along a water free surface in the weakly nonlinear weakly dispersive regime in a sheared channel with finite depth and constant vorticity are investigated. We compute the exact two branches of…
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…
We provide high-order approximations to periodic travelling wave profiles and to the velocity field and the pressure beneath the waves, in flows with constant vorticity over a flat bed.
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…
Propagation of surface waves on a background shear flow with constant vorticity is studied and compared against the case when the background flow is uniform in depth. For a shear flow with the linear vertical profile, the dispersion…
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…
While several articles have been written on Electrohydrodynamics (EHD) flows or flows with constant vorticity separately, little is known about the extent to which the combined effects of EHD and constant vorticity affect the flow. This…
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…
The two-dimensional free-boundary problem describing steady gravity waves with vorticity on water of finite depth is considered. Under the assumption that the vorticity is a negative constant whose absolute value is sufficiently large, we…
In this paper we examine the flow generated by coupled surface and internal small-amplitude water waves in a two-fluid layer model, where we take the upper layer to be rotational (constant vorticity) and the lower layer to be irrotational.…
Direct numerical simulations are conducted to study the receptivity and transition mechanisms in a solitary wave boundary layer developing over randomly organized wave-like bottom topography. The boundary layer flow shows a selective…
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 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…
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…
We investigate the existence of solitary gravity waves traversing a two-dimensional body of water that is bounded below by a flat impenetrable ocean bed and above by a free surface of constant pressure. Our main interest is constructing…