Related papers: Gravity water flows with discontinuous vorticity a…
Special features of surface gravity waves in deep fluid flow with constant vertical shear of velocity is studied. It is found that the mean flow velocity shear leads to non-trivial modification of surface gravity wave modes dispersive…
"Consider the [turbidity] current as ... a river" R. A. Bagnold (1962); the foundation of contemporary deep marine sedimentology. Gravity currents, such as sediment-laden turbidity currents, are ubiquitous natural flows that are driven by a…
This paper considers two-dimensional steady solitary waves with constant vorticity propagating under the influence of gravity over an impermeable flat bed. Unlike in previous works on solitary waves, we allow for both internal stagnation…
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.…
In this paper, we consider capillary-gravity waves propagating on the interface separating two fluids of finite depth and constant density. The flow in each layer is assumed to be incompressible and of constant vorticity. We prove the…
This paper considers two-dimensional stably stratified steady periodic gravity water waves with surface profiles monotonic between crests and troughs. We provide sufficient conditions under which such waves are necessarily symmetric. This…
The existence of scalar fields can be probed by observations of stochastic gravitational waves. Scalar fields mediate attractive forces, usually stronger than gravity, on the length scales shorter than their Compton wavelengths, which can…
The standard analytical approach for studying gravity free-surface waves generated by a moving body often relies upon a linearization of the physical geometry, where the body is considered asymptotically small in one or several of its…
We consider one-dimensional model of the interaction between surface and the internal gravity water waves. The internal wave is modeled by its basic form: a non-dispersive field with a horizontal current that is uniform over all depth,…
Analytic global bifurcation theory is used to construct a large variety of families of steady periodic two-dimensional gravity water waves with real-analytic vorticity distributions, propagating in an incompressible fluid. The waves that…
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…
The flow of viscous fluids is considered as the aggregation of the motion of fluid particles when the fluid is conceived to be made up by an infinite number of particles. As an alternative of this conventional model, fluid motion could be…
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…
We construct three-dimensional families of small-amplitude gravity-driven rotational steady water waves on finite depth. The solutions contain counter-currents and multiple crests in each minimal period. Each such wave generically is a…
In this paper we develop an existence theory for small amplitude, steady, two-dimensional water waves in the presence of wind in the air above. The presence of the wind is modeled by a Kelvin--Helmholtz type discontinuity across the…
We prove real analyticity of all the streamlines, including the free surface, of a steady stratified flow of water over a flat bed in the absence of stagnation points, with a H\"older continuous Bernoulli function and a H\"older…
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…
For two-dimensional steady pure-gravity water waves with a unidirectional flow of constant favourable vorticity, we prove an explicit bound on the amplitude of the wave, which decays to zero as the vorticity tends to infinity. Notably, our…
Two dimensional flows on fixed smooth surfaces have been studied in the point of view of vorticity dynamics. Firstly, the related deformation theory including kinematics and kinetics is developed. Secondly, some primary relations in…
The paper deals with the 2D gravity-capillary water waves equations in their Hamiltonian formulation, addressing the question of the nonlinear interaction of a plane wave with its reflection off a vertical wall. The main result is the…