相关论文: On the streamlines and particle paths of gravitati…

Steady linear gravity waves of small amplitude travelling on a current of constant vorticity are found. For negative vorticity we show the appearance of internal waves and vortices, wherein the particle trajectories are not any more closed…

In this paper we present a characterization of the symmetric rotational periodic gravity water waves of finite depth and without stagnation points in terms of the underlying flow. Namely, we show that such a wave is symmetric and has a…

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 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…

A new type of steady steep two-dimensional irrotational symmetric periodic gravity waves on inviscid incompressible fluid of infinite depth is revealed. We demonstrate that these waves have sharper crests in comparison with the Stokes waves…

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 the particle trajectories in an irrotational shallow water flow over a flat bed as periodic waves propagate on the water's free surface. Within the linear water wave theory, we show that there are no closed orbits for the…

We determine the phase portrait of a Hamiltonian system of equations describing the motion of the particles in linear deep-water waves. The particles experience in each period a forward drift which decreases with greater depth.

In order to obtain quite precise information about the shape of the particle paths below small-amplitude gravity waves travelling on irrotational deep water, analytic solutions of the nonlinear differential equation system describing the…

In this article we consider irrotational gravity water waves with finite bottom. Our goal is two-fold. First, we represent the equations in holomorphic coordinates and discuss the local well-posedness of the problem in this context. Second,…

We study the effect of surface gravity waves on the motion of inertial particles in an incompressible fluid. Using the multiple-scale technique, we perform an analytical calculation which allows us to predict the dynamics of such particles;…

We establish the existence of small-amplitude uni- and bimodal steady periodic gravity waves with an affine vorticity distribution, using a bifurcation argument that differs slightly from earlier theory. The solutions describe waves with…

The problem for two-dimensional steady water waves with vorticity is considered. Using methods of spatial dynamics, we reduce the problem to a finite dimensional Hamiltonian system. As an application, we prove the existence of non-symmetric…

A novel mathematical nonlinear theory of surface gravity waves in deep water is presented, in which analytical analysis of the classical nonlinear equations of fluid dynamics is performed under less restrictive assumptions than those…

We study small-amplitude steady water waves with multiple critical layers. Those are rotational two-dimensional gravity-waves propagating over a perfect fluid of finite depth. It is found that arbitrarily many critical layers with cat's-eye…

The evolution of surface gravity waves is driven by nonlinear interactions that trigger an energy cascade similarly to the one observed in hydrodynamic turbulence. This process, known as wave turbulence, has been found to display anomalous…

The dynamics of pseudo-classical spinning particles in spacetime of gravitational plane waves of general polarization and harmonic profile is studied. The resulting equations of motion are solved exactly and the results are compared with…

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.…

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.

Intuitively, crest speeds of water waves are assumed to match their phase velocities. However, this is generally not the case for natural waves within unsteady wave groups. This motivates our study, which presents new insights into the…