Related papers: Particle trajectories in linearized irrotational s…

We study stationary capillary-gravity waves in a two-dimensional body of water that rests above a flat ocean bed and below vacuum. This system is described by the Euler equations with a free surface. Our main result states that there exist…

In this paper we consider two-dimensional, stratified, steady water waves propagating over an impermeable flat bed and with a free surface. The motion is assumed to be driven by capillarity (that is, surface tension) on the surface and a…

Spiral wave solutions are found in linear and weakly nonlinear irrotational water wave equations. These unsteady spiral waves evolve from suitable initial conditions; they are not induced by external forcing. In the linear case, a long-time…

We consider the free boundary problem for a 3-dimensional, incompressible, irrotational liquid drop of nearly spherical shape with capillarity. We study the problem from the beginning, extending some classical results from the flat case…

We present explicit solutions for the ordinary differential equations system describing the motion of the particles beneath small-amplitude capillary-gravity waves which propagate on the surface of an irrotational water flow with a flat…

We present a theoretical and numerical study on the motion of isotropic helicoids in complex flows. These are particles whose motion is invariant under rotations but not under mirror reflections of the particle. This is the simplest, yet…

Effective field theory descriptions of surface waves on flowing fluids have tended to assume that the flow is irrotational, but this assumption is often impractical due to boundary layer friction and flow recirculation. Here we develop an…

We study traveling wave solutions of an equation for surface waves of moderate amplitude arising as a shallow water approximation of the Euler equations for inviscid, incompressible and homogenous fluids. We obtain solitary waves of…

We analyse the angular dynamics of a neutrally buoyant nearly spherical particle immersed in a steady general linear flow. The hydrodynamic torque acting on the particle is obtained by means of a reciprocal theorem, regular perturbation…

The magnetohydrodynamic equations system for heavy fluid over an arbitrary surface in shallow water approximation is studied in the present paper. It is shown that simple wave solutions exist only for underlying surfaces that are slopes of…

We describe traveling waves in a basic model for three-dimensional water-wave dynamics in the weakly nonlinear long-wave regime. Small solutions that are periodic in the direction of translation (or orthogonal to it) form an…

In the context of fluid flows, the coupled Ostrovsky equations arise when two distinct linear long wave modes have nearly coincident phase speeds in the presence of background rotation. In this paper, nonlinear waves in a stratified fluid…

The identification of cells and particles based on their transport properties in microfluidic devices is crucial for numerous applications in biology and medicine. Neutrally buoyant particles transported in microfluidic channels, migrate…

The behavior of a non-spherical particle in a viscous, plane channel flow is studied by means of a combination of analytical technique and geometrical reasoning. An efficient implementation of Lamb's general solution is adopted, allowing…

The dynamics of non-spherical rigid particles immersed in an axisymmetric random flow is studied analytically. The motion of the particles is described by Jeffery's equation; the random flow is Gaussian and has short correlation time.The…

In the linear approximation we study long wave scattering on an axially symmetric flow in a shallow water basin with a drain in the center. This classical problem can be considered as a model of wave scattering on a rotating black hole. For…

We show that in the linear approximation there are three classes of reflectionless wave propagation on a surface of shallow water in the channel with spatially varying depth, width, and current speed. Two of these classes have been…

We investigate both experimentally and theoretically the traffic of particles flowing in microfluidic obstacle networks. We show that the traffic dynamics is a non-linear process: the particle current does not scale with the particle…

We investigate the dynamics of a point-like active particle suspended in fluid flow through a straight channel. For this particle-fluid system, we derive a constant of motion for a general unidirectional fluid flow, and apply it to an…

The Euler's equations describe the motion of inviscid fluid. In the case of shallow water, when a perturbative asymtotic expansion of the Euler's equations is taken (to a certain order of smallness of the scale parameters), relations to…