Related papers: Wave-current interaction on a free surface
Many vesicles have a spherical resting shape and exposure to fluid flows induces an exchange between sub-optical area and visible (systematic) deformation, while the total area is conserved. The dynamics which controls the exchange between…
We study here the propagation of long waves in the presence of vorticity. In the irrotational framework, the Green-Naghdi equations (also called Serre or fully nonlinear Boussinesq equations) are the standard model for the propagation of…
The Whitham equation was proposed as an alternate model equation for the simplified description of uni-directional wave motion at the surface of an inviscid fluid. As the Whitham equation incorporates the full linear dispersion relation of…
The Eulerian system of dynamic equations for the ideal fluid is closed but incomplete. The complete system of dynamic equations arises after appending Lin constraints which describe motion of fluid particles in a given velocity field. The…
A laminar flow of a thin layer of mud down an inclined plane under the action of gravity is considered. The instability of a film flow and the formation of finite amplitude waves are studied in the framework of both two-dimensional…
The propagation of surface water waves interacting with a current and an uneven bottom is studied. Such a situation is typical for ocean waves where the winds generate currents in the top layer of the ocean. The role of the bottom…
Vortical flows in shallow water interact with long surface waves by virtue of the nonlinear terms of the fluid equations. Analytical formulae are derived that quantify the spontaneous generation of such waves by unsteady vorticity as well…
The subject of moving curves (and surfaces) in three dimensional space (3-D) is a fascinating topic not only because it represents typical nonlinear dynamical systems in classical mechanics, but also finds important applications in a…
We review the theory of wave interaction in finite and infinite depth. Both of these strands of water-wave research begin with the deterministic governing equations for water waves, from which simplified equations can be derived to model…
Morphodynamic equations governing the behaviour of active nematic fluids on deformable curved surfaces are constructed in the large deformation limit. Emphasis is placed on the formulation of objective rates that account for normal…
The classical fluid dynamics boundary condition of no-slip suggests that variation in the wettability of a solid should not affect the flow of an adjacent liquid. However experiments and molecular dynamics simulations indicate that this is…
In this investigation we revisit the concept of "effective free surfaces" arising in the solution of the time-averaged fluid dynamics equations in the presence of free boundaries. This work is motivated by applications of the optimization…
We study the interaction of gravity waves on the surface of an infinitely deep ideal fluid. Starting from Zakharov's variational formulation for water waves we derive an expansion of the Hamiltonian to an arbitrary order, in a manner that…
The understanding of the spreading of liquids on solid surfaces is an important challenge for contemporary physics. Today, the motion of the contact line formed at the intersection of two immiscible fluids and a solid is still subject to…
The currents in the ocean have a serious impact on ocean dynamics, since they affect the transport of mass and thus the distribution of salinity, nutrients and pollutants. In many physically important situations the current depends…
New conditions for wave-wave interaction are considered. It is shown that using these conditions allows us to discover and describe new features of wave-wave interaction. Specifically, it is shown that an electromagnetic wave in a…
We study the free boundary evolution between two irrotational, incompressible and inviscid fluids in 2-D without surface tension. We prove local-existence in Sobolev spaces when, initially, the difference of the gradients of the pressure in…
In this paper we study the motion of an internal water wave and an internal wave in a porous medium. For these problems we establish that, if the free boundary and, in the case of the Euler equations, also the tangential velocity at the…
The dynamics of large eddies in the atmosphere and oceans is described by the surface quasi geostrophic equation, which is reminiscent of the Euler equations. Thermal fronts build up rapidly. Two different numerical methods combined with…
The description of free surface flows can often be simplified to thin film (or lubrication) equations, when the slopes of the liquid-gas interface are small. Here we present a long wavelength theory that remains fully quantitative for steep…