Related papers: Internal waves in aquariums with characteristic co…
Following theoretical and experimental work of Maas et al we consider a linearized model for internal waves in effectively two dimensional aquaria. We provide a precise description of singular profiles appearing in long time wave evolution…
We study a model of internal waves under periodic forcing in an effectively 2-dimensional aquarium. When the underlying classical dynamics has sufficiently irrational rotation number, we prove that the solution to the internal waves…
We study a model of internal waves in an effectively 2D aquarium under periodic forcing. In the case when the underlying classical dynamics has sufficiently irrational rotation number, we prove that the energy of the internal waves remains…
We experimentally investigate internal coastal Kelvin waves in a two-layer fluid system on a rotating table. Waves in our system propagate in the prograde direction and are exponentially localized near the boundary. Our experiments verify…
The channeling of spin waves with domain walls in ultrathin ferromagnetic films is demonstrated theoretically and through micromagnetics simulations. It is shown that propagating excitations localized to the wall, which appear in the…
A novel canonical Hamiltonian formalism is developed for long internal waves in a rotating environment. This includes the effects of background vorticity and shear on the waves. By restricting consideration to flows in hydrostatic balance,…
In this paper we prove the propagation of singularities for the wave equation on differential forms with natural (i.e. relative or absolute) boundary conditions on Lorentzian manifolds with corners, which in particular includes a…
We study the propagation in three dimensions of internal waves using ray tracing methods and traditional dynamical systems theory. The wave propagation on a cone that generalizes the Saint Andrew's cross justifies the introduction of an…
We show that the water waves system is locally wellposed in weighted Sobolev spaces which allow for interfaces with corners. No symmetry assumptions are required. These singular points are not rigid: if the initial interface exhibits a…
Internal waves are an important feature of stratified fluids, both in oceanic and lake basins and in other settings. Many works have been published on the generic feature of internal wave trapping onto planar wave attractors and…
We consider the conditions under which solitary waves can exist in elongated clouds of Bose-Einstein condensed atoms. General expressions are derived for the velocity, characteristic size, and spatial profile of solitary waves, and the low-…
For the wave equation associated to the Laplacian on a compact manifold with boundary with a conic metric (with respect to which the boundary is metrically a point) the propagation of singularities through the boundary is analyzed. Under…
Oceanic internal waves often have curvilinear fronts and propagate over various currents. We present the first study of long weakly-nonlinear internal ring waves in a three-layer fluid in the presence of a background linear shear current.…
The density stratification in an incompressible fluid is responsible for the propagation of internal waves. In domains with topography, these waves exhibit interesting features. In particular, numerical and lab experiments show that, in two…
In this paper we describe the propagation of smooth (C^\infty) and Sobolev singularities for the wave equation on smooth manifolds with corners M equipped with a Riemannian metric g. That is, for X=MxR, P=D_t^2-\Delta_M, and u locally in…
We present a large-amplitude existence theory for two-dimensional solitary waves propagating through a two layer body of water. The domain of the fluid is bounded below by an impermeable flat ocean floor and above by a free boundary at…
A family of solitary waves is constructed in Frenkel-Kontorova model and its continuum and quasi-continuum approximations. Each solitary waves is characterised by the number of local maxima in its profile and a relation between external…
A two-dimensional water wave system is examined consisting of two discrete incompressible fluid domains separated by a free common interface. In a geophysical context this is a model of an internal wave, formed at a pycnocline or…
A theory for the spin wave eigenmodes of a Dzyaloshinskii domain wall is presented. These walls are N\'eel-type domain walls that can appear in perpendicularly-magnetized ultrathin ferromagnets in the presence of a sizeable…
One of the pivotal questions in the dynamics of the oceans is related to the cascade of mechanical energy in the abyss and its contribution to mixing. Here, we propose internal wave attractors in the large amplitude regime as a unique…