Related papers: Reflectionless wave propagation on shallow water w…
We propose an extension of the discretization approaches for multilayer shallow water models, aimed at making them more flexible and efficient for realistic applications to coastal flows. A novel discretization approach is proposed, in…
In the last fifteen years, a great progress has been made in the understanding of the nonlinear resonance dynamics of water waves. Notions of scale- and angle-resonances have been introduced, new type of energy cascade due to nonlinear…
When traditional linearised theory is used to study gravity-capillary waves produced by flow past an obstruction, the geometry of the object is assumed to be small in one or several of its dimensions. In order to preserve the nonlinear…
We consider shock reflection which has a well-known local non-uniqueness: the reflected shock can be either of two choices, called weak and strong. We consider cases where existence of a global solution with weak reflected shock has been…
We consider a particular instance of reflection of shock waves in self-similar compressible flow. We prove that local self-similar regular reflection (RR) cannot always be extended into a global flow. Therefore the detachment criterion is…
In order to improve the frequency dispersion effects of irrotational shallow water models in coastal oceanography, several full dispersion versions of classical models were formally derived in the literature. The idea, coming from G.…
We investigate the existence of solitary gravity waves traversing a two-dimensional body of water that is bounded below by a flat impenetrable ocean bed and above by a free surface of constant pressure. Our main interest is constructing…
We investigate the slow, second order motion of thin flexible floating strips drifting in surface gravity waves. We introduce a diffractionless model (Froude-Krylov approximation) that neglects viscosity, surface tension, and radiation…
In this paper, we present a new multiscale method which is capable of coupling atomistic and continuum domains for high frequency wave propagation analysis. The problem of non-physical wave reflection, which occurs due to the change in…
We derived here in a systematic way, and for a large class of scaling regimes, asymptotic models for the propagation of internal waves at the interface between two layers of immiscible fluids of different densities, under the rigid lid…
This study examines whether the dispersion of passive particles at the free surface of a generic (nonturbulent) shallow flow can reliably represent the behavior of depth-keeping particles below the surface. A shallow configuration…
The possibility of asymmetric absorption and reflection for flexural waves is demonstrated though analytical and numerical examples. We focus on the 1D case of flexural motion of a beam and consider combinations of point scatterers which…
The breaking of detailed balance in fluids through Coriolis forces or odd-viscous stresses has profound effects on the dynamics of surface waves. Here we explore both weakly and strongly non-linear waves in a three-dimensional fluid with…
We study the two-dimensional problem of propagation of linear water waves in deep water in the presence of a submerged body. Under some geometrical requirements, we derive an explicit bound for the solution depending on the domain and the…
We examine the applicability of the weak wave turbulence theory in explaining experimental scaling results obtained for the diffusion and relative diffusion of particles moving on turbulent surface waves. For capillary waves our theoretical…
We prove global existence of solutions to the initial value problem for a third order dispersive flow into compact locally Hermitian symmetric spaces. The equation we consider generalizes two-sphere-valued completely integrable systems…
The equations for waves on the surface of an irrotational incompressible fluid are derived in the coordinates of the velocity potential/stream function. The low frequency shallow water approximation for these waves is derived for a varying…
The formulation of a canonical deep-water breaking wave problem is introduced, and the results of a set of three-dimensional numerical simulations for deep-water breaking waves are presented. In this paper fully nonlinear progressive waves…
Thirty years ago, theorists showed that a properly designed combination of incident waves could be fully transmitted through (or reflected by) a disordered medium, based on the existence of propagation channels which are essentially either…
We construct pulse-type approximate solutions to nonlinear hyperbolic equations near diffractive points, allowing arbitrary (even infinite) order of grazing. We show that in low regularity spaces and the high frequency limit, such solutions…