Related papers: Tsunami propagation for singular topographies

Multi-scale wave propagation problems are computationally costly to solve by traditional techniques because the smallest scales must be represented over a domain determined by the largest scales of the problem. We have developed and…

Turbulent relative dispersion is studied theoretically with a focus on the evolution of probability distribution of the relative separation of two passive particles. A finite separation speed and a finite correlation of relative velocity,…

We present a numerical study of essentially nonlinear dynamics of surface gravity waves on deep water with constant vorticity using governing equations in conformal coordinates. The dispersion relation of surface gravity waves on shear flow…

In this paper, we want to understand the Proudman resonance. It is a resonant respond in shallow waters of a water body on a traveling atmospheric disturbance when the speed of the disturbance is close to the typical water wave velocity. We…

We study a singular parabolic equation of the total variation type in one dimension. The problem is a simplification of the singular curvature flow. We show existence and uniqueness of weak solutions. We also prove existence of weak…

The instability and nonlinear evolution of directional ocean waves is investigated numerically by means of simulations of the governing kinetic equation for narrow-band surface waves. Our simulation results reveal the onset of the…

We use physics-informed neural networks for solving the shallow-water equations for tsunami modeling. Physics-informed neural networks are an optimization based approach for solving differential equations that is completely meshless. This…

We report numerical investigations of wave turbulence in a vibrating plate. The possibility to implement advanced measurement techniques and long time numerical simulations makes this system extremely valuable for wave turbulence studies.…

A parabolic equation for the propagation of periodic internal waves over varying bottom topography is derived using the multiple-scale perturbation method. Some computational aspects of the numerical implementation are discussed. The…

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…

In ordinary turbulence research it has been a long standing tradition to solve the equations in spectral space giving the best possible accuracy. This is indeed a natural choice for incompressible problems with periodic boundaries, but it…

This paper considers two-dimensional steady solitary waves with constant vorticity propagating under the influence of gravity over an impermeable flat bed. Unlike in previous works on solitary waves, we allow for both internal stagnation…

We describe the evolution of a paraxial electromagnetic wave characterizing by a non-uniform polarization distribution with singularities and propagating in a weakly anisotropic medium. Our approach is based on the Stokes vector evolution…

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…

The present study describes, first, an efficient algorithm for computing capillary-gravity solitary waves solutions of the irrotational Euler equations with a free surface and, second, provides numerical evidences of the existence of an…

We investigate a hydrodynamic equation system which - with some approximation - is capable to describe the tsunami propagation in the open ocean with the time-dependent self-similar Ansatz. We found analytic solutions how the wave height…

Some of the most impressive singular wave fronts seen in Nature are the transbasin oceanic internal waves, which may be observed from the Space Shuttle as they propagate and interact with each other, for example, in the South China Sea. The…

We examine a degenerate, dispersive, nonlinear wave equation related to the evolution of partially molten rock in dimensions two and higher. This simplified model, for a scalar field capturing the melt fraction by volume, has been studied…

We introduce a general framework for the study of the diffraction of waves by cone points at high frequencies. We prove that semiclassical regularity propagates through cone points with an almost sharp loss even when the underlying operator…

We make some remarks on the linear wave equation concerning the existence and uniqueness of weak solutions, satisfaction of the energy equation, growth properties of solutions, the passage from bounded to unbounded domains, and…