Related papers: Tsunami propagation for singular topographies

In this paper we consider a singular wave equation with distributional and more singular non-distributional coefficients and develop tools and techniques for the phase-space analysis of such problems. In particular we provide a detailed…

In this paper, we use the approximation of shallow water waves (Margaritondo G 2005 Eur. J. Phys. 26 401) to understand the behaviour of a tsunami in a variable depth. We deduce the shallow water wave equation and the continuity equation…

The runup of tsunami waves on the coasts of the barrow bays, channels and straits is studied in the framework of the nonlinear shallow water theory. Using the narrowness of the water channel, the one-dimensional equations are applied; they…

While the propagation of tsunamis is well understood and well simulated by numerical models, there are still a number of unanswered questions related to the generation of tsunamis or the subsequent inundation. We review some of the basic…

Here to represent the propagation of waves I attempted to describe them separately in space and time domains. The time and space wave equations are obtained and investigated, and formulas for the wave propagation are expressed. I also tried…

In this paper, persistence of solitary wave solutions of the regularized long wave equation with small perturbations are investigated by the geometric singular perturbation theory. Two different kinds of the perturbations are considered in…

We study a class of time dependent solutions of the vacuum Einstein equations which are plane waves with weak null singularities. This singularity is weak in the sense that though the tidal forces diverge at the singularity, the rate of…

In this paper, we investigate the geometric propagation and diffraction of singularities of solutions to the wave equation on manifolds with edge singularities.

Let $X$ be a manifold with boundary, endowed with a metric with conic singularities at the boundary components of $X$. Let $u$ be a solution to the wave equation on $\mathbb{R} \times X$. When a singularity of $u$ strikes a cone point of…

In this paper we consider an acoustic problem of wave propagation through a discontinuous medium. The problem is reduced to the dissipative wave equation with distributional dissipation. We show that this problem has a so-called very weak…

We present mathematical proofs on the existence and uniqueness of weak solutions for a special class of non linear parabolic and hyperbolic equations of mathematical physics subject to colored noise (structured turbulence) as random-…

We perform full-scale numerical simulation of instability of weakly nonlinear waves on the surface of deep fluid. We show that the instability development leads to chaotization and formation of wave turbulence. We study instability both of…

A system of two-dimensional nonlinear equations of hydrodynamics is considered. It is shown that for the this system in the general case a solution with weak discontinuity-type singularity behaves as a square root of S(x,y,t), where…

This is the second part of our work initiating the rigorous study of wave turbulence for water waves equations. We combine energy estimates, normal forms, and probabilistic and combinatorial arguments to complete the construction of…

The life of a tsunami is usually divided into three phases: the generation (tsunami source), the propagation and the inundation. Each phase is complex and often described separately. A brief description of each phase is given. Model…

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 give an elementary proof of uniqueness for the integral curve starting from the vertical axis in the phase-plane analysis of the recent model [A. Constantin, R.S. Johnson, Propagation of very long water waves, with vorticity, over…

We prove local unique solvability of the wave equation for a large class of weakly singular, locally bounded space-time metrics in a suitable space of generalised functions.

Tsunamis are often generated by a moving sea bottom. This paper deals with the case where the tsunami source is an earthquake. The linearized water-wave equations are solved analytically for various sea bottom motions. Numerical results…

The present study is devoted to the problem of tsunami wave generation. The main goal of this work is two-fold. First of all, we propose a simple and computationally inexpensive model for the description of the sea bed displacement during…