Related papers: Understanding the tsunami with a simple model
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…
This manuscript is devoted to the modelling of water waves in the deep water regime with some emphasis on the underlying variational structures. The present article should be considered as a review of some existing models and modelling…
We propose and compare methods for the analysis of extreme events in complex systems governed by PDEs that involve random parameters, in situations where we are interested in quantifying the probability that a scalar function of the…
The interaction of waves with structural barriers such as dams breaking plays a critical role in flood defense and tsunami disasters. In this work, we explore the dynamic changes in wave surfaces impacting various structural shapes, e.g.,…
Wave breaking is a critical process in the upper ocean: an energy sink for the surface wave field and a source for turbulence in the ocean surface boundary layer. We apply a novel multi-layer numerical solver resolving upper-ocean dynamics…
We investigate how wave propagation is modified by the presence of heat sources and sinks, in the simple 1D, hydrodynamical case, including chromosphere and solar wind. We integrate the time-dependent hydrodynamic equations of the solar…
Here I present a general formulation of water wave propagation and scattering over topographical bottoms. A simple equation is found and is compared with existing theories. As an application, the theory is extended to the case of water…
The shock wave instability induced when interacting with a small waviness on an interface was investigated analytically and numerically. The perturbation to the shock was phenomenologically treated assuming this as the consequence of the…
Turbulence and large-scale waves in the tropical region are studied using the spherical shallow water equations. With mesoscale vorticity forcing, both moist and dry systems show kinetic energy scaling that is dominated by rotational modes,…
We consider turbulence of waves that interact weakly via four-wave scattering (sea waves, plasma waves, spin waves, and many others). In the first non-vanishing order in the interaction, the occupation number of waves satisfy a closed…
Distributions of wave characteristics of ocean waves, such as wave slope, waveheight or wavelength, are an important tool in a variety of oceanographic applications such as safety of ocean structures or in the study of ship stability, as…
In the linear approximation we study long wave scattering on an axially symmetric flow in a shallow water basin with a drain in the center. This classical problem can be considered as a model of wave scattering on a rotating black hole. For…
This article introduces a physically realistic model for explaining how electromagnetic waves can be internally generated, propagate and interact in strongly magnetized plasmas or in nuclear magnetic resonance experiments. It studies high…
Internal waves, or waves that propagate within a stratified fluid, may break and cause mixing. While each individual mixing event may be small, collectively, internal wave breaking drive processes in the ocean that are critical to…
Sufficient conditions for wave breaking are found for the short-pulse equation describing wave packets of few cycles on the ultra-short pulse scale. The analysis relies on the method of characteristics and conserved quantities of the…
This paper describes the results from a numerical estimation of the force exerted by long surface waves on a fixed and partially immersed rectangular structure. The topic is connected with the need of making decisions on the design,…
The risk posed by tsunami waves is currently modelled over bare-earth representations by tsunami models. The complex flows around buildings and structures are crucial to represent the true state of the tsunami wave elevation, speed and…
A generalized version of the $abcd$-Boussinesq class of systems is derived to accommodate variable bottom topography in two-dimensional space. This extension allows for the conservation of suitable energy functionals in some cases and…
The rotating shallow water model is a simplification of oceanic and atmospheric general circulation models that are used in many applications such as surge prediction, tsunami tracking and ocean modelling. In this paper we introduce a class…
We compare two high order finite-difference methods that solve the elastic wave equation in two dimensional domains with curved boundaries and material discontinuities. Two numerical experiments are designed with focus on wave boundary…