Glossary Deep water A surface wave is said to be in deep water if its wavelength is much shorter than the local water depth. Internal wave A internal wave travels within the interior of a fluid. The maximum velocity and maximum amplitude occur within the fluid or at an internal boundary (interface). Internal waves depend on the density-stratification of the fluid. Shallow water A surface wave i...

The linear shallow water equations on the sphere are discretized on a quasi-uniform, geodesic, icosahedral Voronoi-Delaunay grid with a C-grid variable arrangement and semi-implicit time discretization. A finite volume discretization is employed for the continuity equation in conservation law form, using as control volumes either the hexagonal/pentagonal or the dual triangular cells. A geostrop...

The shallow water magnetohydrodynamic system describes the thin layer evolution of the solar tachocline. It is obtained from the three dimensional incompressible magnetohydrodynamic system similarly as the classical shallow water system is obtained from the incompressible NavierStokes equations. The system is hyperbolic and has two additional waves with respect to the shallow water system, the ...

The transformation of a weakly nonlinear interfacial solitary wave in an ideal twolayer flow over a step is studied. In the vicinity of the step the wave transformation is described in the framework of the linear theory of long interfacial waves, and the coefficients of wave reflection and transmission are calculated. A strong transformation arises for propagation into shallower water, but a we...

Submitted: Nov 12, 2013; Accepted: Dec 18, 2013; Published: Dec 22, 2013 Abstract: In this article, we have employed an enhanced (G′/G)-expansion method to find the exact solutions first and then the solitary wave solutions of the nonlinear generalized shallow water wave equation. Here we have derived solitons, singular solitons and periodic wave solutions through the enhanced (G′/G)-expansion ...

This paper presents an efficient numerical algorithm for the nonlinear wave-wave interactions that can be important in the evolution of coastal waves. Random sea waves of multiple frequencies always interact with each other and with the variable wind and pressure fields. As waves propagate and transform from deep to shallow water, it is generally difficult to determine the actual amount of nonl...

The Ostrovsky–Hunter equation governs evolution of shallow water waves on a rotating fluid in the limit of small high-frequency dispersion. Sufficient conditions for the wave breaking in the Ostrovsky–Hunter equation are found both on an infinite line and in a periodic domain. Using the method of characteristics, we also specify the blow-up rate at which the waves break. Numerical illustrations...

We study the maximum wave amplitude produced by line-soliton interactions of the Kadomtsev-Petviashvili II (KPII) equation, and we discuss a mechanism of generation of large amplitude shallow water waves by multi-soliton interactions of KPII. We also describe a method to predict the possible maximum wave amplitude from asymptotic data. Finally, we report on numerical simulations of multi-solito...

3 Distance defined by optimal transportation problem 33 3.1 A distance functional in the spatially periodic case. Introduction This thesis deals with two strongly nonlinear evolution Partial Differential Equation (in the following named P.D.E.) arising from mathematical physics. The first one was introduced first by Fokas and Fuchssteiner [28] as a bi-Hamiltonian equation, and then was rediscov...