NUMERICAL SIMULATION OF SOLITON PROPAGATION WITH VARIABLE DEPTH (original) (raw)

Shallow-water soliton dynamics beyond the Korteweg–de Vries equation

Physical Review E, 2014

An alternative way for the derivation of the new KdV-type equation is presented. The equation contains terms depending on the bottom topography (there are six new terms in all, three of which are caused by the unevenness of the bottom). It is obtained in the second order perturbative approach in the weakly nonlinear, dispersive and long wavelength limit. Only treating all these terms in the second order perturbation theory made the derivation of this KdV-type equation possible. The motion of a wave, which starts as a KdV soliton, is studied according to the new equation in several cases by numerical simulations. The quantitative changes of a soliton's velocity and amplitude appear to be directly related to bottom variations. Changes of the soliton's velocity appear to be almost linearly anticorrelated with changes of water depth whereas correlation of variation of soliton's amplitude with changes of water depth looks less linear. When the bottom is flat, the new terms narrow down the family of exact solutions, but at least one single soliton survives. This is also checked by numerics.

Soliton interaction as a possible model for extreme waves in shallow water

Nonlinear Processes in Geophysics, 2003

Interaction of two long-crested shallow water waves is analysed in the framework of the two-soliton solution of the Kadomtsev-Petviashvili equation. The wave system is decomposed into the incoming waves and the interaction soliton that represents the particularly high wave hump in the crossing area of the waves. Shown is that extreme surface elevations up to four times exceeding the amplitude of the incoming waves typically cover a very small area but in the near-resonance case they may have considerable extension. An application of the proposed mechanism to fast ferries wash is discussed.

Two New Approaches in Solving the Nonlinear Shallow Water Equations for Tsunami Waves

2007

One key component of tsunami research is numerical simulation of tsunamis, which helps us to better understand the fundamental physics and phenomena and leads to better mitigation decisions. However, writing the simulation program itself imposes a large burden on the user. In this survey, we review some of the basic ideas behind the numerical simulation of tsunamis, and introduce two new approaches to construct the simulation using powerful, general-purpose software kits, PETSc and FEPG. PETSc and FEPG support various discretization methods such as finitedierence, finite-element and finite-volume, and provide a stable solution to the numerical problem. Our application uses the nonlinear shallow-water equations in Cartesian coordinates as the governing equations of tsunami wave propagation.

Shallow water soliton dynamics beyond KdV

A new nonlinear equation in the shallow water wave problem

Physica Scripta, 2014

In the paper a new nonlinear equation describing shallow water waves with the topography of the bottom directly taken into account is derived. This equation is valid in the weakly nonlinear, dispersive and long wavelength limit. Some examples of soliton motion for various bottom shapes obtained in numerical simulations according to the derived equation are presented.

Soliton basis states in shallow-water ocean surface waves

Physical Review Letters, 1991

The inverse scattering transform for the periodic Korteweg-de Vries equation is used to analyze surface-wave data obtained in the Adriatic Sea and a robust soliton spectrum is found. While the solitons are not observable in the data due to the presence of energetic radiation modes, a new nonlinear filtering technique renders the solitons visible. Numerical simulations support the existence of solitons in the measurements and suggest that, as a wave train propagates into shallow water, the solitons grow at the expense of the radiation.

Nonlinear mechanism of tsunami wave generation by atmospheric disturbances

Natural Hazards and Earth System Science, 2001

The problem of tsunami wave generation by variable meteo-conditions is discussed. The simplified linear and nonlinear shallow water models are derived, and their analytical solutions for a basin of constant depth are discussed. The shallow-water model describes well the properties of the generated tsunami waves for all regimes, except the resonance case. The nonlinear-dispersive model based on the forced Korteweg-de Vries equation is developed to describe the resonant mechanism of the tsunami wave generation by the atmospheric disturbances moving with near-critical speed (long wave speed). Some analytical solutions of the nonlinear dispersive model are obtained. They illustrate the different regimes of soliton generation and the focusing of frequency modulated wave packets.

AN ALTERNATIVE ANALYTICAL MODEL FOR PROPAGATION OF TSUNAMI WAVES

Catastrophic oceanic waves, termed Tsunami is considered a mysterious and inexplicable phenomenon. The mercurial behavior of this giant waves should be predicted in advance to avoid damage of properties and loss of lives. It is necessary to extend the use of various models and develop new models that will provide the study and accurate prediction of waves spread needed in future. To model the spread of tsunami waves, the initial wave can be considered as a two-dimensional continuous closed curve, and each point in its parametric representation on the curve will act as a point source, which expands as small ellipses, the envelope of these ellipses describes the new wave front, an implementation of Huygens Principle. Also, overlapping and tangling of the

DYNAMICS OF TWO-LAYERED SHALLOW WATER WAVES WITH COUPLED KdV EQUATIONS

2014

The dynamics of two-layered shallow water waves is studied in this paper by the aid of coupled potential-Korteweg-de Vries (pKdV) equation. There are two types of models that are considered. The first model yields solitary waves as well as shock wave solutions. The second model yields shock wave solutions only. The ansatz method is applied to retrieve the solitary wave as well as the shock wave solutions of both models. In both cases the time-dependent coefficients of dispersion and nonlinearity are considered, in order to keep the model closer to reality. Numerical simulations demonstrate the presence of soliton behaviour that is both rich and diverse.

Development of a nonlinear and dispersive numerical model of wave propagation in the coastal zone

2018

Nonlinear and dispersive effects are significant for nearshore waves, leading to the study and development of a fully nonlinear and dispersive potential-flow model solving the Euler-Zakharov equations, which determine the temporal evolution of the free surface elevation and velocity potential. The mathematical model and its numerical implementation are presented, as well as the approach chosen to extend the model to two horizontal dimensions. The nonlinear and dispersive capabilities of the 1DH version of the model are demonstrated by applying the model to two test cases: (1) the generation of regular waves created by a piston-like wave maker and the propagation of the associated free and bound harmonics over a flat bottom, following the experiments of CHAPALAIN et al. (1992), and (2) the propagation of irregular waves over a barred beach profile, following the experiments of BECQ-GIRARD et al. (1999). The accuracy of the model in representing high-order nonlinear and dispersive eff...

NUMERICAL SIMULATION OF SOLITON PROPAGATION WITH VARIABLE DEPTH (original) (raw)

Related papers