3D Modeling of Nonlinear Wave Phenomena on Shallow Water Surfaces

Iftikhar B. Abbasov

• Publisher: Wiley-Scrivener
• Year: 2018
• ISBN:
  9781119488217
• Edition: 1
• Topic: Technology & Engineering
• Subtopic: Mechanical Engineering
• Index: Technology & Engineering

With climate change, erosion, and human encroachment on coastal environments growing all over the world, it is increasingly important to protect populations and environments close to the sea from storms, tsunamis, and other events that can be not just costly to property but deadly. This book is one step in bringing the science of protection from these events forward, the most in-depth study of its kind ever published.

The analytic and numerical modeling problems of nonlinear wave activities in shallow water are analyzed in this work. Using the author's unique method described herein, the equations of shallow water are solved, and asymmetries that cannot be described by the Stokes theory are solved. Based on analytical expressions, the impacts of dispersion effects to wave profiles transformation are taken into account. The 3D models of the distribution and refraction of nonlinear surface gravity wave at the various coast formations are introduced, as well.

The work covers the problems of numerical simulation of the run-up of nonlinear surface gravity waves in shallow water, transformation of the surface waves for the 1D case, and models for the refraction of numerical modeling of the run-up of nonlinear surface gravity waves at beach approach of various slopes. 2D and 3D modeling of nonlinear surface gravity waves are based on Navier-Stokes equations. In 2D modeling the influence of the bottom of the coastal zone on flooding of the coastal zone during storm surges was investigated. Various stages of the run-up of nonlinear surface gravity waves are introduced and analyzed. The 3D modeling process of the run-up is tested for the coast protection work of the slope type construction.

Useful for students and veteran engineers and scientists alike, this is the only book covering these important issues facing anyone working with coastal models and ocean, coastal, and civil engineering in this area.

Chapter 1
Equations of Hydrodynamics

1.1 Features of the Problems in the Formulation of Mathematical Physics

When examining a physical process, the scientist needs to describe it in mathematical terms. A mathematical description or a process modeling could be quite varied. Mathematical modeling does not investigate the actual physical process itself, and some of its models are the ideal process written in the form of mathematics. The mathematical model should preserve the basic features of the actual physical process and, at the same time, should be simple enough to be solved by known methods. In the future, the consistency of the mathematical model with the actual process needs to be tested.

Many ways of mathematically describing physical processes lead to differential equations with private derivatives, and in some cases to Integro-differential equations. It is this group of tasks that is assigned the term mathematical physics, and the methods of solving them are referred to as mathematical physics methods.

The subject of mathematical physics is the mathematical theory of physical phenomena. The wide distribution of mathematical physics is connected to the commonality of mathematical models based on fundamental laws of nature: the laws of mass, energy, charge conservation, kinetic momentum. This results in the same mathematical models describing the physical phenomena of different natures.

Mathematical physics usually examines processes in a certain spatial area filled with a continuous material environment called the solid environment. Values that describe the state of the environment and the physical processes that occur in it depend on the spatial coordinates and time. In general, mathematical physics models describe the behavior of the system at three levels: the interaction of the system as a whole with the external environment; the interaction between the system’s basic volumes and the properties of a single, basic system volume.

The interaction of the system with the external environment is the wording of the boundary conditions, i.e., the conditions at the border of the task area, which include in general the boundary and initial conditions. The second level describes the interaction of elementary volumes based on laws for the preservation of physical substances and their transfer in space. The third level corresponds to the establishment of the state equations of the environment, i.e., the creation of a mathematical model of the basic environment behavior.

The equations of ...

Table of contents

• Cover
• Title page
• Copyright page
• Preface
• Introduction
• Chapter 1: Equations of Hydrodynamics
• Chapter 2: Modeling of Wave Phenomena on the Shallow Water Surface
• Chapter 3: Modeling of Nonlinear Surface Gravity Waves in Shallow Water
• Chapter 4: Numerical Simulation of Nonlinear Surface Gravity Waves in Shallow Water
• Chapter 5: Two-Dimensional Numerical Simulation of the Run-Up of Nonlinear Surface Gravity Waves
• Chapter 6: Three-Dimensional Numerical Modeling of the Runup of Nonlinear Surface Gravity Waves
• Conclusion
• References
• Index
• End User License Agreement