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E-raamat: 3D Modeling of Nonlinear Wave Phenomena on Shallow Water Surfaces

(Southern Federal University, Russia)
  • Formaat: EPUB+DRM
  • Ilmumisaeg: 01-Feb-2018
  • Kirjastus: Wiley-Scrivener
  • Keel: eng
  • ISBN-13: 9781119488217
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  • Formaat: EPUB+DRM
  • Ilmumisaeg: 01-Feb-2018
  • Kirjastus: Wiley-Scrivener
  • Keel: eng
  • ISBN-13: 9781119488217

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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.
Preface vii
Introduction ix
1 Equations of Hydrodynamics
1(22)
1.1 Features of the Problems in the Formulation of Mathematical Physics
1(2)
1.2 Classification of Linear Differential Equations with Partial Derivatives of the Second Order
3(2)
1.3 Nonlinear Equations of Fluid Dynamics
5(4)
1.4 Methods for Solving Nonlinear Equations
9(2)
1.5 The Basic Laws of Hydrodynamics of an Ideal Fluid
11(5)
1.6 Linear Equations of Hydrodynamic Waves
16(7)
Conclusions
20(3)
2 Modeling of Wave Phenomena on the Shallow Water Surface
23(42)
2.1 Waves on the Sea Surface
23(3)
2.2 Review of Research on Surface Gravity Waves
26(13)
2.3 Investigation of Surface Gravity Waves
39(11)
2.4 Spatial modeling of Wave Phenomena on Shallow Water Surface
50(7)
2.5 Actual Observations of Wave Phenomena on the Surface of Shallow Water
57(1)
2.6 Ship Waves. "Reactive" Ducks of the Alexander Garden
58(7)
Conclusions
64(1)
3 Modeling of Nonlinear Surface Gravity Waves in Shallow Water
65(54)
3.1 Overview of Studies on Nonlinear Surface Gravity Waves in Shallow Water
65(9)
3.2 Nonlinear Models of Surface Gravity Waves in Shallow Water
74(7)
3.3 Solution of the Nonlinear Shallow Water Equation by the Method of Successive Approximations
81(5)
3.4 Modeling the Propagation of Nonlinear Surface Gravity Waves in Shallow Water
86(13)
3.5 Modeling the Refraction of Nonlinear Surface Gravity Waves
99(10)
3.6 Modeling of Propagation and Refraction of Nonlinear Surface Gravity Waves Under Shallow Water Conditions with Account of Dispersion
109(10)
Conclusions
117(2)
4 Numerical Simulation of Nonlinear Surface Gravity Waves in Shallow Water
119(36)
4.1 Review of Studies on Computational Modeling of Surface Waves
119(13)
4.2 Statement of the Problem
132(6)
4.3 The Research of a Discrete Model
138(1)
4.4 Results of Numerical Modeling based on Shallow Water Equations
139(9)
4.5 Discussion and Comparison of Results
148(7)
Conclusions
152(3)
5 Two-Dimensional Numerical Simulation of the Run-Up of Nonlinear Surface Gravity Waves
155(36)
5.1 Statement of the Problem
155(5)
5.2 Construction of a Discrete Finite-Volume Model
160(9)
5.3 Discrete Model Research
169(2)
5.4 Results of Two-Dimensional Numerical Modeling and Their Analysis
171(14)
5.5 Discussion and Comparison of Results
185(6)
Conclusions
188(3)
6 Three-Dimensional Numerical Modeling of the Runup of Nonlinear Surface Gravity Waves
191(54)
6.1 Statement of the Problem. Boundary and Initial Conditions
191(4)
6.2 Construction of a Discrete Model
195(11)
6.3 The Construction of a Discrete Finite-Volume Model
206(23)
6.4 Discrete Model Research
229(1)
6.5 Results of Three-Dimensional Numerical Modeling and Their Analysis
230(11)
6.6 Discussion and Comparison of Results
241(4)
Conclusions
242(3)
Conclusion 245(2)
References 247(14)
Index 261
I.B. Abbasov PhD, is a specialist in computer engineering, aerospace engineering, and industrial design at the Southern Federal University in Russia. He has numerous publications to his credit, focusing on the use of mathematical modeling and high-level computer programming for practical applications, such as ocean exploration.