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.

Table of Contents:
Preface vii Introduction ix 1 Equations of Hydrodynamics 1 1.1 Features of the Problems in the Formulation of Mathematical Physics 1 1.2 Classification of Linear Differential Equations with Partial Derivatives of the Second Order 3 1.3 Nonlinear Equations of Fluid Dynamics 5 1.4 Methods for Solving Nonlinear Equations 9 1.5 The Basic Laws of Hydrodynamics of an Ideal Fluid 11 1.6 Linear Equations of Hydrodynamic Waves 16 Conclusions 20 2 Modeling of Wave Phenomena on the Shallow Water Surface 23 2.1 Waves on the Sea Surface 23 2.2 Review of Research on Surface Gravity Waves 26 2.3 Investigation of Surface Gravity Waves 39 2.4 Spatial modeling of Wave Phenomena on Shallow Water Surface 50 2.5 Actual Observations of Wave Phenomena on the Surface of Shallow Water 57 2.6 Ship Waves. “Reactive” Ducks of the Alexander Garden 58 Conclusions 64 3 Modeling of Nonlinear Surface Gravity Waves in Shallow Water 65 3.1 Overview of Studies on Nonlinear Surface Gravity Waves in Shallow Water 65 3.2 Nonlinear Models of Surface Gravity Waves in Shallow Water 74 3.3 Solution of the Nonlinear Shallow Water Equation by the Method of Successive Approximations 81 3.4 Modeling the Propagation of Nonlinear Surface Gravity Waves in Shallow Water 86 3.5 Modeling the Refraction of Nonlinear Surface Gravity Waves 99 3.6 Modeling of Propagation and Refraction of Nonlinear Surface Gravity Waves Under Shallow Water Conditions with Account of Dispersion 109 Conclusions 117 4 Numerical Simulation of Nonlinear Surface Gravity Waves in Shallow Water 119 4.1 Review of Studies on Computational Modeling of Surface Waves 119 4.2 Statement of the Problem 132 4.3 The Research of a Discrete Model 138 4.4 Results of Numerical Modeling based on Shallow Water Equations 139 4.5 Discussion and Comparison of Results 148 Conclusions 152 5 Two-Dimensional Numerical Simulation of the Run-Up of Nonlinear Surface Gravity Waves 155 5.1 Statement of the Problem 155 5.2 Construction of a Discrete Finite-Volume Model 160 5.3 Discrete Model Research 169 5.4 Results of Two-Dimensional Numerical Modeling and Their Analysis 171 5.5 Discussion and Comparison of Results 185 Conclusions 188 6 Three-Dimensional Numerical Modeling of the Runup of Nonlinear Surface Gravity Waves 191 6.1 Statement of the Problem. Boundary and Initial Conditions 191 6.2 Construction of a Discrete Model 195 6.3 The Construction of a Discrete Finite-Volume Model 206 6.4 Discrete Model Research 229 6.5 Results of Three-Dimensional Numerical Modeling and Their Analysis 230 6.6 Discussion and Comparison of Results 241 Conclusions 242 Conclusion 245 References 24