Wave Propagation and Diffraction Mathematical Methods and Applications 1st Edition by Igor Selezov, Yuriy Kryvonos, Ivan Gandzha 9811049231 9789811049231

Wave Propagation and Diffraction Mathematical Methods and Applications 1st Edition by Igor T. Selezov, Yuriy G. Kryvonos, Ivan S. Gandzha – Ebook PDF Instant Download/DeliveryISBN:  9811049231, 9789811049231 

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ISBN-10 :  9811049231 

ISBN-13 :  9789811049231

Author:  Igor T. Selezov, Yuriy G. Kryvonos, Ivan S. Gandzha 

This book presents two distinct aspects of wave dynamics – wave propagation and diffraction – with a focus on wave diffraction. The authors apply different mathematical methods to the solution of typical problems in the theory of wave propagation and diffraction and analyze the obtained results. The rigorous diffraction theory distinguishes three approaches: the method of surface currents, where the diffracted field is represented as a superposition of secondary spherical waves emitted by each element (the Huygens–Fresnel principle); the Fourier method; and the separation of variables and Wiener–Hopf transformation method. Chapter 1 presents mathematical methods related to studying the problems of wave diffraction theory, while Chapter 2 deals with spectral methods in the theory of wave propagation, focusing mainly on the Fourier methods to study the Stokes (gravity) waves on the surface of inviscid fluid. Chapter 3 then presents some results of modeling the refraction of surface gravity waves on the basis of the ray method, which originates from geometrical optics. Chapter 4 is devoted to the diffraction of surface gravity waves and the final two chapters discuss the diffraction of waves by semi-infinite domains on the basis of method of images and present some results on the problem of propagation of tsunami waves. Lastly, it provides insights into directions for further developing the wave diffraction theory.

 Wave Propagation and Diffraction Mathematical Methods and Applications 1st Table of contents:

1 Some Analytical and Numerical Methods in the Theory of Wave Propagation and Diffraction
1.1 Method of Separation of Variables
1.2 Method of Power Series
1.3 Method of Spline Functions
1.4 Method of an Auxiliary Boundary
1.5 Some Algorithms for the Numerical Inversion of the Laplace Transform
1.5.1 Shifted Legendre Polynomials
1.5.2 Fourier Sine Series
1.5.3 Exponential Functions
1.5.4 Power Series Combined with Numerical Inversion
1.5.5 Fourier–Bessel Series
1.6 Method of Multiple Scales
References
2 Spectral Methods in the Theory of Wave Propagation
2.1 Equations of Motion of an Ideal Fluid. Small-Amplitude Waves
2.1.1 Euler and Laplace Equations with Boundary Conditions
2.1.2 Stationary Fluid Motion
2.1.3 Wave Energy, Momentum and Power
2.1.4 General Solution of the Laplace Equation
2.1.5 Small-Amplitude Waves (Linear Approximation)
2.1.6 Dimensionless Equations and Parameters
2.1.7 Complex Potential
2.2 Stokes Waves and Methods of Their Calculation
2.2.1 Stokes Waves
2.2.2 Steep Stokes Waves and Their Main Properties
2.2.3 Spectral Methods of Calculating the Stokes Waves
2.3 The Limiting Stokes Wave with a Corner at the Crest and Its Calculation
2.4 High-Order Nonlinear Schrödinger Equation and Split-Step Fourier Technique
2.5 Two-parameter Method for Describing the Nonlinear Evolution ƒ
References
3 Ray Method of Investigating the Wave Evolution over Arbitrary Topography
3.1 On the Geometric Theory of Water Wave Refraction
3.2 Wave Refraction over Inhomogeneous Bottom
3.2.1 Equations of the Ray Method
3.2.2 Ray Separation Factor
3.2.3 Wave Amplitude
3.2.4 Specifying the Bottom Relief in Analytical Form. The Case of Linear Depth Variation
3.2.5 The Case of Parabolic Depth Variation
3.2.6 The Case of Hyperbolic Depth Variation
3.2.7 Specifying the Fluid Depth in Tabular Form
3.2.8 Comparing the Theoretical Results and Field Observations
3.2.9 Wave Transformation in the Zones of Caustics
3.3 Nonlinear Theory of Wave Refraction in a Fluid with Variable Depth
References
4 Analytical and Numerical Solutions to the Wave Diffraction Problems
4.1 On the Formulation and Solution of Wave-Diffraction Problems
4.2 Wave Diffraction by a Partially Submerged Elliptical Cylinder
4.3 Wave Diffraction by a Submerged Circular Cylinder
4.4 Scattering of Magnetoacoustic Cylindrical Waves by a Cylinder
4.5 Wave Diffraction by a System of Cylinders
4.6 Wave Scattering by an Asymmetrically Inhomogeneous Cylinder
4.7 Numerical-Analytical Method of an Auxiliary Boundary for Studying the Wave Diffraction by a Vert
4.8 Numerical Study of the Acoustic Wave Diffraction by a Body of Revolution
4.8.1 Symmetric Inhomogeneities
4.8.2 Asymmetric Inhomogeneities
References
5 Wave Diffraction by Convex Bodies in Semi-infinite Domains
5.1 Formulation of the Wave-Diffraction Problems in Semi-infinite Domains
5.2 Method of Images in the case of Finite Bodies
5.3 Scattering of Plane Acoustic Waves by a Circular Cylinder
5.4 Scattering of Plane Acoustic Waves by a Sphere
5.5 Scattering of Electromagnetic Waves by a Circular Cylinder
5.6 Diffraction of Elastic Waves by a Cylinder
5.7 Diffraction of Elastic Waves by a Sphere
References
6 Propagation and Evolution of Transient Water Waves
6.1 Generation of Tsunami Waves by Underwater Earthquakes
6.2 Wave Generation by Repeated Disturbances
6.3 Evolution of Long Water Waves Over a Disturbed Bottom
6.4 Diffraction of Cylindrical Waves by a Radial Inhomogeneity
6.5 Wave Evolution in a Two-Layer Fluid
6.5.1 Problem Formulation and Solution Method
6.5.2 Linear Approximations
6.5.3 Analysis of the First Linear Problem

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Tags: Wave Propagation, Diffraction Mathematical, Applications, Igor Selezov, Yuriy Kryvonos, Ivan Gandzh