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Wave Propagation and Diffraction

Mathematical Methods and Applications

  • Igor T. Selezov
  • Yuriy G. Kryvonos
  • Ivan S. Gandzha

Part of the Foundations of Engineering Mechanics book series (FOUNDATIONS)

Table of contents

  1. Front Matter
    Pages i-xv
  2. Igor T. Selezov, Yuriy G. Kryvonos, Ivan S. Gandzha
    Pages 1-24
  3. Igor T. Selezov, Yuriy G. Kryvonos, Ivan S. Gandzha
    Pages 25-75
  4. Igor T. Selezov, Yuriy G. Kryvonos, Ivan S. Gandzha
    Pages 77-111
  5. Igor T. Selezov, Yuriy G. Kryvonos, Ivan S. Gandzha
    Pages 113-162
  6. Igor T. Selezov, Yuriy G. Kryvonos, Ivan S. Gandzha
    Pages 163-200
  7. Igor T. Selezov, Yuriy G. Kryvonos, Ivan S. Gandzha
    Pages 201-235
  8. Back Matter
    Pages 237-241

About this book

Introduction

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 t
he 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.

Keywords

Fourier expansions spline functions Laplace transform Stokes waves Split-step Fourier water wave refraction tsunami wave propagation Diffraction in convex bodies auxiliary boundary underwater earthquakes Meixner boundary conditions

Authors and affiliations

  • Igor T. Selezov
    • 1
  • Yuriy G. Kryvonos
    • 2
  • Ivan S. Gandzha
    • 3
  1. 1.Institute of HydromechanicsNational Academy of Sciences of UkraineKyivUkraine
  2. 2.Institute of CyberneticsNational Academy of Sciences of UkraineKyivUkraine
  3. 3.Institute of PhysicsNational Academy of Sciences of UkraineKyivUkraine

Bibliographic information

  • DOI https://doi.org/10.1007/978-981-10-4923-1
  • Copyright Information Springer Nature Singapore Pte Ltd. 2018
  • Publisher Name Springer, Singapore
  • eBook Packages Engineering
  • Print ISBN 978-981-10-4922-4
  • Online ISBN 978-981-10-4923-1
  • Series Print ISSN 1612-1384
  • Series Online ISSN 1860-6237
  • Buy this book on publisher's site