Wave Propagation and Diffraction

Igor T. Selezov's monograph examines wave propagation and diffraction, concentrating on how waves bend around obstacles and edges. Its central question is how mathematical techniques can be used to solve standard problems in these fields and to interpret the results they produce.

The rigorous diffraction theory is built on three approaches. The first is the surface current method, which treats the diffracted field as the sum of secondary spherical waves radiated from every point on a surface, in line with the Huygens-Fresnel principle. The second is the Fourier method. The third combines separation of variables with the Wiener-Hopf transformation.

The chapters move from general mathematical tools to applications. Chapter 1 presents the methods used in diffraction theory. Chapter 2 covers spectral techniques for wave propagation, with particular emphasis on Fourier methods applied to Stokes gravity waves on the surface of an inviscid fluid. Chapter 3 models the refraction of surface gravity waves using the ray method, which comes from geometrical optics. Chapter 4 addresses the diffraction of surface gravity waves. Later chapters treat diffraction by semi-infinite domains using the method of images and examine the propagation of tsunami waves. The book closes by outlining directions for future work in wave diffraction theory.