Waves and Oscillations in Nature : An Introduction book cover
1st Edition

Waves and Oscillations in Nature
An Introduction

ISBN 9781466590939
Published May 20, 2015 by CRC Press
551 Pages 129 B/W Illustrations

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Book Description

Waves and oscillations are found in large scales (galactic) and microscopic scales (neutrino) in nature. Their dynamics and behavior heavily depend on the type of medium through which they propagate.

Waves and Oscillations in Nature: An Introduction clearly elucidates the dynamics and behavior of waves and oscillations in various mediums. It presents different types of waves and oscillations that can be observed and studied from macroscopic to microscopic scales. The book provides a thorough introduction for researchers and graduate students in assorted areas of physics, such as fluid dynamics, plasma physics, optics, and astrophysics.

The authors first explain introductory aspects of waves and electromagnetism, including characteristics of waves, the basics of electrostatics and magnetostatics, and Maxwell’s equations. They then explore waves in a uniform media, waves and oscillations in hydrodynamics, and waves in a magnetized medium for homogeneous and nonhomogeneous media. The book also describes types of shock waves, such as normal and oblique shocks, and discusses important details pertaining to waves in optics, including polarization from experimental and observational points of view. The book concludes with a focus on plasmas, covering different plasma parameters, quasilinear and nonlinear aspects of plasma waves, and various instabilities in hydrodynamics and plasmas.

Table of Contents

Introduction to Waves and Oscillations
What Is a Wave
Harmonic Wave
Monochromatic Fields
Intensity of Waves

Electromagnetic Waves
Time-Varying Fields
Maxwell’s Equations
Energy Flux of Electrodynamics
Electromagnetic Field Equations

Waves in a Uniform Media
Simple Harmonic Oscillation
Damped Oscillations
Coupled Oscillations
One-Dimensional Wave Equation: D’Alembert’s Solution
Helmholtz Equation
Normal Mode Eigenvalue Problem
Longitudinal Waves
Traveling Waves
Dispersive Waves

Hydrodynamic Waves
Basic Equations
Small-Amplitude Waves
Gravity Waves
Linear Capillary and Gravity Waves
Surface Waves Generated by a Local Disturbance in the Field
Klein–Gordon Equation
Shallow Water Waves
Boussinesq Equation
Finite Amplitude Shallow Water Waves (Nonlinear Aspects)
Plane Waves in a Layer of Constant Depth
Poincaré and Kelvin Waves
Lamb and Rayleigh Waves
Inertial Waves
Rossby Waves
Forced Stationary Waves in the Atmosphere
Solitary Waves: KdV Equation

MHD Waves in a Uniform Media
Basic Equations
Sound Waves
Alfven Waves
Shear Alfven Waves
Compressional Alfven Waves
Magneto Acoustic Waves
Internal and Magneto Acoustic Gravity Waves
Phase Mixing of Waves
Resonant Absorption of Waves
Nonlinear Aspects

MHD Waves in a Nonuniform Media
Waves at a Magnetic Interface
Surface and Interfacial Waves
Tangential Discontinuity with Inclined Fields and Flows
Two-Mode Structure of Alfven Surface Waves
Magneto Acoustic-Gravity Surface Waves with Flows
Waves in a Magnetic Slab
Negative Energy Waves
Waves in Cylindrical Geometries
Slender Flux Tube Equations
Waves in Untwisted and Twisted Tubes
Applications to Coronal Waves
Nonlinear Aspects

Shock Waves
Discontinuities in Surfaces
Normal Shock Waves
Oblique Shock Waves
Blast Waves: Similarity Solution of Taylor–Sedov
Weak Shock Waves
Waves in a Polytropic Gas
An Application of Shock Waves in the Sun
Shock Waves in Collisionless Plasmas
Shocks in MHD
Nonlinear Studies

Waves in Optics
Optical Phenomena
Nonmonochromatic Fields
Emission of Wave-Trains
Polarization of Plane Monochromatic Waves

Plasma Waves
What Is a Plasma?
Plasma Parameters
Electrostatic Waves in Magnetized Plasma
Waves in a Cold Plasma
Plasma Waves (Warm)-Langmuir Waves
Ion-Acoustic Waves
Waves in Nonhomogeneous Plasmas
Quasilinear Theory for Nonhomogeneous Plasmas
Nonlinear Waves in Plasmas

Fluid and Plasma Instabilities
Stability of Parallel Shear Flows
Taylor–Goldstein Equation
Orr–Sommerfeld Equation
Rayleigh–Taylor (RT) Instability
Kelvin–Helmholtz (KH) Instability
Parametric Instability
Two-Stream Instability
Interchange (Flute) Instability
Sausage Instability
Kink Instability
Ballooning Instability

Appendix A: Typical Tables
Appendix B: Vector Operators



Exercises appear at the end of each chapter.

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A. Satya Narayanan is an associate professor at the Indian Institute of Astrophysics. Dr. Narayanan has written two books and numerous research papers. His research interests include solar magnetohydrodynamics (MHD), waves, and oscillations.

Now retired, Swapan K. Saha was a professor at the Indian Institute of Astrophysics. Dr. Saha has written numerous research papers and several books, including High Resolution Imaging: Detectors and Applications. His research interests include observational astronomy, high-resolution imaging, aperture synthesis, adaptive optics, atmospheric science, and image processing.


"The range of topics covered in this introduction for researchers and reference volume can be summarized by a list of the nouns appearing just before the word 'waves' in the table of contents: harmonic, electromagnetic, longitudinal, dispersive, hydrodynamic, surface, Poincare and Kelvin, Lamb and Rayleigh, Rossby, MHD, sound, Alfven, magnetoacoustic, solitary, gravity (meaning the kind in a fluid with gravitation as the restoring force), inertial, and shock. ... Specific astronomical applications appear in discussions of radio antennae, ionospheric processes, and shock waves in the Sun, in connection with solar flares and coronal mass ejections. ... Indeed the bibliography is one of the joys of this treatise, including original papers by Hertz, Strutt (Rayleigh to most of us), Brillouin, Compton, Planck, Doppler, Young, Michelson & Morley, Kirchhoff, Babinet, Coulomb, Hall, Oersted, Thompson, Poynting, Taylor, Heisenberg, Einstein, Bohr, Schrodinger, and Poincare. ... On the plus side, the numbers used in some MHD wave problems are appropriate for the solar corona."
—Virginia Trimble, from The Observatory, February 2016

"... Since the authors present a very rich compendium on waves and oscillations, the book is not only of an introductory character, but rather a kind of vademecum. It leads the reader through the very rich domain of oscillations and waves, starting from the most elementary simple ones and collecting nearly all chapters in physics, where the problems of oscillations and wave-like phenomena occur. ... The work is an excellent contribution with special aims. Namely, it offers an extremely broad treatment of the problems of oscillations and waves throughout the whole of physics. ... It is meant to be accessible to undergraduates, though readers among the 'elder' researchers also may make practical use of it. This is because the style of the presentation is rather concise; it does not spend too much space for the detailed explanation of the starting points of the cited results. In summary, we are persuaded that this work will be quite valuable for beginners (after obtaining some basic experience) as well as for working professionals."
—Ivan Abonyi (Budapest), from Zentralblatt MATH 1323 — 1