1st Edition

Waves and Oscillations in Nature An Introduction

By A Satya Narayanan, Swapan K Saha Copyright 2015
    552 Pages 129 B/W Illustrations
    by CRC Press

    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.

    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.


    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