An introduction to magnetohydrodynamics
type: Item
instance of: scholarly article
zbMATH Open document ID: 0974.76002
DOI: 10.1017/CBO9780511626333
author: P. A. Davidson
publication date: 2001-03-28T00:00:00Z
Mathematics Subject Classification ID: 76-01
Mathematics Subject Classification ID: 76W05
zbMATH DE Number: 1582488
zbMATH Keywords: Kelvin theorem
zbMATH Keywords: electrodynamics
zbMATH Keywords: fluid mechanics
zbMATH Keywords: viscous flow
zbMATH Keywords: boundary layer
zbMATH Keywords: Navier-Stokes equations
zbMATH Keywords: vorticity
zbMATH Keywords: helicity
zbMATH Keywords: advection
zbMATH Keywords: diffusion
zbMATH Keywords: flows at low magnetic Reynolds number
zbMATH Keywords: flows at moderate and high magnetic Reynolds number
zbMATH Keywords: Hartmann flows
zbMATH Keywords: MHD-generators
zbMATH Keywords: pumps
zbMATH Keywords: Alfvén waves
zbMATH Keywords: dynamo theory
zbMATH Keywords: solar MHD
zbMATH Keywords: energy method
zbMATH Keywords: MHD stability
zbMATH Keywords: magnetic stirring
zbMATH Keywords: magnetic damping
zbMATH Keywords: interfacial instabilities
zbMATH Keywords: magnetic levitation
MaRDI profile type: Publication
full work available at URL: cbo9780511626333
OpenAlex ID: W936481127
title: An introduction to magnetohydrodynamics
published in: Cambridge Texts in Applied Mathematics
review text: This book written by an experienced teacher is divided into two main parts A and B, where the theoretical part A is subdivided into 7 chapters, and part B devoted to applications is subdivided into 5 chapters.NEWLINENEWLINENEWLINEIn part A, the author discusses different aspects of magnetohydrodynamics from theoretical as well as from physical point of view, which is especially important for understanding the basics of the subject. More precisely, chapter 1 presents the interesting history of MHD starting from 1930, without much mathematical rigor. The author includes some simple applications which promoted the development of MHD, like 1) sunspot formation; 2) the study of terrestrial magnetic field; 3) controlled thermonuclear fusion; 4) the theory of electromagnetic pumps; 5) magnetic stirring of an ingot; 6) magnetic damping of motion during casting process; 7) the theory of electromagnetic valve; 8) interfacial gravity waves in magnetic fluids; 9) applications in military operations. Chapter 2 contains a detailed discussion of basic equations of electrodynamics (Maxwell equations. Ohm's law, formula for Lorentz force, Ampère's law, Faraday's laws). Chapter 3 does not involve MHD but is very important as it describes the fundamentals of fluid mechanics: viscous flow theory, boundary-layer concept, a short derivation of non-MHD Navier-Stokes equations, vorticity, angular momentum, a brief sketch of nonviscous flow theory (Kelvin theorem, Helmholtz laws and helicity), and an introduction to turbulence. As applications, the author discusses von Kármán and Bödewadt problems. Finally, the author derives the MHD form of Navier-Stokes equations. Chapter 4 describes advection and diffusion in magnetic fields.NEWLINENEWLINENEWLINEFrom chapter 5, the author starts with the presentation of genuinely MHD topics. First, the author subdivides the MHD theory into two main parts: flows at low magnetic Reynolds number \(R_m\), and flows at moderate and high magnetic Reynolds numb…
reviewed by: V. M. Soundalgekar
description: scientific article