Book contents
- Frontmatter
- Contents
- Preface
- Part A The Fundamentals of MHD
- Introduction: The Aims of Part A
- 1 A Qualitative Overview of MHD
- 2 The Governing Equations of Electrodynamics
- 3 The Governing Equations of Fluid Mechanics
- 4 Kinematics of MHD: Advection and Diffusion of a Magnetic Field
- 5 Dynamics at Low Magnetic Reynolds Numbers
- 6 Dynamics at Moderate to High Magnetic Reynolds' Number
- 7 MHD Turbulence at Low and High Magnetic Reynolds Number
- Part B Applications in Engineering and Metallurgy
- Appendices
- Bibliography
- Subject Index
3 - The Governing Equations of Fluid Mechanics
Published online by Cambridge University Press: 26 February 2010
- Frontmatter
- Contents
- Preface
- Part A The Fundamentals of MHD
- Introduction: The Aims of Part A
- 1 A Qualitative Overview of MHD
- 2 The Governing Equations of Electrodynamics
- 3 The Governing Equations of Fluid Mechanics
- 4 Kinematics of MHD: Advection and Diffusion of a Magnetic Field
- 5 Dynamics at Low Magnetic Reynolds Numbers
- 6 Dynamics at Moderate to High Magnetic Reynolds' Number
- 7 MHD Turbulence at Low and High Magnetic Reynolds Number
- Part B Applications in Engineering and Metallurgy
- Appendices
- Bibliography
- Subject Index
Summary
In his 1964 lectures on physics, R P Feynman noted that:
The efforts of a child trying to dam a small stream flowing in the street, and his surprise at the strange way the water works its way out, has its analog in our attempts over the years to understand the flow of fluids. We have tried to dam the water by getting the laws and equations… but the water has broken through the dam and escaped our attempt to understand it.
In this chapter we build the dam and write down the equations. Later, particularly in Chapter 7 where we discuss turbulence, we shall see how the dam bursts open.
Fluid Flow in the Absence of Lorentz Forces
In the first seven sections of this chapter we leave aside MHD and focus on fluid mechanics in the absence of the Lorentz force. We return to MHD in Section 3.8. Readers who have studied fluid mechanics before may be familiar with much of the material in Sections 3.1 to 3.7, and may wish to proceed directly to Section 3.8. The first seven sections provide a self-contained introduction to the subject, with particular emphasis on vortex dynamics, which is so important in the study of MHD.
Elementary Concepts
Different categories of fluid flow
The beginner in fluid mechanics is often bewildered by the many diverse categories of fluid flow which appear in the text books. There are entire books dedicated to such subjects as potential flow, boundary layers, turbulence, vortex dynamics and so on.
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- Information
- An Introduction to Magnetohydrodynamics , pp. 47 - 101Publisher: Cambridge University PressPrint publication year: 2001