Elementary Fluid Mechanics

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World Scientific, 2007 - Science - 386 pages
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This textbook describes the fundamental ?physical? aspects of fluid flows for beginners of fluid mechanics in physics, mathematics and engineering, from the point of view of modern physics.It also emphasizes the dynamical aspects of fluid motions rather than the static aspects, illustrating vortex motions, waves, geophysical flows, chaos and turbulence. Beginning with the fundamental concepts of the nature of flows and the properties of fluids, the book presents fundamental conservation equations of mass, momentum and energy, and the equations of motion for both inviscid and viscous fluids.In addition to the fundamentals, this book also covers water waves and sound waves, vortex motions, geophysical flows, nonlinear instability, chaos, and turbulence. Furthermore, it includes the chapters on superfluids and the gauge theory of fluid flows.The material in the book emerged from the lecture notes for an intensive course on Elementary Fluid Mechanics for both undergraduate and postgraduate students of theoretical physics given in 2003 and 2004 at the Nankai Institute of Mathematics (Tianjin) in China. Hence, each chapter may be presented separately as a single lecture.
 

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Contents

1 Flows
1
2 Fluids
17
3 Fundamental equations of ideal fluids
31
4 Viscous fluids
45
5 Flows of ideal fluids
77
6 Water waves and sound waves
115
7 Vortex motions
143
8 Geophysical flows
177
12 Gauge theory of ideal fluid flows
277
Appendix A Vector analysis
315
Appendix B Velocity potential stream function
323
Appendix C Ideal fluid and ideal gas
327
Differential operators
329
Appendix E First three structure functions
335
Appendix F Lagrangians
337
Solutions
343

9 Instability and chaos
203
10 Turbulence
239
11 Superfluid and quantized circulation
263

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