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Elementary Fluid Mechanics

Elementary Fluid Mechanics

Elementary Fluid Mechanics

Elementary Fluid Mechanics

Why Elementary Fluid Mechanics? 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.
Contents:
Flows
Fluids
Fundamental Equations of Ideal Fluids
Viscous Fluids
Flows of Ideal Fluids
Water Waves and Sound Waves
Vortex Motions
Geophysical Flows
Instability and Chaos
Turbulence
Superfluid and Quantized Circulation
Gauge Theory of Ideal Fluid Flows
Appendices:
Vector Analysis
Velocity Potential, Stream Function
Ideal Fluid and Ideal Gas
Curvilinear Reference Frames: Differential Operators
First Three Structure Functions
Lagrangians
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