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, water waves and sound waves, vortex motions, geophysical flows, nonlinear instability and chaos, turbulence, and the gauge theory of fluid flows are also covered. 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; Gauge Principle for Ideal-Fluid Flows; Appendices: Vector Analysis; Velocity Potential and Stream Function; Ideal Fluid and Ideal Gas; Curvilinear Reference Frames: Differential Operators. Key Features Textbook with a new and modern approach Includes concise and compact presentations of important new areas in fluid mechanics from the viewpoint of physics, such as flows in rotating frames, stratified flows, recent results of the Earth Simulator, Lorenz chaotic system, fully developed turbulence, and the gauge theory of fluid flows Readership: Undergraduate and postgraduate students in physics, mathematics, and engineering as well as scientists and engineers who are not specialists in fluid mechanics.