Fluid Dynamics - Fundamentals and Applications

Description

This introductory book addresses a broad range of classical Fluid Dynamics topics, interesting applications, and related problems in everyday life. The geophysical and astrophysical applications discussed concern e.g. the shape and internal structure of the Earth and stars, the dynamics of the atmosphere and ocean, hydrodynamic instabilities, and the different kinds of waves that can be found in the atmosphere, ocean and solid Earth. Non-linear waves (solitons) are also mentioned. In turn, the book explores problems from everyday life, including the motion of golf balls, life at low Reynolds numbers, the physics of sailing, and the aerodynamics of airplanes and Grand Prix cars. No book on this topic would be complete without a look at chaos and turbulence; here the problems span from Gaussian plumes to chaotic dynamos, to stochastic climate modeling. Advances in fluid dynamics have produced a wealth of numerical methods and techniques, which are used in many of the applications. Given its structure, the book can be used both for an introductory course to fluid dynamics and as preparation for more advanced problems typical of graduate-level courses. Preface Contents Nomenclature 1 Fundamentals 1 1.1 Hydrostatics 1.2 Some Applications 1.2.1 Atmospheric Pressure 1.2.2 A First Glimpse at Stability 1.2.3 Archimedes' Law 1.2.4 Models of Earth's Interior 1.2.5 Shape of the Earth 1.3 Pressure Distribution in Rigid Body Motion References 2 Fundamentals 2 2.1 The Continuity Equation 2.2 The Equations of Motion 2.3 The Bernoulli Theorem 2.4 Simple Applications 2.4.1 Flow from a Tank 2.4.2 The Pitot Tube 2.5 Thrust for a Propeller 2.6 Circulation and Vorticity 2.6.1 Kelvin Circulation Theorem References 3 Fundamentals 3 3.1 Viscosity 3.2 The Equation of Navier Stokes 3.2.1 The Diffusion Equation 3.3 The Reynolds Number 3.3.1 The Blasius Boundary Layer 3.4 Plane Poiseuille Flow and Pipe Flow: A Plumber Application … 3.5 Flow Past a Sphere at Low Reynolds Number 3.6 Life at Low Reynolds Number References 4 Aerodynamics and All That 4.1 Velocity Potential 4.2 Elementary Potential Flows 4.2.1 Source and Sink of a Fluid 4.2.2 Line Vortex 4.2.3 Plane Doublet 4.2.4 Non-lifting Flow over a Circular Cylinder 4.2.5 Lifting Flow over a Rotating Circular Cylinder 4.2.6 The Kutta-Zhukhovsky Lift Theorem 4.2.7 Lift from the Deflection of Air Stream References 5 Waves 5.1 Sound Waves 5.2 Supersonic Flow Past Thin Plates 5.3 Wave Velocities and Energy 5.3.1 Energy and Intensity of an Acoustic Wave 5.4 Gravity Waves 5.4.1 Deep Water Waves 5.4.2 Shallow Water Waves 5.4.3 Capillary Waves 5.5 Energy Flux in Water Gravity Waves 5.6 Ship Waves 5.7 Wave Drag on Ships 5.8 Non-linear Shallow Water Waves: Solitons References 6 Instabilities 6.1 Stability, Instability and Bifurcations 6.2 Gravitational (Jeans) Instability 6.3 Instability of Shear Flows 6.3.1 Rayleigh–Taylor Instability 6.3.2 Kelvin–Helmholtz Instability 6.4 Stratified Shear Flows 6.4.1 The Richardson Number 6.4.2 A Useful Example References 7 Non-linearities, Randomness and Chaos 7.1 Non-linear Behaviour and Navier–Stokes Equation 7.2 Stochastic Behaviour 7.2.1 White or Gaussian Noise 7.3 A Couple of Examples of Randomness 7.3.1 The Brownian Motion 7.3.2 Climate Variability 7.4 Chaotic Behaviour 7.4.1 Generating Chaos 7.4.2 Lyapunov Exponents 7.4.3 Visualization of Chaos: Attractors, Poincarè Sections and Fractals 7.5 Chaos in a Fluid: The Loop Oscillator 7.6 The Lorenz System 7.7 ENSO: A Very Complex System References 8 Turbulence 8.1 Some General Matter 8.2 Statistical Description of Turbulence 8.2.1 Examples of Probability Distribution 8.3 Smoke Plumes as an Application of Pdf 8.4 The Atmospheric Boundary Layer: The Mixing Length 8.5 Two-Dimensional Turbulence 8.5.1 Energy and Enstrophy Transfer References 9 Magnetohydrodynamics 9.1 Some Preliminaries 9.1.1 Particles Motion 9.1.2 Plasma Oscillations 9.1.3 Debye Length 9.2 The MHD Equations 9.3 Vorticity and Magnetic Field 9.4 The Frozen Field 9.5 The Planetary Dynamos 9.5.1 The Faraday Self-Excited Dynamo 9.6 The Turbulent Dynamo 9.7 Magnetohydrodynamic Waves 9.7.1 Dispersion Relations for MHD Waves References Index