Fluid Mechanics

Dedication  About the Authors  Preface  Acknowledgments  Nomenclature  Chapter 1. Introduction  1.1. Fluid Mechanics  1.2. Units of Measurement  1.3. Solids, Liquids, and Gases  1.4. Continuum Hypothesis  1.5. Molecular Transport Phenomena  1.6. Surface Tension  1.7. Fluid Statics  1.8. Classical Thermodynamics  1.9. Perfect Gas  1.10. Stability of Stratified Fluid Media  1.11. Dimensional Analysis  Exercises  Chapter 2. Cartesian Tensors  2.1. Scalars, Vectors, Tensors, Notation  2.2. Rotation of Axes: Formal Definition of a Vector  2.3. Multiplication of Matrices  2.4. Second-Order Tensors  2.5. Contraction and Multiplication  2.6. Force on a Surface  2.7. Kronecker Delta and Alternating Tensor  2.8. Vector Dot and Cross Products  2.9. Gradient, Divergence, and Curl  2.10. Symmetric and Antisymmetric Tensors  2.11. Eigenvalues and Eigenvectors of a Symmetric Tensor  2.12. Gauss’ Theorem  2.13. Stokes’ Theorem  Exercises  Chapter 3. Kinematics  3.1. Introduction and Coordinate Systems  3.2. Particle and Field Descriptions of Fluid Motion  3.3. Flow Lines, Fluid Acceleration, and Galilean Transformation  3.4. Strain and Rotation Rates  3.5. Kinematics of Simple Plane Flows  3.6. Reynolds Transport Theorem  Exercises  Chapter 4. Conservation Laws  4.1. Introduction  4.2. Conservation of Mass  4.3. Stream Functions  4.4. Conservation of Momentum  4.5. Constitutive Equation for a Newtonian Fluid  4.6. Navier-Stokes Momentum Equation  4.7. Noninertial Frame of Reference  4.8. Conservation of Energy  4.9. Special Forms of the Equations  4.10. Boundary Conditions  4.11. Dimensionless Forms of the Equations and Dynamic Similarity  Exercises  Chapter 5. Vorticity Dynamics  5.1. Introduction  5.2. Kelvin’s and Helmholtz’s Theorems  5.3. Vorticity Equation in an Inertial Frame of Reference  5.4. Velocity Induced by a Vortex Filament: Law of Biot and Savart  5.5. Vorticity Equation in a Rotating Frame of Reference  5.6. Interaction of Vortices  5.7. Vortex Sheet  Exercises  Chapter 6. Computational Fluid Dynamics  6.1. Introduction  6.2. The Advection-Diffusion Equation  6.3. Incompressible Flows in Rectangular Domains  6.4. Flow in Complex Domains  6.5. Velocity-Pressure Method for Compressible Flow  6.6. More to Explore  Exercises  Chapter 7. Ideal Flow  7.1. Relevance of Irrotational Constant-Density Flow Theory  7.2. Two-Dimensional Stream Function and Velocity Potential  7.3. Construction of Elementary Flows in Two Dimensions  7.4. Complex Potential  7.5. Forces on a Two-Dimensional Body  7.6. Conformal Mapping  7.7. Axisymmetric Ideal Flow  7.8. Three-Dimensional Potential Flow and Apparent Mass  7.9. Concluding Remarks  Exercises  Chapter 8. Gravity Waves  8.1. Introduction  8.2. Linear Liquid-Surface Gravity Waves  8.3. Influence of Surface Tension  8.4. Standing Waves  8.5. Group Velocity, Energy Flux, and Dispersion  8.6. Nonlinear Waves in Shallow and Deep Water  8.7. Waves on a Density Interface  8.8. Internal Waves in a Continuously Stratified Fluid  Exercises  Chapter 9. Laminar Flow  9.1. Introduction  9.2. Exact Solutions for Steady Incompressible Viscous Flow  9.3. Elementary Lubrication Theory  9.4. Similarity Solutions for Unsteady Incompressible Viscous Flow  9.5. Flows with Oscillations  9.6. Low Reynolds Number Viscous Flow Past a Sphere  9.7. Final Remarks  Exercises  Chapter 10. Boundary Layers and Related Topics  10.1. Introduction  10.2. Boundary-Layer Thickness Definitions  10.3. Boundary Layer on a Flat Plate: Blasius Solution  10.4. Falkner-Skan Similarity Solutions of the Laminar Boundary-Layer Equations  10.5. von Karman Momentum Integral Equation  10.6. Thwaites’ Method  10.7. Transition, Pressure Gradients, and Boundary-Layer Separation  10.8. Flow Past a Circular Cylinder  10.9. Flow Past a Sphere and the Dynamics of Sports Balls  10.10. Two-Dimensional Jets  10.11. Secondary Flows  Exercises  Chapter 11. Instability  11.1. Introduction  11.2. Method of Normal Modes  11.3. Kelvin-Helmholtz Instability  11.4. Thermal Instability: The Bénard Problem  11.5. Double-Diffusive Instability  11.6. Centrifugal Instability: Taylor Problem  11.7. Instability of Continuously Stratified Parallel Flows  11.8. Squire’s Theorem and the Orr-Sommerfeld Equation  11.9. Inviscid Stability of Parallel Flows  11.10. Results for Parallel and Nearly Parallel Viscous Flows  11.11. Experimental Verification of Boundary-Layer Instability  11.12. Comments on Nonlinear Effects  11.13. Transition  11.14. Deterministic Chaos  Exercises  Chapter 12. Turbulence  12.1. Introduction  12.2. Historical Notes  12.3. Nomenclature and Statistics for Turbulent Flow  12.4. Correlations and Spectra  12.5. Averaged Equations of Motion  12.6. Homogeneous Isotropic Turbulence  12.7. Turbulent Energy Cascade and Spectrum  12.8. Free Turbulent Shear Flows  12.9. Wall-Bounded Turbulent Shear Flows  12.10. Turbulence Modeling  12.11. Turbulence in a Stratified Medium  12.12. Taylor’s Theory of Turbulent Dispersion  Exercises  Chapter 13. Geophysical Fluid Dynamics  13.1. Introduction  13.2. Vertical Variation of Density in the Atmosphere and Ocean  13.3. Equations of Motion for Geophysical Flows  13.4. Geostrophic Flow  13.5. Ekman Layers  13.6. Shallow-Water Equations  13.7. Normal Modes in a Continuously Stratified Layer  13.8. High- and Low-Frequency Regimes in Shallow-Water Equations  13.9. Gravity Waves with Rotation  13.10. Kelvin Wave  13.11. Potential Vorticity Conservation in Shallow-Water Theory  13.12. Internal Waves  13.13. Rossby Wave  13.14. Barotropic Instability  13.15. Baroclinic Instability  13.16. Geostrophic Turbulence  Exercises  Chapter 14. Aerodynamics  14.1. Introduction  14.2. Aircraft Terminology  14.3. Characteristics of Airfoil Sections  14.4. Conformal Transformation for Generating Airfoil Shapes  14.5. Lift of a Zhukhovsky Airfoil  14.6. Elementary Lifting Line Theory for Wings of Finite Span  14.7. Lift and Drag Characteristics of Airfoils  14.8. Propulsive Mechanisms of Fish and Birds  14.9. Sailing against the Wind  Exercises  Chapter 15. Compressible Flow  15.1. Introduction  15.2. Acoustics  15.3. One-Dimensional Steady Isentropic Compressible Flow in Variable-Area Ducts  15.4. Normal Shock Waves  15.5. Operation of Nozzles at Different Back Pressures  15.6. Effects of Friction and Heating in Constant-Area Ducts  15.7. One-Dimensional Unsteady Compressible Flow in Constant-Area Ducts  15.8. Two-Dimensional Steady Compressible Flow  15.9. Thin-Airfoil Theory in Supersonic Flow  Exercises  Chapter 16. Introduction to Biofluid Mechanics  16.1. Introduction  16.2. The Circulatory System in the Human Body  16.3. Modeling of Flow in Blood Vessels  16.4. Introduction to the Fluid Mechanics of Plants  Exercises  Appendix A. Conversion Factors, Constants, and Fluid Properties  Appendix B. Mathematical Tools and Resources  Appendix C. Founders of Modern Fluid Dynamics  Appendix D. Visual Resources  Index