目錄
Preface
Acknowledgments
Nomenclature
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
Literature Cited
Supplemental Reading
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
Literature Cited
Supplemental Reading
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
Literature Cited
Supplemental Reading
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
Literature Cited
Supplemental Reading
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
Literature Cited
Supplemental Reading
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
Literature Cited
Supplemental Reading
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
Literature Cited
Supplemental Reading
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
Literature Cited
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
Literature Cited
Supplemental Reading
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
Literature Cited
Supplemental Reading
11. Instability
11.1. Introduction
11.2. Method of Normal Modes
11.3. Kelvin-Helmholtz Instability
11.4. Thermal Instability: The B?nard 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
Literature Cited
Supplemental Reading
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
Literature Cited
Supplemental Reading
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. Highand 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
Literature Cited
Supplemental Reading
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
Literature Cited
Supplemental Reading
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
Literature Cited
Supplemental Reading
Appendix A
Appendix B
Appendix C
Appendix D
Index
16. Introduction to Biofluid Mechanics (Online Chapter)
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
Acknowledgments
Literature Cited
Supplemental Reading
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