This volume studies the motion of fluids and the forces acting on them. It develops continuum models, governing equations, and analytical and computational methods.
Part I. Foundations of Fluid Mechanics
Chapter 1. Fluid Description
1.1 Continuum hypothesis 1.2 Properties of fluids 1.3 Fields: velocity, pressure, density 1.4 Eulerian and Lagrangian viewpoints 1.5 Examples
Chapter 2. Kinematics of Fluids
2.1 Flow maps 2.2 Velocity fields 2.3 Streamlines and pathlines 2.4 Deformation of fluid elements 2.5 Examples
Chapter 3. Conservation Laws
3.1 Mass conservation (continuity equation) 3.2 Momentum conservation 3.3 Energy conservation 3.4 Integral and differential forms 3.5 Applications
Part II. Governing Equations
Chapter 4. Euler Equations
4.1 Inviscid flow 4.2 Derivation 4.3 Properties 4.4 Applications 4.5 Examples
Chapter 5. Navier–Stokes Equations
5.1 Viscous flow 5.2 Stress tensor for fluids 5.3 Derivation 5.4 Boundary conditions 5.5 Applications
Chapter 6. Special Flows
6.1 Potential flow 6.2 Incompressible flow 6.3 Compressible flow 6.4 Applications 6.5 Examples
Part III. Analytical Methods
Chapter 7. Exact Solutions
7.1 Simple flows 7.2 Laminar flows 7.3 Similarity solutions 7.4 Applications 7.5 Examples
Chapter 8. Vorticity and Circulation
8.1 Vorticity 8.2 Kelvin’s theorem 8.3 Vortex dynamics 8.4 Applications 8.5 Examples
Chapter 9. Boundary Layers
9.1 Boundary layer theory 9.2 Prandtl equations 9.3 Separation phenomena 9.4 Applications 9.5 Examples
Part IV. Turbulence and Stability
Chapter 10. Stability of Flows
10.1 Linear stability analysis 10.2 Instabilities 10.3 Transition to turbulence 10.4 Applications 10.5 Examples
Chapter 11. Turbulence
11.1 Characteristics 11.2 Statistical description 11.3 Energy cascade 11.4 Applications 11.5 Examples
Chapter 12. Modeling Turbulence
12.1 Reynolds-averaged equations 12.2 Closure models 12.3 Large eddy simulation (overview) 12.4 Applications 12.5 Examples
Part V. Compressible and Multiphase Flow
Chapter 13. Compressible Flow
13.1 Equations of state 13.2 Shock waves 13.3 Expansion waves 13.4 Applications 13.5 Examples
Chapter 14. Multiphase Flow
14.1 Mixture models 14.2 Interface dynamics 14.3 Applications 14.4 Examples 14.5 Connections
Chapter 15. Free Surface Flows
15.1 Surface tension 15.2 Capillarity 15.3 Waves 15.4 Applications 15.5 Examples
Part VI. Numerical Methods
Chapter 16. Discretization Methods
16.1 Finite difference methods 16.2 Finite volume methods 16.3 Finite element methods 16.4 Applications 16.5 Examples
Chapter 17. Computational Fluid Dynamics
17.1 Grid generation 17.2 Stability and convergence 17.3 Simulation techniques 17.4 Applications 17.5 Examples
Chapter 18. High-Performance Simulation
18.1 Parallel computing 18.2 Large-scale simulations 18.3 Visualization 18.4 Applications 18.5 Examples
Part VII. Applications
Chapter 19. Aerodynamics
19.1 Airfoil theory 19.2 Lift and drag 19.3 Flow around bodies 19.4 Applications 19.5 Examples
Chapter 20. Geophysical Fluid Dynamics
20.1 Ocean and atmosphere 20.2 Rotation effects 20.3 Waves and circulation 20.4 Applications 20.5 Examples
Chapter 21. Engineering Systems
21.1 Pipelines 21.2 Turbomachinery 21.3 Heat transfer 21.4 Applications 21.5 Examples
Part VIII. Research Directions
Chapter 22. Advanced Topics
22.1 Nonlinear PDE analysis 22.2 Turbulence theory 22.3 Multiscale flows 22.4 Modern developments 22.5 Emerging areas
Chapter 23. Open Problems
23.1 Navier–Stokes existence and smoothness 23.2 Turbulence modeling 23.3 Computational challenges 23.4 High Reynolds number flows 23.5 Future directions
Chapter 24. Historical and Conceptual Notes
24.1 Development of fluid mechanics 24.2 Key contributors 24.3 Evolution of governing equations 24.4 Cross-disciplinary impact 24.5 Summary
Appendix
A. Fluid mechanics formulas B. Dimensionless numbers reference C. Proof techniques checklist D. Numerical schemes reference E. Cross-reference to other MSC branches