Physical Fluid Dynamics

1. Introduction. - 1. 1 Preamble. - 1. 2 Scope of book. - 1. 3 Notation and definitions. - 2. Pipe and Channel Flow. - 2. 1 Introduction. - 2. 2 Laminar flow theory: channel. - 2. 3 Laminar flow theory: pipe. - 2. 4 The Reynolds number. - 2. 5 The entry length. - 2. 6 Transition to turbulent flow. - 2. 7 Relationship between flow rate and pressure gradient. - 3. Flow Past a Circular Cylinder. - 3. 1 Introduction. - 3. 2 The Reynolds number. - 3. 3 Flow patterns. - 3. 4 Drag. - 4. Convection in Horizontal Layers. - 4. 1 The configuration. - 4. 2 Onset of motion. - 4. 3 Flow regimes. - 5. Equations of Motion. - 5. 1 Introduction. - 5. 2 Fluid particles and continuum mechanics. - 5. 3 Eulerian and Langrangian co-ordinates. - 5. 4 Continuity equation. - 5. 5 The substantive derivative. - 5. 6 The NavierStokes equation. - 5. 7 Boundary conditions. - 5. 8 Condition for incompressibility. - Appendix: Derivation of viscous term of dynamical equation. - 6. Further Basic Ideas. - 6. 1 Streamlines streamtubes particle paths and streaklines. - 6. 2 Computations for flow past a circular cylinder. - 6. 3 The stream function. - 6. 4 Vorticity. - 6. 5 Vorticity equation. - 6. 6 Circulation. - 7. Dynamical Similarity. - 7. 1 Introduction. - 7. 2 Condition for dynamical similarity: Reynolds number. - 7. 3 Dependent quantities. - 7. 4 Other governing non-dimensional parameters. - 8. Low and High Reynolds Numbers. - 8. 1 Physical significance of the Reynolds number. - 8. 2 Low Reynolds number. - 8. 3 High Reynolds number. - 9. Some Solutions of the Viscous Flow Equations. - 9. 1 Introduction. - 9. 2 Poiseuille flow. - 9. 3 Rotating Couette flow. - 9. 4 Stokes flow past a sphere. - 9. 5 Low Reynolds number flow past a cylinder. - 10. Inviscid Flow. - 10. 1 Introduction. - 10. 2 Kelvin circulation theorem. - 10. 3 Irrotational motion. - 10. 4 Bernoulli's equation. - 10. 5 Drag in inviscidflow: d'Alembert's paradox'. - 10. 6 Applications of Bernoulli's equation. - 10. 7 Some definitions. - 11. Boundary Layers and Related Topics. - 11. 1 Boundary layer formation. - 11. 2 The boundary layer approximation. - 11. 3 Zero pressure gradient solution. - 11. 4 Boundary layer separation. - 11. 5 Drag on bluff bodies. - 11. 6 Streamlining. - 11. 7 Wakes. - 11. 8 Jets. - 11. 9 Momentum and energy in viscous flow. - 12. Lift. - 12. 1 Introduction. - 12. 2 Two-dimensional aerofoils. - 12. 3 Three-dimensional aerofoils. - 12. 4 Spinning bodies. - 13. Thermal Flows: Basic Equations and Concepts. - 13. 1 Introduction. - 13. 2 Equations of convection. - 13. 3 Classification of convective flows. - 13. 4 Forced convection. - 13. 5 Flow with concentration variations (mass transfer). - 14. Free Convection. - 14. 1 Introduction. - 14. 2 The governing non-dimensional parameters. - 14. 3 The adiabatic temperature gradient. - 14. 4 Free convection as a heat engine. - 14. 5 Convection from a heated vertical surface. - 14. 6 Thermal plumes. - 14. 7 Convection in fluid layers. - Appendix: The Boussinesq approximation in free convection. - 15. Flow in Rotating Fluids. - 15. 1 Introduction. - 15. 2 Centrifugal and Coriolis forces. - 15. 3 Geostrophic flow and the TaylorProud man theorem. - 15. 4 Taylor columns. - 15. 5 Ekman layers. - 15. 6 Intrinsic stability and inertial waves. - 15. 7 Rossby waves. - 15. 8 Convection in a rotating annulus. - 16. Stratified Flow. - 16. 1 Basic concepts. - 16. 2 Blocking. - 16. 3 Lee waves. - 16. 4 Internal waves. - 16. 5 Stratification and rotation. - 17. Instability Phenomena. - 17. 1 Introduction. - 17. 2 Surface tension instability of a liquid column. - 17. 3 Convection due to internal heat generation. - 17. 4 Convection due to surface tension variations. - 17. 5 Instability of rotating Couette flow. - 17. 6 Shear flowinstability. - 18. The Theory of Hydro Dynamic Stability. - 18. 1 The nature of linear stability theory. - 18. 2 Onset of Bénard convection. - 18. 3 Overstability. - 18. 4 Rotating Couette flow. - 18. 5 Boundary layer stability. - 19. Transition to Turbulence. - 19. 1 Boundary layer transition. - 19. 2 Transition in jets and other free shear flows. - 19. 3 Pipe flow transition. - 20. Turbulence. - 20. 1 The nature of turbulent motion. - 20. 2 Introduction to the statistical description of turbulent motion. - 20. 3 Formulation of the statistical description. - 20. 4 Turbulence equations. - 20. 5 Calculation methods. - 20. 6 Interpretation of correlations. - 20. 7 Spectra. - 20. 8 The concept of eddies. - 21. Homogeneous Isotropic Turbulence. - 21. 1 Introduction. - 21. 2 Space correlations and the closure problem. - 21. 3 Spectra and the energy cascade. - 21. 4 Dynamical processes of the energy cascade. - 22. The Structure of Turbulent Flows. - 22. 1 Introduction. - 22. 2 Reynolds number similarity and self-preservation. - 22. 3 Intermittency and entrainment. - 22. 4 The structure of a turbulent wake. - 22. 5 Turbulent motion near a wall. - 22. 6 Large eddies in a boundary layer. - 22. 7 The Coanda effect. -