Modern University in Physics

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 Navier-Stokes 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 inviscid flow: 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 Taylor-Proud 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 flow instability.- 18. The Theory of Hydro Dynamic Stability.- 18.1 The nature of linear stability theory.- 18.2 Onset of Be1. 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 Navier-Stokes 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 inviscid flow: 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 Taylor-Proud 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 flow instability.- 18. The Theory of Hydro Dynamic Stability.- 18.1 The nature of linear stability theory.- 18.2 Onset of Benard 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.- 22.8 Stratified shear flows.- 22.9 Reverse transition.- 23. Experimental Methods.- 23.1 General aspects of experimental fluid dynamics.- 23.2 Velocity measurement.- 23.3 Pressure and temperature measurement.- 23.4 Flow visualization.- 24. Practical Situations.- 24.1 Introduction.- 24.2 Cloud patterns.- 24.3 Waves in the atmospheric circulation.- 24.4 Continental drift and convection in the Earth's mantle.- 24.5 Solar granulation.- 24.6 Effluent dispersal.- 24.7 Wind effects on structures.- 24.8 Boundary layer control: vortex generators.- 24.9 Fluidics.- 24.10 Undulatory swimming.- 24.11 Convection from the human body.- 24.12 The flight of a boomerang.- Notation.- Problems.- Bibliography and References.