Course of Theoretical Physics Vol- VI : Fluid Mechanics

Preface to the English Edition

Notation

I. Ideal Fluids

§1. The Equation of Continuity

§2. Euler's Equation

§3. Hydrostatics

§4. The Condition that Convection is Absent

§5. Bernoulli's Equation

§6. The Energy Flux

§7. The Momentum Flux

§8. The Conservation of Circulation

§9. Potential Flow

§10. Incompressible Fluids

§11. The Drag Force in Potential Flow Past a Body

§12. Gravity Waves

§13. Long Gravity Waves

§14. Waves in an Incompressible Fluid

II. Viscous Fluids

§15. The Equations of Motion of a Viscous Fluid

§16. Energy Dissipation in an Incompressible Fluid

§17. Flow in a Pipe

§18. Flow between Rotating Cylinders

§19. The Law of Similarity

§20. Stokes Formula

§21. The Laminar Wake

§22. The Viscosity of Suspensions

§23. Exact Solutions of the Equations of Motion for a Viscous Fluid

§24. Oscillatory Motion in a Viscous Fluid

§25. Damping of Gravity Waves

III. Turbulence

§26. Stability of Steady Flow

§27. The Onset of Turbulence

§28. Stability of Flow between Rotating Cylinders

§29. Stability of Flow in a Pipe

§30. Instability of Tangential Discontinuities

§31. Fully Developed Turbulence

§32. Local Turbulence

§33. The Velocity Correlation

§34. The Turbulent Region and the Phenomenon of Separation

§35. The Turbulent Jet

§36. The Turbulent Wake

§37. Zhukovskii's Theorem

§38. Isotropic Turbulence

IV. Boundary Layers

§39. The Laminar Boundary Layer

§40. Flow Near the Line of Separation

§41. Stability of Flow in the Laminar Boundary Layer

§42. The Logarithmic Velocity Profile

§43. Turbulent Flow in Pipes

§44. The Turbulent Boundary Layer

§45. The Drag Crisis

§46. Flow Past Streamlined Bodies

§47. Induced Drag

§48. The Lift of a Thin Wing

V. Thermal Conduction in Fluids

§49. The General Equation of Heat Transfer

§50. Thermal Conduction in an Incompressible Fluid

§51. Thermal Conduction in an Infinite Medium

§52. Thermal Conduction in a Finite Medium

§53. The Similarity Law for Heat Transfer

§54. Heat Transfer in a Boundary Layer

§55. Heating of a Body in a Moving Fluid

§56. Free Convection

VI. Diffusion

§57. The Equations of Fluid Dynamics for a Mixture of Fluids

§58. Coefficients of Mass Transfer and Thermal Diffusion

§59. Diffusion of Particles Suspended in a Fluid

VII. Surface Phenomena

§60. Laplace's Formula

§61. Capillary Waves

§62. The Effect of Adsorbed Films on the Motion of a Liquid

VIII. Sound

§63. Sound Waves

§64. The Energy and Momentum of Sound Waves

§65. Reflection and Refraction of Sound Waves

§66. Geometrical Acoustics

§67. Propagation of Sound in a Moving Medium

§68. Characteristic Vibrations

§69. Spherical Waves

§70. Cylindrical Waves

§71. The General Solution of the Wave Equation

§72. The Lateral Wave

§73. The Emission of Sound

§74. The Reciprocity Principle

§75. Propagation of Sound in a Tube

§76. Scattering of Sound

§77. Absorption of Sound

§78. Second Viscosity

IX. Shock Waves

§79. Propagation of Disturbances in a Moving Gas

§80. Steady fFow of a Gas

§81. Surfaces of Discontinuity

§82. The Shock Adiabatic

§83. Weak Shock Waves

§84. The Direction of Variation of Quantities in a Shock Wave

§85. Shock Waves in a Perfect Gas

§86. Oblique Shock Waves

§87. The Thickness of Shock Waves

§88. The Isothermal Discontinuity

§89. Weak Discontinuities

X. One-dimensional Gas Flow

§90. Flow of Gas Through a Nozzle

§91. Flow of a Viscous Gas in a Pipe

§92. One-dimensional Similarity Flow

§93. Discontinuities in the Initial Conditions

§94. One-dimensional Traveling Waves

§95. Formation of Discontinuities in a Sound Wave

§96. Characteristics

§97. Riemann Invariants

§98. Arbitrary One-dimensional Gas Flow

§99. The Propagation of Strong Shock Waves

§100. Shallow-water Theory

XI. The Intersection of Surfaces of Discontinuity

§101. Rarefaction Waves

§102. The Intersection of Shock Waves

§103. The Intersection of Shock Waves with a Solid Surface

§104. Supersonic Flow Round an Angle

§105. Flow Past a Conical Obstacle

XII. Two-dimensional Gas Flow

§106. Potential Flow of a Gas

§107. Steady Simple Waves

§108. Chaplygin's Equation: The General Problem of Steady Two-dimensional Gas Flow

§109. Characteristics in Steady Two-dimensional Flow

§110. The Euler-Tricomi Equation. Transonic Flow

§111. Solutions of the Euler-Tricomi Equation near non-singular Points of the Sonic Surface

§112. Flow at the Velocity of Sound

§113. The Intersection of Discontinuities with the Transition Line

XIII. Flow Past Finite Bodies

§114. The Formation of Shock Waves in Supersonic Flow Past Bodies

§115. Supersonic Flow Past a Pointed Body

§116. Subsonic Flow Past a Thin Wing

§117. Supersonic Flow Past a Wing

§118. The Law of Transonic Similarity

§119. The Law of Hypersonic Similarity

XIV. Fluid Dynamics of Combustion

§120. Slow Combustion

§121. Detonation

§122. The Propagation of a Detonation Wave

§123. The Relation between the Different Modes of Combustion

§124. Condensation Discontinuities

XV. Relativistic Fluid Dynamics

§125. The Energy-momentum Tensor

§126. The Equations of Relativistic Fluid Dynamics

§127. Relativistic Equations for Dissipative Processes

XVI. Dynamics of Super-fluids

§128. Principal Properties of Super-fluids

§129. The Thermo-mechanical Effect

§130. The Equations of Super-fluid Dynamics

§131. The Propagation of Sound in a Super-fluid

XVII. Fluctuations in Fluid Dynamics

§132. The General Theory of Fluctuations in Fluid Dynamics

§133. Fluctuations in an Infinite Medium

Index