Fluid Mechanics

Prefaces to the English Editions
E. M. Lifshitz
Notation
I. Ideal Fluids
§1 The Equation of Continuity
§2 Euler's Equation
§3 Hydrostatics
§4 The Condition That Convection Be 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 Internal Waves in an Incompressible Fluid
§14 Waves in a Rotating 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 Flow with Small Reynolds Numbers
§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 Stability of Rotary Flow
§28 Stability of Flow in a Pipe
§29 Instability of Tangential Discontinuities
§30 Quasi-periodic Flow and Frequency Locking
§31 Strange Attractors
§32 Transition to Turbulence by Period Doubling
§33 Fully Developed Turbulence
§34 The Velocity Correlation Functions
§35 The Turbulent Region and the Phenomenon of Separation
§36 The Turbulent Jet
§37 The Turbulent Wake
§38 Zhukovskiï's Theorem
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
§57 Convective Instability of a Fluid at Rest
VI. Diffusion
§58 The Equations of Fluid Dynamics for a Mixture of Fluids
§59 Coefficients of Mass Transfer and Thermal Diffusion
§60 Diffusion of Particles Suspended in a Fluid
VII. Surface Phenomena
§61 Laplace's Formula
§62 Capillary Waves
§63 The Effect of Adsorbed Films on the Motion of a Liquid
VIII. Sound
§64 Sound Waves
§65 The Energy and Momentum of Sound Waves
§66 Reflection and Refraction of Sound Waves
§67 Geometrical Acoustics
§68 Propagation of Sound in a Moving Medium
§69 Characteristic Vibrations
§70 Spherical Waves
§71 Cylindrical Waves
§72 The General Solution of the Wave Equation
§73 The Lateral Wave
§74 The Emission of Sound
§75 Sound Excitation by Turbulence
§76 The Reciprocity Principle
§77 Propagation of Sound in a Tube
§78 Scattering of Sound
§79 Absorption of Sound
§80 Acoustic Streaming
§81 Second Viscosity
IX. Shock Waves
§82 Propagation of Disturbances in a Moving Gas
§83 Steady Flow of a Gas
§84 Surfaces of Discontinuity
§85 The Shock Adiabatic
§86 Weak Shock Waves
§87 The Direction of Variation of Quantities in a Shock Wave
§88 Evolutionary Shock Waves
§89 Shock Waves in a Polytropic Gas
§90 Corrugation Instability of Shock Waves
§91 Shock Wave Propagation in a Pipe
§92 Oblique Shock Waves
§93 The Thickness of Shock Waves
§94 Shock Waves in a Relaxing Medium
§95 The Isothermal Discontinuity
§96 Weak Discontinuities
X. One-dimensional Gas Flow
§97 Flow of Gas Through a Nozzle
§98 Flow of a Viscous Gas in a Pipe
§99 One-dimensional Similarity Flow
§100 Discontinuities in the Initial Conditions
§101 One-dimensional Traveling Waves
§102 Formation of Discontinuities in a Sound Wave
§103 Characteristics
§104 Riemann Invariants
§105 Arbitrary One-dimensional Gas Flow
§106 A Strong Explosion
§107 An Imploding Spherical Shock Wave
§108 Shallow-water Theory
XI. The Intersection of Surfaces of Discontinuity
§109 Rarefaction Waves
§110 Classification of Intersections of Surfaces of Discontinuity
§111. The Intersection of Shock Waves with a Solid Surface
§112. Supersonic Flow Round an Angle
§113. Flow Past a Conical Obstacle
XII. Two-dimensional Gas Flow
§114. Potential Flow of a Gas
§115. Steady Simple Waves 438
§116. Chaplygin's Equation: The General Problem of Steady Two-dimensional Gas Flow
§117. Characteristics in Steady Two-dimensional Flow
§118. The Euler-Tricomi Equation. Transonic Flow
§119. Solutions of the Euler-Tricomi Equation Near non-singular Points of the Sonic Surface
§120. Flow at the Velocity of Sound
§121. The Reflection of a Weak Discontinuity from the Sonic Line
XIII. Flow Past Finite Bodies
§122. The Formation of Shock Waves in Supersonic Flow Past Bodies
§123. Supersonic Flow Past a Pointed Body
§124. Subsonic Flow Past a Thin Wing
§125. Supersonic Flow Past a Wing
§126. The Law of Transonic Similarity
§127. The Law of Hypersonic Similarity
XIV. Fluid Dynamics of Combustion
§128. Slow Combustion
§129. Detonation
§130. The Propagation of a Detonation Wave
§131. The Relation between the Different Modes of Combustion
§132. Condensation Discontinuities
XV. Relativistic Fluid Dynamics
§133. The Energy-momentum Tensor
§134. The Equations of Relativistic Fluid Dynamics
§135. Shock Waves in Relativistic Fluid Dynamics
§136. Relativistic Equations for Flow with Viscosity and Thermal Conduction
XVI. Dynamics of Superfluids
§137. Principal Properties of Superfluids
§138. The Thermo-mechanical Effect
§139. The Equations of Superfluid Dynamics
§14§. Dissipative Processes in Superfluids
§141. The Propagation of Sound in Superfluids
Index