# Fluid Mechanics

### Landau and Lifshitz: Course of Theoretical Physics, Volume 6

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Fluid Mechanics, Second Edition deals with fluid mechanics, that is, the theory of the motion of liquids and gases. Topics covered range from ideal fluids and viscous fluids to turbulence, boundary layers, thermal conduction, and diffusion. Surface phenomena, sound, and shock waves are also discussed, along with gas flow, combustion, superfluids, and relativistic fluid dynamics. This book is comprised of 16 chapters and begins with an overview of the fundamental equations of fluid dynamics, including Euler's equation and Bernoulli's equation. The reader is then introduced to the equations of motion of a viscous fluid; energy dissipation in an incompressible fluid; damping of gravity waves; and the mechanism whereby turbulence occurs. The following chapters explore the laminar boundary layer; thermal conduction in fluids; dynamics of diffusion of a mixture of fluids; and the phenomena that occur near the surface separating two continuous media. The energy and momentum of sound waves; the direction of variation of quantities in a shock wave; one- and two-dimensional gas flow; and the intersection of surfaces of discontinuity are also also considered. This monograph will be of interest to theoretical physicists.

## Table of Contents

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

## Product details

- No. of pages: 554
- Language: English
- Copyright: © Pergamon 1987
- Published: August 17, 1987
- Imprint: Pergamon
- eBook ISBN: 9781483161044

## About the Authors

### L D Landau

#### Affiliations and Expertise

Institute of Physical Problems, U.S.S.R. Academy of Sciences

### E. M. Lifshitz

## Ratings and Reviews

### Latest reviews

(Total rating for all reviews)

**Shoji W.**Tue May 15 2018**Fluid Mechanics**It's a great book. It covers the wide range of this subject. The description about acoustics in this book gives me a deeper insight than any other book.