Kip S. Thorne, winner of the Nobel Prize in physics, is the Feynman Professor Emeritus of Theoretical Physics at Caltech. His books include Gravitation (Princeton) and Black Holes and Time Warps: Einstein’s Outrageous Legacy. Roger D. Blandford, winner of the Crafoord and Shaw prizes in astronomy, is the Luke Blossom Professor in the School of Humanities and Sciences and founding director of the Kavli Institute for Particle Astrophysics and Cosmology at Stanford University.

• List of BoxesPrefaceContents of Modern Classical Physics, volumes 1–5PART IV ELASTICITY11 Elastostatics11.1 Overview11.2 Displacement and Strain11.2.1 Displacement Vector and Its Gradient11.2.2 Expansion, Rotation, Shear, and Strain11.3 Stress, Elastic Moduli, and Elastostatic Equilibrium11.3.1 Stress Tensor11.3.2 Realm of Validity for Hooke’s Law11.3.3 Elastic Moduli and Elastostatic Stress Tensor11.3.4 Energy of Deformation11.3.5 Thermoelasticity11.3.6 Molecular Origin of Elastic Stress; Estimate of Moduli11.3.7 Elastostatic Equilibrium: Navier-Cauchy Equation11.4 Young’s Modulus and Poisson’s Ratio for an Isotropic Material: A Simple Elastostatics Problem11.5 Reducing the Elastostatic Equations to 1 Dimension for a Bent Beam: Cantilever Bridge, Foucault Pendulum, DNA Molecule, Elastica11.6 Buckling and Bifurcation of Equilibria11.6.1 Elementary Theory of Buckling and Bifurcation11.6.2 Collapse of theWorld Trade Center Buildings11.6.3 Buckling with Lateral Force; Connection to Catastrophe Theory11.6.4 Other Bifurcations: Venus Fly Trap, Whirling Shaft, Triaxial Stars, and Onset of Turbulence11.7 Reducing the Elastostatic Equations to 2 Dimensions for a Deformed Thin Plate: Stress Polishing a Telescope Mirror11.8 Cylindrical and Spherical Coordinates: Connection Coefficients and Components of the Gradient of the Displacement Vector11.9 Solving the 3-Dimensional Navier-Cauchy Equation in Cylindrical Coordinates11.9.1 Simple Methods: Pipe Fracture and Torsion Pendulum11.9.2 Separation of Variables and Green’s Functions: Thermoelastic Noise in MirrorsBibliographic Note12 Elastodynamics12.1 Overview12.2 Basic Equations of Elastodynamics; Waves in a Homogeneous Medium12.2.1 Equation of Motion for a Strained Elastic Medium12.2.2 Elastodynamic Waves12.2.3 Longitudinal Sound Waves12.2.4 Transverse Shear Waves12.2.5 Energy of Elastodynamic Waves12.3 Waves in Rods, Strings, and Beams12.3.1 Compression Waves in a Rod12.3.2 Torsion Waves in a Rod12.3.3 Waves on Strings12.3.4 Flexural Waves on a Beam12.3.5 Bifurcation of Equilibria and Buckling (Once More)12.4 Body Waves and Surface Waves—Seismology and Ultrasound12.4.1 Body Waves12.4.2 Edge Waves12.4.3 Green’s Function for a Homogeneous Half-Space12.4.4 Free Oscillations of Solid Bodies12.4.5 Seismic Tomography12.4.6 Ultrasound; Shock Waves in Solids12.5 The Relationship of Classical Waves to Quantum Mechanical ExcitationsBibliographic NotePART V FLUID DYNAMICS13 Foundations of Fluid Dynamic13.1 Overview13.2 The Macroscopic Nature of a Fluid: Density, Pressure, Flow Velocity; Liquids versus Gases13.3 Hydrostatics13.3.1 Archimedes’ Law13.3.2 Nonrotating Stars and Planets13.3.3 Rotating Fluids13.4 Conservation Laws13.5 The Dynamics of an Ideal Fluid13.5.1 Mass Conservation13.5.2 Momentum Conservation13.5.3 Euler Equation13.5.4 Bernoulli’s Theorem13.5.5 Conservation of Energy13.6 Incompressible Flows13.7 Viscous Flows with Heat Conduction13.7.1 Decomposition of the Velocity Gradient into Expansion, Vorticity, and Shear13.7.2 Navier-Stokes Equation13.7.3 Molecular Origin of Viscosity13.7.4 Energy Conservation and Entropy Production13.7.5 Reynolds Number13.7.6 Pipe Flow13.8 Relativistic Dynamics of a Perfect Fluid13.8.1 Stress-Energy Tensor and Equations of Relativistic Fluid Mechanics13.8.2 Relativistic Bernoulli Equation and Ultrarelativistic Astrophysical Jets13.8.3 Nonrelativistic Limit of the Stress-Energy TensorBibliographic Note14 Vorticity14.1 Overview14.2 Vorticity, Circulation, and Their Evolution14.3 Low-Reynolds-Number Flow—Stokes Flow and Sedimentation14.3.1 Motivation: Climate Change14.3.2 Stokes Flow14.3.3 Sedimentation Rate14.4 High-Reynolds-Number Flow—Laminar Boundary Layers14.4.1 Blasius Velocity Profile Near a Flat Plate: Stream Function and Similarity Solution14.4.2 Blasius Vorticity Profile14.4.3 Viscous Drag Force on a Flat Plate14.4.4 Boundary Layer Near a Curved Surface: Separation14.5 Nearly Rigidly Rotating Flows—Earth’s Atmosphere and Oceans14.5.1 Equations of Fluid Dynamics in a Rotating Reference Frame14.5.2 Geostrophic Flows14.5.3 Taylor-Proudman Theorem14.5.4 Ekman Boundary Layers14..6 Instabilities of Shear Flows—Billow Clouds and Turbulence in the Stratosphere14.6.1 Discontinuous Flow: Kelvin-Helmholtz Instability14.6.2 Discontinuous Flow with Gravity14.6.3 Smoothly Stratified Flows: Rayleigh and Richardson Criteria for InstabilityBibliographic Note15 Turbulence15.1 Overview15.2 The Transition to Turbulence—Flow Past a Cylinder15.3 Empirical Description of Turbulence15.4 Semiquantitative Analysis of Turbulence15.4.1 Weak-Turbulence Formalism15.4.2 Turbulent Viscosity15.4.3 TurbulentWakes and Jets; Entrainment; the Coanda Effect15.4.4 Kolmogorov Spectrum for Fully Developed, Homogeneous, Isotropic Turbulence15.5 Turbulent Boundary Layers15.5.1 Profile of a Turbulent Boundary Layer15.5.2 Coanda Effect and Separation in a Turbulent Boundary Layer15.5.3 Instability of a Laminar Boundary Layer15.5.4 Flight of a Ball15.6 The Route to Turbulence—Onset of Chaos15.6.1 Rotating Couette Flow15.6.2 Feigenbaum Sequence, Poincaré Maps, and the Period-Doubling Route to Turbulence in Convection15.6.3 Other Routes to Turbulent Convection15.6.4 Extreme Sensitivity to Initial ConditionsBibliographic Note16 Waves16.1 Overview16.2 Gravity Waves on and beneath the Surface of a Fluid16.2.1 Deep-Water Waves and Their Excitation and Damping16.2.2 Shallow-Water Waves16.2.3 Capillary Waves and Surface Tension16.2.4 Helioseismology16.3 Nonlinear Shallow-Water Waves and Solitons16.3.1 Korteweg–de Vries (KdV) Equation16.3.2 Physical Effects in the KdV Equation16.3.3 Single-Soliton Solution16.3.4 Two-Soliton Solution16.3.5 Solitons in Contemporary Physics16.4 Rossby Waves in a Rotating Fluid16.5 Sound Waves16.5.1 Wave Energy16.5.2 Sound Generation16.5.3 Radiation Reaction, Runaway Solutions, and Matched Asymptotic ExpansionsBibliographic Note17 Compressible and Supersonic Flow17.1 Overview17.2 Equations of Compressible Flow17.3 Stationary, Irrotational, Quasi-1-Dimensional Flow17.3.1 Basic Equations; Transition from Subsonic to Supersonic Flow17.3.2 Setting up a Stationary, Transonic Flow17.3.3 Rocket Engines17.4 Dimensional, Time-Dependent Flow17.4.1 Riemann Invariants17.4.2 Shock Tube17.5 Shock Fronts17.5.1 Junction Conditions across a Shock; Rankine-Hugoniot Relations17.5.2 Junction Conditions for Ideal Gas with Constant γ17.5.3 Internal Structure of a Shock17.5.4 Mach Cone17.6 Self-Similar Solutions—Sedov-Taylor BlastWave17.6.1 The Sedov-Taylor Solution17.6.2 Atomic Bomb17.6.3 SupernovaeBibliographic Note18 Convection18.1 Overview18.2 Diffusive Heat Conduction—Cooling a Nuclear Reactor; Thermal Boundary Layers18.3 Boussinesq Approximation18.4 Rayleigh-Bénard Convection18.5 Convection in Stars18.6 Double Diffusion—Salt FingersBibliographic NoteApp. A Newtonian Physics: Geometric Viewpoint1.1 Introduction1.1.1 The Geometric Viewpoint on the Laws of Physics1.1.2 Purposes of This Chapter1.1.3 Overview of This Chapter1.2 Foundational Concepts1.3 Tensor Algebra without a Coordinate System1.4 Particle Kinetics and Lorentz Force in Geometric Language1.5 Component Representation of Tensor Algebra1.5.1 Slot-Naming Index Notation1.5.2 Particle Kinetics in Index Notation1.6 Orthogonal Transformations of Bases1.7 Differentiation of Scalars, Vectors, and Tensors; Cross Product and Curl1.8 Volumes, Integration, and Integral Conservation Laws1.8.1 Gauss’s and Stokes’ Theorems11.9 The Stress Tensor and Momentum Conservation1.9.1 Examples: Electromagnetic Field and Perfect Fluid1.9.2 Conservation of Momentum1.10 Geometrized Units and Relativistic Particles for Newtonian Readers1.10.1 Geometrized Units1.10.2 Energy and Momentum of a Moving ParticleBibliographic NoteReferencesName IndexContents of the Unified Work, Modern Classical PhysicsPreface to Modern Classical PhysicsAcknowledgments for Modern Classical Physics

"Kip S. Thorne, Co-Winner of the 2017 Nobel Prize in Physics"

Kip S. Thorne, winner of the Nobel Prize in physics, is the Feynman Professor Emeritus of Theoretical Physics at Caltech. His books include Gravitation (Princeton) and Black Holes and Time Warps: Einstein’s Outrageous Legacy. Roger D. Blandford, winner of the Crafoord and Shaw prizes in astronomy, is the Luke Blossom Professor in the School of Humanities and Sciences and founding director of the Kavli Institute for Particle Astrophysics and Cosmology at Stanford University.

• List of BoxesPrefaceContents of Modern Classical Physics, volumes 1–5PART IV ELASTICITY11 Elastostatics11.1 Overview11.2 Displacement and Strain11.2.1 Displacement Vector and Its Gradient11.2.2 Expansion, Rotation, Shear, and Strain11.3 Stress, Elastic Moduli, and Elastostatic Equilibrium11.3.1 Stress Tensor11.3.2 Realm of Validity for Hooke’s Law11.3.3 Elastic Moduli and Elastostatic Stress Tensor11.3.4 Energy of Deformation11.3.5 Thermoelasticity11.3.6 Molecular Origin of Elastic Stress; Estimate of Moduli11.3.7 Elastostatic Equilibrium: Navier-Cauchy Equation11.4 Young’s Modulus and Poisson’s Ratio for an Isotropic Material: A Simple Elastostatics Problem11.5 Reducing the Elastostatic Equations to 1 Dimension for a Bent Beam: Cantilever Bridge, Foucault Pendulum, DNA Molecule, Elastica11.6 Buckling and Bifurcation of Equilibria11.6.1 Elementary Theory of Buckling and Bifurcation11.6.2 Collapse of theWorld Trade Center Buildings11.6.3 Buckling with Lateral Force; Connection to Catastrophe Theory11.6.4 Other Bifurcations: Venus Fly Trap, Whirling Shaft, Triaxial Stars, and Onset of Turbulence11.7 Reducing the Elastostatic Equations to 2 Dimensions for a Deformed Thin Plate: Stress Polishing a Telescope Mirror11.8 Cylindrical and Spherical Coordinates: Connection Coefficients and Components of the Gradient of the Displacement Vector11.9 Solving the 3-Dimensional Navier-Cauchy Equation in Cylindrical Coordinates11.9.1 Simple Methods: Pipe Fracture and Torsion Pendulum11.9.2 Separation of Variables and Green’s Functions: Thermoelastic Noise in MirrorsBibliographic Note12 Elastodynamics12.1 Overview12.2 Basic Equations of Elastodynamics; Waves in a Homogeneous Medium12.2.1 Equation of Motion for a Strained Elastic Medium12.2.2 Elastodynamic Waves12.2.3 Longitudinal Sound Waves12.2.4 Transverse Shear Waves12.2.5 Energy of Elastodynamic Waves12.3 Waves in Rods, Strings, and Beams12.3.1 Compression Waves in a Rod12.3.2 Torsion Waves in a Rod12.3.3 Waves on Strings12.3.4 Flexural Waves on a Beam12.3.5 Bifurcation of Equilibria and Buckling (Once More)12.4 Body Waves and Surface Waves—Seismology and Ultrasound12.4.1 Body Waves12.4.2 Edge Waves12.4.3 Green’s Function for a Homogeneous Half-Space12.4.4 Free Oscillations of Solid Bodies12.4.5 Seismic Tomography12.4.6 Ultrasound; Shock Waves in Solids12.5 The Relationship of Classical Waves to Quantum Mechanical ExcitationsBibliographic NotePART V FLUID DYNAMICS13 Foundations of Fluid Dynamic13.1 Overview13.2 The Macroscopic Nature of a Fluid: Density, Pressure, Flow Velocity; Liquids versus Gases13.3 Hydrostatics13.3.1 Archimedes’ Law13.3.2 Nonrotating Stars and Planets13.3.3 Rotating Fluids13.4 Conservation Laws13.5 The Dynamics of an Ideal Fluid13.5.1 Mass Conservation13.5.2 Momentum Conservation13.5.3 Euler Equation13.5.4 Bernoulli’s Theorem13.5.5 Conservation of Energy13.6 Incompressible Flows13.7 Viscous Flows with Heat Conduction13.7.1 Decomposition of the Velocity Gradient into Expansion, Vorticity, and Shear13.7.2 Navier-Stokes Equation13.7.3 Molecular Origin of Viscosity13.7.4 Energy Conservation and Entropy Production13.7.5 Reynolds Number13.7.6 Pipe Flow13.8 Relativistic Dynamics of a Perfect Fluid13.8.1 Stress-Energy Tensor and Equations of Relativistic Fluid Mechanics13.8.2 Relativistic Bernoulli Equation and Ultrarelativistic Astrophysical Jets13.8.3 Nonrelativistic Limit of the Stress-Energy TensorBibliographic Note14 Vorticity14.1 Overview14.2 Vorticity, Circulation, and Their Evolution14.3 Low-Reynolds-Number Flow—Stokes Flow and Sedimentation14.3.1 Motivation: Climate Change14.3.2 Stokes Flow14.3.3 Sedimentation Rate14.4 High-Reynolds-Number Flow—Laminar Boundary Layers14.4.1 Blasius Velocity Profile Near a Flat Plate: Stream Function and Similarity Solution14.4.2 Blasius Vorticity Profile14.4.3 Viscous Drag Force on a Flat Plate14.4.4 Boundary Layer Near a Curved Surface: Separation14.5 Nearly Rigidly Rotating Flows—Earth’s Atmosphere and Oceans14.5.1 Equations of Fluid Dynamics in a Rotating Reference Frame14.5.2 Geostrophic Flows14.5.3 Taylor-Proudman Theorem14.5.4 Ekman Boundary Layers14..6 Instabilities of Shear Flows—Billow Clouds and Turbulence in the Stratosphere14.6.1 Discontinuous Flow: Kelvin-Helmholtz Instability14.6.2 Discontinuous Flow with Gravity14.6.3 Smoothly Stratified Flows: Rayleigh and Richardson Criteria for InstabilityBibliographic Note15 Turbulence15.1 Overview15.2 The Transition to Turbulence—Flow Past a Cylinder15.3 Empirical Description of Turbulence15.4 Semiquantitative Analysis of Turbulence15.4.1 Weak-Turbulence Formalism15.4.2 Turbulent Viscosity15.4.3 TurbulentWakes and Jets; Entrainment; the Coanda Effect15.4.4 Kolmogorov Spectrum for Fully Developed, Homogeneous, Isotropic Turbulence15.5 Turbulent Boundary Layers15.5.1 Profile of a Turbulent Boundary Layer15.5.2 Coanda Effect and Separation in a Turbulent Boundary Layer15.5.3 Instability of a Laminar Boundary Layer15.5.4 Flight of a Ball15.6 The Route to Turbulence—Onset of Chaos15.6.1 Rotating Couette Flow15.6.2 Feigenbaum Sequence, Poincaré Maps, and the Period-Doubling Route to Turbulence in Convection15.6.3 Other Routes to Turbulent Convection15.6.4 Extreme Sensitivity to Initial ConditionsBibliographic Note16 Waves16.1 Overview16.2 Gravity Waves on and beneath the Surface of a Fluid16.2.1 Deep-Water Waves and Their Excitation and Damping16.2.2 Shallow-Water Waves16.2.3 Capillary Waves and Surface Tension16.2.4 Helioseismology16.3 Nonlinear Shallow-Water Waves and Solitons16.3.1 Korteweg–de Vries (KdV) Equation16.3.2 Physical Effects in the KdV Equation16.3.3 Single-Soliton Solution16.3.4 Two-Soliton Solution16.3.5 Solitons in Contemporary Physics16.4 Rossby Waves in a Rotating Fluid16.5 Sound Waves16.5.1 Wave Energy16.5.2 Sound Generation16.5.3 Radiation Reaction, Runaway Solutions, and Matched Asymptotic ExpansionsBibliographic Note17 Compressible and Supersonic Flow17.1 Overview17.2 Equations of Compressible Flow17.3 Stationary, Irrotational, Quasi-1-Dimensional Flow17.3.1 Basic Equations; Transition from Subsonic to Supersonic Flow17.3.2 Setting up a Stationary, Transonic Flow17.3.3 Rocket Engines17.4 Dimensional, Time-Dependent Flow17.4.1 Riemann Invariants17.4.2 Shock Tube17.5 Shock Fronts17.5.1 Junction Conditions across a Shock; Rankine-Hugoniot Relations17.5.2 Junction Conditions for Ideal Gas with Constant γ17.5.3 Internal Structure of a Shock17.5.4 Mach Cone17.6 Self-Similar Solutions—Sedov-Taylor BlastWave17.6.1 The Sedov-Taylor Solution17.6.2 Atomic Bomb17.6.3 SupernovaeBibliographic Note18 Convection18.1 Overview18.2 Diffusive Heat Conduction—Cooling a Nuclear Reactor; Thermal Boundary Layers18.3 Boussinesq Approximation18.4 Rayleigh-Bénard Convection18.5 Convection in Stars18.6 Double Diffusion—Salt FingersBibliographic NoteApp. A Newtonian Physics: Geometric Viewpoint1.1 Introduction1.1.1 The Geometric Viewpoint on the Laws of Physics1.1.2 Purposes of This Chapter1.1.3 Overview of This Chapter1.2 Foundational Concepts1.3 Tensor Algebra without a Coordinate System1.4 Particle Kinetics and Lorentz Force in Geometric Language1.5 Component Representation of Tensor Algebra1.5.1 Slot-Naming Index Notation1.5.2 Particle Kinetics in Index Notation1.6 Orthogonal Transformations of Bases1.7 Differentiation of Scalars, Vectors, and Tensors; Cross Product and Curl1.8 Volumes, Integration, and Integral Conservation Laws1.8.1 Gauss’s and Stokes’ Theorems11.9 The Stress Tensor and Momentum Conservation1.9.1 Examples: Electromagnetic Field and Perfect Fluid1.9.2 Conservation of Momentum1.10 Geometrized Units and Relativistic Particles for Newtonian Readers1.10.1 Geometrized Units1.10.2 Energy and Momentum of a Moving ParticleBibliographic NoteReferencesName IndexContents of the Unified Work, Modern Classical PhysicsPreface to Modern Classical PhysicsAcknowledgments for Modern Classical Physics

"Kip S. Thorne, Co-Winner of the 2017 Nobel Prize in Physics"

Kip S. Thorne, winner of the Nobel Prize in physics, is the Feynman Professor Emeritus of Theoretical Physics at Caltech. His books include Gravitation (Princeton) and Black Holes and Time Warps: Einstein’s Outrageous Legacy. Roger D. Blandford, winner of the Crafoord and Shaw prizes in astronomy, is the Luke Blossom Professor in the School of Humanities and Sciences and founding director of the Kavli Institute for Particle Astrophysics and Cosmology at Stanford University.

• List of BoxesPrefaceContents of Modern Classical Physics, volumes 1–5PART IV ELASTICITY11 Elastostatics11.1 Overview11.2 Displacement and Strain11.2.1 Displacement Vector and Its Gradient11.2.2 Expansion, Rotation, Shear, and Strain11.3 Stress, Elastic Moduli, and Elastostatic Equilibrium11.3.1 Stress Tensor11.3.2 Realm of Validity for Hooke’s Law11.3.3 Elastic Moduli and Elastostatic Stress Tensor11.3.4 Energy of Deformation11.3.5 Thermoelasticity11.3.6 Molecular Origin of Elastic Stress; Estimate of Moduli11.3.7 Elastostatic Equilibrium: Navier-Cauchy Equation11.4 Young’s Modulus and Poisson’s Ratio for an Isotropic Material: A Simple Elastostatics Problem11.5 Reducing the Elastostatic Equations to 1 Dimension for a Bent Beam: Cantilever Bridge, Foucault Pendulum, DNA Molecule, Elastica11.6 Buckling and Bifurcation of Equilibria11.6.1 Elementary Theory of Buckling and Bifurcation11.6.2 Collapse of theWorld Trade Center Buildings11.6.3 Buckling with Lateral Force; Connection to Catastrophe Theory11.6.4 Other Bifurcations: Venus Fly Trap, Whirling Shaft, Triaxial Stars, and Onset of Turbulence11.7 Reducing the Elastostatic Equations to 2 Dimensions for a Deformed Thin Plate: Stress Polishing a Telescope Mirror11.8 Cylindrical and Spherical Coordinates: Connection Coefficients and Components of the Gradient of the Displacement Vector11.9 Solving the 3-Dimensional Navier-Cauchy Equation in Cylindrical Coordinates11.9.1 Simple Methods: Pipe Fracture and Torsion Pendulum11.9.2 Separation of Variables and Green’s Functions: Thermoelastic Noise in MirrorsBibliographic Note12 Elastodynamics12.1 Overview12.2 Basic Equations of Elastodynamics; Waves in a Homogeneous Medium12.2.1 Equation of Motion for a Strained Elastic Medium12.2.2 Elastodynamic Waves12.2.3 Longitudinal Sound Waves12.2.4 Transverse Shear Waves12.2.5 Energy of Elastodynamic Waves12.3 Waves in Rods, Strings, and Beams12.3.1 Compression Waves in a Rod12.3.2 Torsion Waves in a Rod12.3.3 Waves on Strings12.3.4 Flexural Waves on a Beam12.3.5 Bifurcation of Equilibria and Buckling (Once More)12.4 Body Waves and Surface Waves—Seismology and Ultrasound12.4.1 Body Waves12.4.2 Edge Waves12.4.3 Green’s Function for a Homogeneous Half-Space12.4.4 Free Oscillations of Solid Bodies12.4.5 Seismic Tomography12.4.6 Ultrasound; Shock Waves in Solids12.5 The Relationship of Classical Waves to Quantum Mechanical ExcitationsBibliographic NotePART V FLUID DYNAMICS13 Foundations of Fluid Dynamic13.1 Overview13.2 The Macroscopic Nature of a Fluid: Density, Pressure, Flow Velocity; Liquids versus Gases13.3 Hydrostatics13.3.1 Archimedes’ Law13.3.2 Nonrotating Stars and Planets13.3.3 Rotating Fluids13.4 Conservation Laws13.5 The Dynamics of an Ideal Fluid13.5.1 Mass Conservation13.5.2 Momentum Conservation13.5.3 Euler Equation13.5.4 Bernoulli’s Theorem13.5.5 Conservation of Energy13.6 Incompressible Flows13.7 Viscous Flows with Heat Conduction13.7.1 Decomposition of the Velocity Gradient into Expansion, Vorticity, and Shear13.7.2 Navier-Stokes Equation13.7.3 Molecular Origin of Viscosity13.7.4 Energy Conservation and Entropy Production13.7.5 Reynolds Number13.7.6 Pipe Flow13.8 Relativistic Dynamics of a Perfect Fluid13.8.1 Stress-Energy Tensor and Equations of Relativistic Fluid Mechanics13.8.2 Relativistic Bernoulli Equation and Ultrarelativistic Astrophysical Jets13.8.3 Nonrelativistic Limit of the Stress-Energy TensorBibliographic Note14 Vorticity14.1 Overview14.2 Vorticity, Circulation, and Their Evolution14.3 Low-Reynolds-Number Flow—Stokes Flow and Sedimentation14.3.1 Motivation: Climate Change14.3.2 Stokes Flow14.3.3 Sedimentation Rate14.4 High-Reynolds-Number Flow—Laminar Boundary Layers14.4.1 Blasius Velocity Profile Near a Flat Plate: Stream Function and Similarity Solution14.4.2 Blasius Vorticity Profile14.4.3 Viscous Drag Force on a Flat Plate14.4.4 Boundary Layer Near a Curved Surface: Separation14.5 Nearly Rigidly Rotating Flows—Earth’s Atmosphere and Oceans14.5.1 Equations of Fluid Dynamics in a Rotating Reference Frame14.5.2 Geostrophic Flows14.5.3 Taylor-Proudman Theorem14.5.4 Ekman Boundary Layers14..6 Instabilities of Shear Flows—Billow Clouds and Turbulence in the Stratosphere14.6.1 Discontinuous Flow: Kelvin-Helmholtz Instability14.6.2 Discontinuous Flow with Gravity14.6.3 Smoothly Stratified Flows: Rayleigh and Richardson Criteria for InstabilityBibliographic Note15 Turbulence15.1 Overview15.2 The Transition to Turbulence—Flow Past a Cylinder15.3 Empirical Description of Turbulence15.4 Semiquantitative Analysis of Turbulence15.4.1 Weak-Turbulence Formalism15.4.2 Turbulent Viscosity15.4.3 TurbulentWakes and Jets; Entrainment; the Coanda Effect15.4.4 Kolmogorov Spectrum for Fully Developed, Homogeneous, Isotropic Turbulence15.5 Turbulent Boundary Layers15.5.1 Profile of a Turbulent Boundary Layer15.5.2 Coanda Effect and Separation in a Turbulent Boundary Layer15.5.3 Instability of a Laminar Boundary Layer15.5.4 Flight of a Ball15.6 The Route to Turbulence—Onset of Chaos15.6.1 Rotating Couette Flow15.6.2 Feigenbaum Sequence, Poincaré Maps, and the Period-Doubling Route to Turbulence in Convection15.6.3 Other Routes to Turbulent Convection15.6.4 Extreme Sensitivity to Initial ConditionsBibliographic Note16 Waves16.1 Overview16.2 Gravity Waves on and beneath the Surface of a Fluid16.2.1 Deep-Water Waves and Their Excitation and Damping16.2.2 Shallow-Water Waves16.2.3 Capillary Waves and Surface Tension16.2.4 Helioseismology16.3 Nonlinear Shallow-Water Waves and Solitons16.3.1 Korteweg–de Vries (KdV) Equation16.3.2 Physical Effects in the KdV Equation16.3.3 Single-Soliton Solution16.3.4 Two-Soliton Solution16.3.5 Solitons in Contemporary Physics16.4 Rossby Waves in a Rotating Fluid16.5 Sound Waves16.5.1 Wave Energy16.5.2 Sound Generation16.5.3 Radiation Reaction, Runaway Solutions, and Matched Asymptotic ExpansionsBibliographic Note17 Compressible and Supersonic Flow17.1 Overview17.2 Equations of Compressible Flow17.3 Stationary, Irrotational, Quasi-1-Dimensional Flow17.3.1 Basic Equations; Transition from Subsonic to Supersonic Flow17.3.2 Setting up a Stationary, Transonic Flow17.3.3 Rocket Engines17.4 Dimensional, Time-Dependent Flow17.4.1 Riemann Invariants17.4.2 Shock Tube17.5 Shock Fronts17.5.1 Junction Conditions across a Shock; Rankine-Hugoniot Relations17.5.2 Junction Conditions for Ideal Gas with Constant γ17.5.3 Internal Structure of a Shock17.5.4 Mach Cone17.6 Self-Similar Solutions—Sedov-Taylor BlastWave17.6.1 The Sedov-Taylor Solution17.6.2 Atomic Bomb17.6.3 SupernovaeBibliographic Note18 Convection18.1 Overview18.2 Diffusive Heat Conduction—Cooling a Nuclear Reactor; Thermal Boundary Layers18.3 Boussinesq Approximation18.4 Rayleigh-Bénard Convection18.5 Convection in Stars18.6 Double Diffusion—Salt FingersBibliographic NoteApp. A Newtonian Physics: Geometric Viewpoint1.1 Introduction1.1.1 The Geometric Viewpoint on the Laws of Physics1.1.2 Purposes of This Chapter1.1.3 Overview of This Chapter1.2 Foundational Concepts1.3 Tensor Algebra without a Coordinate System1.4 Particle Kinetics and Lorentz Force in Geometric Language1.5 Component Representation of Tensor Algebra1.5.1 Slot-Naming Index Notation1.5.2 Particle Kinetics in Index Notation1.6 Orthogonal Transformations of Bases1.7 Differentiation of Scalars, Vectors, and Tensors; Cross Product and Curl1.8 Volumes, Integration, and Integral Conservation Laws1.8.1 Gauss’s and Stokes’ Theorems11.9 The Stress Tensor and Momentum Conservation1.9.1 Examples: Electromagnetic Field and Perfect Fluid1.9.2 Conservation of Momentum1.10 Geometrized Units and Relativistic Particles for Newtonian Readers1.10.1 Geometrized Units1.10.2 Energy and Momentum of a Moving ParticleBibliographic NoteReferencesName IndexContents of the Unified Work, Modern Classical PhysicsPreface to Modern Classical PhysicsAcknowledgments for Modern Classical Physics

"Kip S. Thorne, Co-Winner of the 2017 Nobel Prize in Physics"