Physical hydrodynamics / Etienne Guyon ... [et al. ; translated by Catalin D. Mitescu].

Format:

Book

Contributor:

Guyon, Etienne.

Standardized Title:

Hydrodynamique physique. English.

Language:

English

French

Subjects (All):

Hydrodynamics.

Physical Description:

xxii, 505 pages : illustrations ; 24 cm

Place of Publication:

Oxford ; New York : Oxford University Press, 2001.

Contents:

1 The physics of fluids 1

1.1 The liquid state 1

1.1.1 The different states of matter: model systems and real media 2

1.1.2 The solid

liquid transition: a sometimes nebulous process 7

1.2 Macroscopic transport coefficients 8

1.2.1 Thermal conductivity 9

1.2.2 Mass diffusion 18

1.3 Microscopic models for transport coefficients 21

1.3.1 A different approach to mass diffusion: the random walk 21

1.3.2 Transport coefficients for an ideal gas 24

1.3.3 Diffusive transport phenomena in liquids 28

1.4 Surface and surface tension effects 31

1.4.1 Surface tension 31

1.4.2 The pressure difference between the two sides of a curved interface: Laplace's law 32

1.4.3 Variations in the surface tension due to a surfactant 35

1.4.4 The Rayleigh

Taylor instability 37

1.5 The spectroscopy of liquids 40

1.5.1 Some common techniques for probing the microscopic structure of liquids 40

1.5.2 The form factor and elastic X-ray diffraction: an example of the use of scattering on an atomic scale 42

1.5.3 Elastic and quasi-elastic scattering of light: a tool for the study of the structure and diffusive transport in liquids 46

1.5.4 Inelastic scattering of light in liquids 52

Appendix Typical orders of magnitude for a number of physical parameters characteristic of the interfacial properties of ordinary liquids 55

2 The diffusion of momentum under various flow conditions 57

2.1 Diffusive and convective momentum transport in flowing fluids 57

2.1.1 Diffusion and convection of momentum: two illustrative experiments 57

2.1.2 Momentum transport in shear flow: an introduction to the concept of viscosity 59

2.2 Microscopic models of viscosity 64

2.2.1 The viscosity of gases 64

2.2.2 The viscosity of liquids 67

2.2.3 Numerical simulation of the particle trajectories in a flowing fluid 69

2.3 A comparison of diffusion and convection mechanisms 71

2.3.1 The Reynolds number 71

2.3.2 Convective and diffusive mass and heat transport 73

2.4 The description of different flow regimes 76

2.4.1 Different flow regimes in the wake of a cylinder 77

2.4.2 Transitions in the shedding of vortices behind a cylinder: the Landau model 79

3 The kinematics of fluids 89

3.1 The description of motion of a fluid 89

3.1.1 Characteristic linear scales and the hypothesis of continuity 89

3.1.2 The Eulerian and Lagrangian descriptions of fluid motion 90

3.1.3 Acceleration of a particle of fluid 91

3.1.4 Streamlines and stream-tubes, pathlines, and streaklines 93

3.1.5 Visualization of flows 95

3.2 Deformations in flows 99

3.2.1 The local components of the velocity gradient field 100

3.2.2 Analysis of the symmetric component: pure strain (deformation) 100

3.2.3 Analysis of the antisymmetric component: pure rotation 104

3.2.4 Small and large deformations 106

3.3 The conservation of mass in fluid flow 110

3.3.1 The equation of continuity 110

3.3.2 The incompressibility of a fluid 112

3.3.3 Analogies with electromagnetic theory 114

3.4 The stream function 115

3.4.1 The introduction and significance of the stream function 115

3.4.2 Examples of two-dimensional flows and of their stream functions 117

3.4.3 Axially symmetric flows 121

3.5 Some measurements of velocity and of velocity gradients in fluid flows 122

3.5.1 Measurement of the local velocity of a fluid: laser Doppler anemometry 122

3.5.2 Determination of the local velocity gradients 125

4 The dynamics of fluids: local equations 128

4.1 Surface forces 128

4.1.1 The general expression for the surface forces 128

4.1.2 The characteristics of the viscous shear stress tensor 132

4.1.3 The viscous shear stress for a Newtonian fluid 134

4.1.4 Non-Newtonian fluids 136

4.2 The equation of motion for a fluid 140

4.2.1 The general equation for the dynamics of a fluid 140

4.2.2 The Navier-Stokes equation of motion for a Newtonian fluid 142

4.2.3 Euler's equation of motion for an ideal fluid 143

4.2.4 The dimensionless form of the Navier-Stokes equation 143

4.3 Boundary conditions for fluid flow 144

4.3.1 The boundary condition at a solid wall 144

4.3.2 Boundary conditions at the interface between two fluids: surface tension effects 145

4.4 A few specific solutions of the Navier-Stokes equations 147

4.4.1 The Navier-Stokes equation for one-dimensional flow 147

4.4.2 Simple shear flow (plane Couette flow) 148

4.4.3 Poiseuille flow (a viscous fluid flowing in a stationary conduit) 149

4.4.4 Oscillating flows in a viscous fluid 155

4.4.5 Flow driven by a gradient in the surface tension (the Marangoni effect) 160

4.4.6 Cylindrical Couette flow 163

Appendix Representation of the stress tensor, the equation of continuity, and the Navier-Stokes equations, for Newtonian fluids, in the most commonly used co-ordinate systems 167

A.1 Cartesian co-ordinates (x, y, z) 167

A.2 Cylindrical co-ordinates ([rho], [open phi], z) 167

A.3 Spherical polar co-ordinates (r, [theta], [open phi]) 168

5 The conservation laws 170

5.1 Conservation of mass 170

5.2 Conservation of momentum 171

5.2.1 The local equation 171

5.2.2 The integral expression of the law of conservation of momentum 172

5.3 The conservation of kinetic energy: Bernoulli's equation 176

5.3.1 The conservation of energy for a flowing incompressible fluid with or without viscosity 177

5.3.2 Bernoulli's equation: applications 180

5.4 Applications of the laws of conservation of energy and momentum 189

5.4.1 A jet incident on to a plane 189

5.4.2 The exit jet from an opening in a reservoir 192

5.4.3 The force on the walls of an axially symmetric conduit with variable cross-section 194

5.4.4 The hydraulic jump 197

5.4.5 Another application: a discharge sluice gate in a channel 205

6 Potential flow 208

6.2 Definitions, properties, and examples of potential flow 210

6.2.1 Characteristics and examples of the velocity potential 210

6.2.2 The uniqueness of the velocity potential 210

6.2.3 Velocity potentials for simple flows and combinations of potential functions 214

6.2.4 Examples of simple potential flows 221

6.3 Forces acting on an obstacle in potential flow 230

6.3.1 Two-dimensional flow 230

6.3.2 The case of an obstacle in three dimensions 236

6.4 Linear surface waves on an ideal fluid 240

6.4.1 Swells, cat's paws, and breaking waves 241

6.4.2 Trajectories of fluid particles during the passing of a wave 245

6.4.3 Solitons 246

6.5 An electrical analogue for two-dimensional potential flows 248

6.5.1 Direct analogue 249

6.5.2 Inverse analogue 249

6.6 The complex velocity potential 252

6.6.1 The definition of a complex potential 252

6.6.2 Complex potentials for several types of flow 253

6.6.3 Conformal mapping 256

Appendix A1 Velocity potentials and stream functions for two-dimensional flows 266

A2.1 Derivation of the velocity components from the stream function 267

A2.2 Derivation of the velocity components from the velocity potential 267

7 Vorticity: dynamics of vortices 268

7.1 Vorticity and its electromagnetic analogue 268

7.1.1 The vorticity vector 268

7.1.2 The electromagnetic analogue 269

7.1.3 Straight vortex tubes: the analogy with the magnetic field due to a current-carrying wire 271

7.1.4 The application of the electromagnetic analogy in dealing with arbitrary distributions of vorticity 277

7.2 The dynamics of circulation 279

7.2.1 Kelvin's theorem: the conservation of circulation 280

7.2.2 Sources of circulation in the flow of viscous or compressible fluids, or in the presence of non-conservative forces 284

7.3 The dynamics of vorticity 289

7.3.1 The transport equation for vorticity, and its consequences 289

7.3.2 Equilibrium between elongation and diffusion in the dynamics of vorticity 295

7.4 A few examples of distributions of vorticity concentrated along singularities: systems of vortex lines 298

7.4.1 A few cases with vorticity concentrated in vortex filaments 298

7.4.2 The dynamics of a system of parallel line vortices 300

7.4.3 Vortex rings 305

8 Flow at low Reynolds numbers 311

8.1 Examples of low-Reynolds-number flows 311

8.2 The equation of motion at low Reynolds number 313

8.2.1 The Stokes equation 313

8.2.2 Further equivalent representations of the Stokes equation 314

8.2.3 Properties of solutions of the Stokes equation 315

8.2.4 Dimensional-analysis predictions for flows at low Reynolds number 323

8.3 The forces and torques acting on a moving solid body 324

8.3.1 Linear proportionality between the velocity of the solid body and the external forces 325

8.3.2 General symmetry properties of the tensors A[subscript ij], B[subscript ij], C[subscript ij], and D[subscript ij] 326

8.3.3 The effect of the symmetry of solid bodies on the applied forces and torques 327

8.4 Uniform-velocity motion of a sphere in a viscous fluid 333

8.4.1 The velocity field around a moving sphere 333

8.4.2 The force acting on a moving sphere in a fluid of infinite extent: the drag coefficient 338

8.4.3 The generalization of the solution of the Stokes equation to other experiments 340

8.4.4 Limitations on the Stokes treatment of flow at low Reynolds numbers: the Oseen equation 343

8.5 Quasi-parallel flows at low Reynolds numbers: lubrication 347

8.6 Dynamics of suspensions 351

8.6.1 The rheology of suspensions 352

8.6.2 Sedimentation of particles in a suspension 357

8.7 Flow in porous media 361

8.7.1 A few characteristic examples of the different types of flows 361

8.7.2 Parameters characterising a porous medium 362

8.7.3 Flow in porous media: Darcy's law 366

8.7.4 Permeability models for media with cylindrical pores 370

8.7.5 The permeability of porous media containing channels of variable cross-section 373

8.7.6 The flow of immiscible fluids in a porous medium 377

9 Laminar boundary layers 383

9.2 A qualitative physical discussion of the structure of the boundary layer near a flat plate in uniform flow 385

9.3 The equations of motion within the boundary layer: Prandtl theory 388

9.3.1 The equations of motion near a flat plate 388

9.3.2 Transport of vorticity in the boundary layer 390

9.3.3 Self-similarity of the velocity profiles in the boundary layer for the case of uniform, constant, external velocity 390

9.4 Velocity profiles within boundary layers 393

9.4.1 The Blasius equation for uniform external flow along a flat plate 393

9.4.2 An approximate solution of the Blasius equation 394

9.4.3 The frictional force on a flat plate in a uniform flow 397

9.4.4 The thickness of boundary layers 397

9.4.5 The hydrodynamic stability of a laminar boundary layer: turbulent boundary layers 399

9.5 The laminar boundary layer in the presence of an external pressure gradient: boundary layer separation 400

9.5.1 A simplified physical treatment of the problem 400

9.5.2 Self-similar velocity profiles: flows such that U(x) = Cx[superscript m] 401

9.5.3 Boundary layers with constant thickness 406

9.5.4 Flows lacking self-similarity: boundary layer separation 407

9.5.5 The practical consequences of boundary layer separation 409

9.5.6 Separation of turbulent boundary layers: the decrease of the drag force 409

9.6 A few applications of boundary layer separation problems in aerodynamics 412

9.6.1 The aerodynamics of airplane wings 412

9.6.2 Controlling boundary layer separation by suction 417

9.6.3 The control of boundary layer separation by adjustment of the profile of the solid object 417

9.7 Thermal and mass boundary layers 420

9.7.1 Thermal boundary layers 421

9.7.2 Concentration boundary layers and polarography 428

9.8 The laminar wake 432

9.8.1 A qualitative approach to the problem 432

9.8.2 The solution of the equation of motion in the wake far from the object 433

9.8.3 The drag force on a body: the relationship with the velocity profile in the wake 435

10 Hydrodynamic instabilities 439

10.1 Thermal convection 439

10.1.1 Convective transport equations for heat 439

10.1.2 Thermal convection resulting from a horizontal temperature gradient 440

10.2 The Rayleigh-Benard instability 443

10.2.1 A description of the Rayleigh-Benard instability 444

10.2.2 The mechanism of the Rayleigh-Benard instability, and orders of magnitude 445

10.2.3 The two-dimensional solution of the Rayleigh-Benard problem 448

10.3 Other examples of threshold instabilities 455

10.3.1 The Taylor-Couette instability 455

10.3.2 The Benard-Marangoni instability 459

10.4 Other classes of instability 462

10.4.1 The Kelvin-Helmholtz instability 463

10.4.2 Poiseuille flow in a tube, and between parallel plates 469

10.4.3 The role of the shape of the velocity and vorticity profiles 470

Appendix A1 Transition to chaos 471

Appendix A2 Experiments in fully developed turbulence 476

A2.1 Two-dimensional flows 477

A2.2 Three-dimensional flows 479

Appendix Superfluid helium: an (almost) ideal fluid 482

A.1 Important properties of Helium II at finite temperatures 482

A.1.1 The two-fluid model for Helium II 482

A.1.2 Quantization of the circulation of the superfluid velocity v[subscript s] 483

A.1.3 Experimental evidence for the existence of a superfluid component flowing with no energy dissipation 484

A.2 Vortices in superfluid helium 485

A.2.1 The existence of vortex filaments in superfluid helium 485

A.2.2 Setting a volume of superfluid helium in rotation 485

A.2.3 Experimental evidence for the quantisation of circulation in superfluid helium: the Hall and Vinen experiment 486

A.2.4 Dynamics of vortex rings in superfluid helium 488.

Notes:

Includes bibliographical references (pages [489]-495) and index.

ISBN:

0198517467

0198517459

OCLC:

44153112