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More About This Textbook
Overview
About the Author:
Professor Howe is in the Department of Aerospace and Mechanical Engineering at Boston University
Editorial Reviews
From the Publisher
"It would make an excellent graduate level text...I found it to be clearly written...remarkably free of errors and contains many well thought out problems and interesting examples...I was impressed by the large number of practical results that could be obtained by using only very simple mathematics."Marvin Goldstein, Chief Scientist
NASA Glenn Research Center, Cleveland, OH 441353191, USA
Journal of Sound and Vibration
Volume 309, Issues 12, 8 January 2008, Pages 347348
"Professor Howe is not only a wellestablished researcher but also an excellent pedagogue. He succeeded in explaining in a comprehensive manner complex topics of hydrodynamics...This book has all the chances to become a classical textbook on this subject...recommended to all students willing to discover the wonderful world of hydrodynamics."
Denys Dutykh, ENS Cachan, CMLA, France
European Journal of Mechanics B/Fluids 27 (2008) 218
Product Details
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Meet the Author
Table of Contents
Preface xv
Equations of Motion 1
The fluid state 1
The material derivative 1
Conservation of mass: Equation of continuity 2
Momentum equation 3
Relative motion of neighbouring fluid elements 3
Viscous stress tensor 5
NavierStokes equation 7
The Reynolds equation and Reynolds stress 7
The energy equation 8
Alternative treatment of the energy equation 9
Energy equation for incompressible flow 10
Summary of governing equations 11
Boundary conditions 12
Problems 1 12
Potential Flow of an Incompressible Fluid 14
Ideal fluid 14
Kelvin's circulation theorem 14
The velocity potential 16
Bernoulli's equation 16
Impulsive pressure 18
Streamlines and intrinsic equations of motion 18
Bernoulli's equation in steady flow 20
Motion produced by a pulsating sphere 21
The point source 22
Freespace Green's function 24
Monopoles, dipoles, andquadrupoles 24
The vibrating sphere 26
Streamlines 28
Far field of a monopole distribution of zero strength 29
Green's formula 30
Volume and surface integrals 30
Green's formula 32
Sources adjacent to a plane wall 34
Determinancy of the motion 35
Fluid motion expressed in terms of monopole or dipole distributions 37
Determinancy of cyclic irrotational flow 39
Kinetic energy of cyclic irrotational flow 40
The kinetic energy 41
Converse of Kelvin's minimumenergy theorem 43
Energy of motion produced by a translating sphere 43
Problems with spherical boundaries 45
Legendre polynomials 45
Velocity potential of a point source in terms of Legendre polynomials 50
Interpretation in terms of images 52
The Stokes stream function 53
Stream function examples 55
Rankine solids 56
Rankine ovoid 58
Drag in ideal flow 58
Axisymmetric flow from a nozzle 60
Irrotational flow from a circular cylinder 63
Borda's mouthpiece 65
The incompressible far field 67
Deductions from Green's formula 68
Far field produced by motion of a rigid body 69
Inertia coefficients 70
Pressure in the far field 70
Force on a rigid body 71
Moment exerted on a rigid body 73
Sources near solid boundaries 75
The reciprocal theorem 76
Farfield Green's function 78
The Kirchhoff vector 80
Farfield Green's function for a sphere 80
Farfield Green's function for cylindrical bodies 84
The circular cylinder 85
The rigid strip 86
Symmetric farfield Green's function 89
Far field of an arbitrarily moving body 90
Farfield Green's function summary and special cases 91
General form 91
Airfoil of variable chord 92
Projection or cavity on a plane wall 93
Rankine ovoid 94
Circular aperture 95
Circular disc 96
Problems 2 96
Ideal Flow in Two Dimensions 102
Complex representation of fluid motion 102
The stream function 102
The complex potential 104
Uniform flow 104
Flow past a cylindrical surface 105
The circular cylinder 106
Circle theorem 106
Uniform flow past a circular cylinder 106
The line vortex 109
Circular cylinder with circulation 110
Equation of motion of a cylinder with circulation 112
The Blasius force and moment formulae 115
Blasius's force formula for a stationary rigid body 116
Blasius's moment formula for a stationary rigid body 117
KuttaJoukowski lift force 117
Leadingedge suction 118
Sources and line vortices 119
Line vorrtices 122
Motion of a line vortex 122
Karman vortex street 127
Kinetic energy of a system of rectilinear vortices 127
Conformal transformations 128
Transformation of Laplace's equation 129
Equation of motion of a line vortex 132
Numerical integration of the vortex path equation 133
The SchwarzChristoffel transformation 135
Irrotational flow from an infinite duct 138
Irrotational flow through a wall aperture 140
Freestreamline theory 142
Coanda edge flow 142
Mapping from the w plane to the t plane 147
Separated flow through an aperture 147
The wake of a flat plate 151
Flow past a curved boundary 152
The hodograph transformation formula 158
Chaplygin's singular point method 159
Jet produced by a point source 160
Deflection of trailingedge flow by a source 161
The Joukowski transformation 167
The flatplate airfoil 170
Calculation of the lift 173
Lift calculated from the Kirchhoff vector force formula 173
Lift developed by a starting airfoil 174
The Joukowski airfoil 175
Streamline flow past an airfoil 176
Separation and stall 179
Linear theory of separation 180
Sedov's method 183
Boundary conditions 184
Sedov's formula 185
Tandem airfoils 187
Highlift devices 190
Plain flap or aileron 192
Point sources and vortices 192
Flow through a cascade 193
Unsteady thinairfoil theory 195
The vortex sheet wake 195
Translational oscillations 197
The unsteady lift 198
Leadingedge suction force 199
Energy dissipated by vorticity production 201
Hankel function formulae 202
Problems 3 203
Rotational Incompressible Flow 211
The vorticity equation 211
Vortex lines 212
Vortex tubes 212
Movement of vortex lines: Helmholtz's vortex theorem 213
Crocco's equation 214
Convection and diffusion of vorticity 215
Vortex sheets 218
The BiotSavart law 221
The far field 223
Kinetic energy 227
The BiotSavart formula in the presence of an internal boundary 228
The BiotSavart formula for irrotational flow 229
Examples of axisymmetric vortical flow 232
Circular vortex filament 232
Rate of production of vorticity at a nozzle 233
Blowing out a candle 235
Axisymmetric steady flow of an ideal fluid 236
Hill's spherical vortex 237
Some viscous flows 239
Diffusion of vorticity from an impulsively started plane wall 239
Diffusion of vorticity from a line vortex 240
Creeping flow 242
Motion of a sphere at very small Reynolds number 242
The Oseen approximation 245
Laminar flow in a tube (HagenPoiseuille flow) 247
Boundary layer on a flat plate; Karman momentum integral method 249
Force on a rigid body 253
Surface force in terms of the impulse 254
The Kirchhoff vector force formula 256
The Kirchhoff vector force formula for irrotational flow 258
Arbitrary motion in a viscous fluid 258
Body moving without rotation 239
Surface force in two dimensions 261
Bluff body drag at high Reynolds number 261
Modelling vortex shedding from a sphere 265
Force and impulse in fluid of nonuniform density 270
Integral identities 271
Surface moment 273
Moment for a nonrotating body 273
Airfoil lift, drag, and moments 274
Vortexsurface interactions 276
Pressure expressed in terms of the total enthalpy 276
Equation for B 277
Solution of the B equation 278
The far field 279
Problems 4 281
Surface Gravity Waves 286
Introduction 286
Conditions at the free surface 286
Wave motion within the fluid 287
Linearised approximation 288
Time harmonic, plane waves on deep water 288
Water of finite depth 290
Surface wave energy 291
Waveenergy density 293
Waveenergy flux 294
Group velocity 295
Viscous damping of surface waves 297
The interior damping 297
Boundarylayer damping 298
Comparison of boundarylayer and internal damping for long waves 299
Shallowwater waves 299
Waves on water of variable depth 300
Shallowwater Green's function 301
Waves generated by a localised pressure rise 302
Waves approaching a sloping beach 307
Method of stationary phase 309
Formulation of initialvalue dispersivewave problems 309
Evaluation of Fourier integrals by the method of stationary phase 311
Numerical results for the surface displacement 313
Conservation of energy 315
Rayleigh's proof that energy propagates at the group velocity 317
Surface waveenergy equation 318
Waves generated by a submarine explosion 319
Initialvalue problems in two surface dimensions 321
Waves generated by a surface elevation symmetric about the origin 322
The energy equation in two dimensions 324
Surface motion near a wavefront 325
Onedimensional waves 325
Waves generated by motion of the seabed 328
Tsunami produced by an undersea earthquake 332
Periodic wave sources 333
Onedimensional waves 334
Periodic sources in two surface dimensions 336
The surface wave power 339
Surface wave amplitude 340
Ship waves 341
Moving line pressure source 342
Wavemaking resistance 343
Moving pointlike pressure source 345
Plotting the wave crests 349
Behaviour at the caustic 351
Wavemaking power 352
Wave amplitude calculated from the power 354
Ray theory 354
Kinematic theory of wave crests 354
Ray tracing in an inhomogeneous medium 357
Refraction of waves at a sloping beach 357
Wave action 364
Variational description of a fully dispersed wave group 365
Fully dispersed waves in a nonuniformly moving medium 366
General wavebearing media 369
Diffraction of surface waves by a breakwater 373
Diffraction by a long, straight breakwater 373
Solution of the diffraction problem 374
The surface wave pattern 377
Uniform asymptotic approximation: Method of steepest descents 379
Problems 5 384
Introduction to Acoustics 390
The wave equation 390
The linear wave equation 391
Plane waves 392
Speed of sound 393
Acoustic Green's function 395
The impulsive point source 395
Green's function 396
Retarded potential 397
Sound from a vibrating sphere 397
Acoustic energy flux 399
Green's function in one space dimension: Method of descent 400
Waves generated by a onedimensional volume source 401
Kirchhoff's formula 401
Compact Green's function 403
Generalized Kirchhoff formula 403
The time harmonic wave equation 404
The compact approximation 404
Rayleigh scattering: Scattering by a compact body 407
Onedimensional propagation through junctions 409
Continuity of volume velocity 410
Continuity of pressure 410
Reflection and transmission at a junction 411
Branching systems 413
Fundamental formula 414
Energy transmission 415
Acoustically compact cavity 416
The Helmholtz resonator 417
Acoustic filter 418
Admittance of a narrow constriction 419
Radiation from an open end 421
Rayleigh's method for lowfrequency sound 421
The reflection coefficient 423
Admittance of the open end 423
Openend input admittance 424
Flanged opening 426
Physical significance of the end correction 428
Admittance of a circular aperture 431
Webster's equation 432
Radiation into a semiinfinite duct 435
The compact Green's function 435
Wave generation by a train entering a tunnel 439
Damping of sound in a smoothwalled duct 445
Time harmonic propagation in a duct 446
The viscous contribution 447
The thermal contribution 449
The thermoviscous damping coefficient 450
Problems 6 450
Bibliography 455
Index 457