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020 _a9781119101505
020 _a9781119765158
_q(electronic bk. : oBook)
020 _a1119765153
_q(electronic bk. : oBook)
020 _a9781119101512
_qelectronic book
020 _a1119101514
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020 _a9781119101529
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020 _a1119101522
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020 _a9781119101536
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020 _a1119101530
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020 _z9781119101505
_qhardcover
024 7 _a10.1002/9781119765158
_2doi
024 8 _a17506634
035 _a(OCoLC)1266201675
040 _aDLC
_beng
_erda
_cDLC
_dOCLCO
_dOCLCF
_dOCLCO
_dYDX
_dDG1
_dYUS
041 _aeng
042 _apcc
050 0 4 _aQA911
_b.S462 2023
082 0 0 _a532.05
_223
100 1 _aShivamoggi, Bhimsen K.,
_0https://id.loc.gov/authorities/names/n84105159
_eauthor.
245 1 0 _aIntroduction to theoretical and mathematical fluid dynamics /
_cBhimsen K. Shivamoggi, University of Central Florida, Orlando, United States.
250 _aThird edition.
264 1 _aHoboken, NJ :
_bJohn Wiley & Sons, Inc.,
_c2023.
264 4 _c©2023.
300 _a1 online resource (xviii, 558 pages) :
_billustrations.
336 _atext
_btxt
_2rdacontent.
337 _acomputer
_bc
_2rdamedia.
338 _aonline resource
_bcr
_2rdacarrier.
340 _2rdacc
_0http://rdaregistry.info/termList/RDAColourContent/1003.
504 _aIncludes bibliographical references and index.
505 0 _aTable of Contents Contents Preface to the Third Edition xv Acknowledgments xvii Part I Basic Concepts and Equations of Fluid Dynamics 1 1 Introduction to the Fluid Model 3 1.1 The Fluid State 4 1.2 Description of the Flow-Field 5 1.3 Volume Forces and Surface Forces 7 1.4 Relative Motion Near a Point 10 1.5 Stress–Strain Relations 13 2 Equations of Fluid Flows 15 2.1 The Transport Theorem 16 2.2 The Material Derivative 18 2.3 The Law of Conservation of Mass 18 2.4 Equation of Motion 19 2.5 The Energy Equation 19 2.6 The Equation of Vorticity 22 2.7 The Incompressible Fluid 23 2.8 Boundary Conditions 24 2.9 A Program for Analysis of the Governing Equations 25 3 Hamiltonian Formulation of Fluid-Flow Problems 27 3.1 Hamiltonian Dynamics of Continuous Systems 28 3.2 Three-Dimensional Incompressible Flows 32 3.3 Two-Dimensional Incompressible Flows 35 4 Surface Tension Effects 39 4.1 Shape of the Interface between Two Fluids 39 4.2 Capillary Rises in Liquids 41 Part II Dynamics of Incompressible Fluid Flows 45 5 Fluid Kinematics and Dynamics 47 5.1 Stream Function 47 5.2 Equations of Motion 50 5.3 Integrals of Motion 50 5.4 Capillary Waves on a Spherical Drop 51 5.5 Cavitation 54 5.6 Rates of Change of Material Integrals 55 5.7 The Kelvin Circulation Theorem 57 5.8 The Irrotational Flow 58 5.9 Simple-Flow Patterns 62 (i) The Source Flow 62 (ii) The Doublet Flow 63 (iii) The Vortex Flow 66 (iv) Doublet in a Uniform Stream 66 (v) Uniform Flow Past a Circular Cylinder with Circulation 67 6 The Complex-Variable Method 71 6.1 The Complex Potential 71 6.2 Conformal Mapping of Flows 74 6.3 Hydrodynamic Images 82 6.4 Principles of Free-Streamline Flow 84 (i) Schwarz-Christoffel Transformation 84 (ii) Hodograph Method 93 7 Three-Dimensional Irrotational Flows 99 7.1 Special Singular Solutions 99 (i) The Source Flow 99 (ii) The Doublet Flow 101 7.2 d’Alembert’s Paradox 104 7.3 Image of a Source in a Sphere 105 7.4 Flow Past an Arbitrary Body 107 7.5 Unsteady Flows 109 7.6 Renormalized (or Added) Mass of Bodies Moving through a Fluid 111 8 Vortex Flows 115 8.1 Vortex Tubes 115 8.2 Induced Velocity Field 117 8.3 Biot-Savart’s Law 117 8.4 von Kármán Vortex Street 121 8.5 Vortex Ring 124 8.6 Hill’s Spherical Vortex 129 8.7 Vortex Sheet 131 8.8 Vortex Breakdown: Brooke Benjamin’s Theory 135 9 Rotating Flows 143 9.1 Governing Equations and Elementary Results 143 9.2 Taylor-Proudman Theorem 144 9.3 Propagation of Inertial Waves in a Rotating Fluid 146 9.4 Plane Inertial Waves 147 9.5 Forced Wavemotion in a Rotating Fluid 150 (i) The Elliptic Case 153 (ii) The Hyperbolic Case 154 9.6 Slow Motion along the Axis of Rotation 155 9.7 Rossby Waves 160 10 Water Waves 167 10.1 Governing Equations 168 10.2 A Variational Principle for Surface Waves 169 10.3 Water Waves in a Semi-Infinite Fluid 171 10.4 Water Waves in a Fluid Layer of Finite Depth 172 10.5 Shallow-Water Waves 174 (i) Analogy with Gas Dynamics 175 (ii) Breaking of Waves 176 10.6 Water Waves Generated by an Initial Displacement over a Localized Region 176 10.7 Waves on a Steady Stream 182 (i) One-Dimensional Gravity Waves 183 (ii) One-Dimensional Capillary-Gravity Waves 184 (iii) Ship Waves 185 10.8 Gravity Waves in a Rotating Fluid 188 10.9 Theory of Tides 193 10.10 Hydraulic Jump 195 (i) Tidal Bores 195 (ii) The Dam-Break Problem 199 10.11 Nonlinear Shallow-Water Waves 202 (i) Solitary Waves 206 (ii) Periodic Cnoidal Waves 208 (iii) Interacting Solitary Waves 214 (iv) Stokes Waves 219 (v) Modulational Instability and Envelope Solutions 220 10.12 Nonlinear Capillary-Gravity Waves 230 (i) Resonant Three-Wave Interactions 230 (ii) Second-Harmonic Resonance 235 11 Applications to Aerodynamics 241 11.1 Airfoil Theory: Method of Complex Variables 242 (i) Force and Moments on an Arbitrary Body 242 (ii) Flow Past an Arbitrary Cylinder 245 (iii) Flow Around a Flat Plate 248 (iv) Flow Past an Airfoil 250 (v) The Joukowski Transformation 253 11.2 Thin Airfoil Theory 259 (i) Thickness Problem 262 (ii) Camber Problem 264 (iii) Flat Plate at an Angle of Attack 269 (iv) Combined Aerodynamic Characteristics 271 (v) The Leading-Edge Problem of a Thin Airfoil 271 11.3 Slender-Body Theory 275 11.4 Prandtl’s Lifting-Line Theory for Wings 277 11.5 Oscillating Thin-Airfoil Problem: Theodorsen’s Theory 282 Part III Dynamics of Compressible Fluid Flows 297 12 Review of Thermodynamics 299 12.1 Thermodynamic System and Variables of State 299 12.2 The First Law of Thermodynamics and Reversible and Irreversible Processes 300 12.3 The Second Law of Thermodynamics 303 12.4 Entropy 304 12.5 Liquid and Gaseous Phases 307 13 Isentropic Fluid Flows 309 13.1 Applications of Thermodynamics to Fluid Flows 309 13.2 Linear Sound Wave Propagation 310 13.3 The Energy Equation 310 13.4 Stream-Tube Area and Flow Velocity Relations 312 14 Potential Flows 317 14.1 Governing Equations 317 14.2 Streamline Coordinates 319 14.3 Conical Flows: Prandtl-Meyer Flow 320 14.4 Small Perturbation Theory 324 14.5 Characteristics 326 (i) Compatibility Conditions in Streamline Coordinates 328 (ii) A Singular-Perturbation Problem for Hyperbolic Systems 331 15 Nonlinear Theory of Plane Sound Waves 343 15.1 Riemann Invariants 343 15.2 Simple Wave Solutions 344 15.3 Nonlinear Propagation of a Sound Wave 352 15.4 Nonlinear Resonant Three-Wave Interactions of Sound Waves 355 15.5 Burgers Equation 361 16 Shock Waves 371 16.1 The Normal Shock Wave 371 16.2 The Oblique Shock Wave 384 16.3 Blast Waves: Taylor’s Self-similarity and Sedov’s Exact Solution 387 17 The Hodograph Method 393 17.1 The Hodograph Transformation of Potential Flow Equations 393 17.2 The Chaplygin Equation 394 17.3 The Tangent-Gas Approximation 396 17.4 The Lost Solution 401 17.5 The Limit Line 402 18 Applications to Aerodynamics 411 18.1 Thin Airfoil Theory 411 (i) Thin Airfoil in Linearized Supersonic Flows 411 (ii) Far-Field Behavior of Supersonic Flow Past a Thin Airfoil 414 (iii) Thin Airfoil in Transonic Flows 417 18.2 Slender Bodies of Revolution 420 18.3 Oscillating Thin Airfoil in Subsonic Flows: Possio’s Theory 427 18.4 Oscillating Thin Airfoils in Supersonic Flows: Stewartson’s Theory 435 Part IV Dynamics of Viscous Fluid Flows 439 19 Exact Solutions to Equations of Viscous Fluid Flows 441 19.1 Channel Flows 442 19.2 Decay of a Line Vortex: The Lamb-Oseen Vortex 443 19.3 Line Vortex in a Uniform Stream 446 19.4 Diffusion of a Localized Vorticity Distribution 446 19.5 Burgers Vortex 451 19.6 Flow Due to a Suddenly Accelerated Plane 453 19.7 The Round Laminar Jet: Landau-Squire Solution 456 19.8 Ekman Layer at a Free Surface in a Rotating Fluid 459 19.9 Centrifugal Flow Due to a Rotating Disk: von Kármán Solution 462 19.10 Shock Structure: Becker’s Solution 464 19.11 Couette Flow of a Gas 467 20 Flows at Low Reynolds Numbers 469 20.1 Dimensional Analysis 469 20.2 Stokes’ Flow Past a Rigid Sphere: Stokes’ Formula 470 20.3 Stokes’ Flow Past a Spherical Drop 474 20.4 Stokes’ Flow Past a Rigid Circular Cylinder: Stokes’ Paradox 478 20.5 Oseen’s Flow Past a Rigid Sphere 479 20.6 Oseen’s Approximation for Periodically Oscillating Wakes 483 21 Flows at High Reynolds Numbers 489 21.1 Prandtl’s Boundary-Layer Concept 489 21.2 The Method of Matched Asymptotic Expansions 490 21.3 Location and Nature of the Boundary Layers 497 21.4 Incompressible Flow Past a Flat Plate 500 (i) The Outer Expansion 501 (ii) The Inner Expansion 502 (iii) Flow Due to Displacement Thickness 507 21.5 Separation of Flow in a Boundary Layer: Landau’s Theory 509 21.6 Boundary Layers in Compressible Flows 512 (i) Crocco’s Integral 514 (ii) Flow Past a Flat Plate: Howarth-Dorodnitsyn Transformation 516 21.7 Flow in a Mixing Layer between Two Parallel Streams 517 (i) Geometrical Characteristics of the Mixing Flow 520 21.8 Narrow Jet: Bickley’s Solution 521 21.9 Wakes 524 21.10 Periodic Boundary Layer Flows 524 22 Jeffrey-Hamel Flow 529 22.1 The Exact Solution 529 (i) Only 𝑒1 Is Real and Positive 531 (ii) 𝑒1, 𝑒2, and 𝑒3 Are Real and Distinct 532 22.2 Flows at Low Reynolds Numbers 535 22.3 Flows at High Reynolds Numbers 541 References 545 Bibliography 549 Index 551
520 _a"In dealing with a fluid, one is in reality dealing with a system which has many particles which interact with one another. The main utility of fluid dynamics is the ability to develop a formalism which deals solely with a few macroscopic quantities like pressure while ignoring the details of the particle interactions. Therefore, the techniques of fluid dynamics have often been found useful in modeling systems with complicated interactions (which are either not known or very difficult to describe) between the constituents. Thus, the first successful model of the nuclear fission of heavy elements was the liquid drop model of the nucleus, which treats the nucleus as a fluid, and hence replaces the many body problem of calculating the interactions of all of the protons and neutrons with the much simpler problem of calculating the pressures and surface tension in this fluid.1 Of course, this treatment gives only a very rough approximation to reality, but it is nonetheless a very useful way of approaching the problem"--
_cProvided by publisher.
545 0 _aAbout the Author Bhimsen K. Shivamoggi, PhD, is Professor in the Departments of Mathematics and Physics at the University of Central Florida. He is a Senior Fellow of the Japan Society for the Promotion of Science. His research is focused on mathematical physics, fluid dynamics, stochastic processes, and nonlinear dynamics.
650 0 _aFluid dynamics.
_0https://id.loc.gov/authorities/subjects/sh85049376.
650 0 _aFluid dynamics
_xMathematical models.
_0https://id.loc.gov/authorities/subjects/sh2008103862.
650 2 _aHydrodynamics.
_0https://id.nlm.nih.gov/mesh/D057446.
655 4 _aElectronic books.
856 _uhttps://onlinelibrary.wiley.com/doi/book/10.1002/9781119765158
_yFull text is available at Wiley Online Library Click here to view.
942 _2ddc
_cER