{"product_id":"introduction-to-theoretical-and-mathematical-fluid-dynamics-isbn-9781119101505","title":"Introduction to Theoretical and Mathematical Fluid Dynamics","description":"\u003cb\u003eINTRODUCTION TO THEORETICAL AND MATHEMATICAL FLUID DYNAMICS\u003c\/b\u003e \u003cp\u003e\u003cb\u003eA practical treatment of mathematical fluid dynamics\u003c\/b\u003e\u003c\/p\u003e \u003cp\u003eIn \u003ci\u003eIntroduction to Theoretical and Mathematical Fluid Dynamics\u003c\/i\u003e, distinguished researcher Dr. Bhimsen K. Shivamoggi delivers a comprehensive and insightful exploration of fluid dynamics from a mathematical point of view. The book introduces readers to the mathematical study of fluid behavior and highlights areas of active research in fluid dynamics. With coverage of advances in the field over the last 15 years, this book provides in-depth examinations of theoretical and mathematical fluid dynamics with a particular focus on incompressible and compressible fluid flows.\u003c\/p\u003e \u003cp\u003e\u003ci\u003eIntroduction to Theoretical and Mathematical Fluid Dynamics\u003c\/i\u003e includes practical applications and exercises to illustrate the concepts discussed within, and real-world examples are explained throughout the text. Clear and explanatory material accompanies the rigorous mathematics, making the book perfect for students seeking to learn and retain this complex subject.\u003c\/p\u003e \u003cp\u003eThe book also offers:\u003c\/p\u003e \u003cul\u003e \u003cli\u003eA thorough introduction to the basic concepts and equations of fluid dynamics, including an introduction to the fluid model, the equations of fluid flows, and surface tension effects\u003c\/li\u003e \u003cli\u003eComprehensive explorations of the dynamics of incompressible fluid flows, fluid kinematics and dynamics, the complex-variable method, and three-dimensional irrotational flows\u003c\/li\u003e \u003cli\u003eDetailed discussions of the dynamics of compressible fluid flows, including a review of thermodynamics, isentropic fluid flows, potential flows, and nonlinear theory of plane sound waves\u003c\/li\u003e \u003cli\u003eSystematic discussions of the dynamics of viscous fluid flows, including shear-layer flow, jet flow and wake flow.\u003c\/li\u003e \u003c\/ul\u003e \u003cp\u003eIdeal for graduate-level students taking courses on mathematical fluid dynamics as part of a program in mathematics, engineering, or physics, \u003ci\u003eIntroduction to Theoretical and Mathematical Fluid Dynamics\u003c\/i\u003e is also an indispensable resource for practicing applied mathematicians, engineers, and physicists.\u003c\/p\u003e \u003cp\u003e\u003cb\u003eContents\u003c\/b\u003e\u003c\/p\u003e \u003cp\u003e\u003cb\u003ePreface to the Third Edition \u003c\/b\u003e\u003ci\u003exv\u003c\/i\u003e\u003c\/p\u003e \u003cp\u003e\u003cb\u003eAcknowledgments \u003c\/b\u003e\u003ci\u003exvii\u003c\/i\u003e\u003c\/p\u003e \u003cp\u003e\u003cb\u003ePart I Basic Concepts and Equations of Fluid Dynamics \u003c\/b\u003e\u003ci\u003e1\u003c\/i\u003e\u003c\/p\u003e \u003cp\u003e\u003cb\u003e1 Introduction to the Fluid Model \u003c\/b\u003e\u003ci\u003e3\u003c\/i\u003e\u003c\/p\u003e \u003cp\u003e1.1 The Fluid State \u003ci\u003e4\u003c\/i\u003e\u003c\/p\u003e \u003cp\u003e1.2 Description of the Flow-Field \u003ci\u003e5\u003c\/i\u003e\u003c\/p\u003e \u003cp\u003e1.3 Volume Forces and Surface Forces \u003ci\u003e7\u003c\/i\u003e\u003c\/p\u003e \u003cp\u003e1.4 Relative Motion Near a Point \u003ci\u003e10\u003c\/i\u003e\u003c\/p\u003e \u003cp\u003e1.5 Stress–Strain Relations \u003ci\u003e13\u003c\/i\u003e\u003c\/p\u003e \u003cp\u003e\u003cb\u003e2 Equations of Fluid Flows \u003c\/b\u003e\u003ci\u003e15\u003c\/i\u003e\u003c\/p\u003e \u003cp\u003e2.1 The Transport Theorem \u003ci\u003e16\u003c\/i\u003e\u003c\/p\u003e \u003cp\u003e2.2 The Material Derivative \u003ci\u003e18\u003c\/i\u003e\u003c\/p\u003e \u003cp\u003e2.3 The Law of Conservation of Mass \u003ci\u003e18\u003c\/i\u003e\u003c\/p\u003e \u003cp\u003e2.4 Equation of Motion \u003ci\u003e19\u003c\/i\u003e\u003c\/p\u003e \u003cp\u003e2.5 The Energy Equation \u003ci\u003e19\u003c\/i\u003e\u003c\/p\u003e \u003cp\u003e2.6 The Equation of Vorticity \u003ci\u003e22\u003c\/i\u003e\u003c\/p\u003e \u003cp\u003e2.7 The Incompressible Fluid \u003ci\u003e23\u003c\/i\u003e\u003c\/p\u003e \u003cp\u003e2.8 Boundary Conditions \u003ci\u003e24\u003c\/i\u003e\u003c\/p\u003e \u003cp\u003e2.9 A Program for Analysis of the Governing Equations \u003ci\u003e25\u003c\/i\u003e\u003c\/p\u003e \u003cp\u003e\u003cb\u003e3 Hamiltonian Formulation of Fluid-Flow Problems \u003c\/b\u003e\u003ci\u003e27\u003c\/i\u003e\u003c\/p\u003e \u003cp\u003e3.1 Hamiltonian Dynamics of Continuous Systems \u003ci\u003e28\u003c\/i\u003e\u003c\/p\u003e \u003cp\u003e3.2 Three-Dimensional Incompressible Flows \u003ci\u003e32\u003c\/i\u003e\u003c\/p\u003e \u003cp\u003e3.3 Two-Dimensional Incompressible Flows \u003ci\u003e35\u003c\/i\u003e\u003c\/p\u003e \u003cp\u003e\u003cb\u003e4 Surface Tension Effects \u003c\/b\u003e\u003ci\u003e39\u003c\/i\u003e\u003c\/p\u003e \u003cp\u003e4.1 Shape of the Interface between Two Fluids \u003ci\u003e39\u003c\/i\u003e\u003c\/p\u003e \u003cp\u003e4.2 Capillary Rises in Liquids \u003ci\u003e41\u003c\/i\u003e\u003c\/p\u003e \u003cp\u003e\u003cb\u003ePart II Dynamics of Incompressible Fluid Flows \u003c\/b\u003e\u003ci\u003e45\u003c\/i\u003e\u003c\/p\u003e \u003cp\u003e\u003cb\u003e5 Fluid Kinematics and Dynamics \u003c\/b\u003e\u003ci\u003e47\u003c\/i\u003e\u003c\/p\u003e \u003cp\u003e5.1 Stream Function \u003ci\u003e47\u003c\/i\u003e\u003c\/p\u003e \u003cp\u003e5.2 Equations of Motion \u003ci\u003e50\u003c\/i\u003e\u003c\/p\u003e \u003cp\u003e5.3 Integrals of Motion \u003ci\u003e50\u003c\/i\u003e\u003c\/p\u003e \u003cp\u003e5.4 Capillary Waves on a Spherical Drop \u003ci\u003e51\u003c\/i\u003e\u003c\/p\u003e \u003cp\u003e5.5 Cavitation \u003ci\u003e54\u003c\/i\u003e\u003c\/p\u003e \u003cp\u003e5.6 Rates of Change of Material Integrals \u003ci\u003e55\u003c\/i\u003e\u003c\/p\u003e \u003cp\u003e5.7 The Kelvin Circulation Theorem \u003ci\u003e57\u003c\/i\u003e\u003c\/p\u003e \u003cp\u003e5.8 The Irrotational Flow \u003ci\u003e58\u003c\/i\u003e\u003c\/p\u003e \u003cp\u003e5.9 Simple-Flow Patterns \u003ci\u003e62\u003c\/i\u003e\u003c\/p\u003e \u003cp\u003e(i) The Source Flow \u003ci\u003e62\u003c\/i\u003e\u003c\/p\u003e \u003cp\u003e(ii) The Doublet Flow \u003ci\u003e63\u003c\/i\u003e\u003c\/p\u003e \u003cp\u003e(iii) The Vortex Flow \u003ci\u003e66\u003c\/i\u003e\u003c\/p\u003e \u003cp\u003e(iv) Doublet in a Uniform Stream \u003ci\u003e66\u003c\/i\u003e\u003c\/p\u003e \u003cp\u003e(v) Uniform Flow Past a Circular Cylinder with Circulation \u003ci\u003e67\u003c\/i\u003e\u003c\/p\u003e \u003cp\u003e\u003cb\u003e6 The Complex-Variable Method \u003c\/b\u003e\u003ci\u003e71\u003c\/i\u003e\u003c\/p\u003e \u003cp\u003e6.1 The Complex Potential \u003ci\u003e71\u003c\/i\u003e\u003c\/p\u003e \u003cp\u003e6.2 Conformal Mapping of Flows \u003ci\u003e74\u003c\/i\u003e\u003c\/p\u003e \u003cp\u003e6.3 Hydrodynamic Images \u003ci\u003e82\u003c\/i\u003e\u003c\/p\u003e \u003cp\u003e6.4 Principles of Free-Streamline Flow \u003ci\u003e84\u003c\/i\u003e\u003c\/p\u003e \u003cp\u003e(i) Schwarz-Christoffel Transformation \u003ci\u003e84\u003c\/i\u003e\u003c\/p\u003e \u003cp\u003e(ii) Hodograph Method \u003ci\u003e93\u003c\/i\u003e\u003c\/p\u003e \u003cp\u003e\u003cb\u003e7 Three-Dimensional Irrotational Flows \u003c\/b\u003e\u003ci\u003e99\u003c\/i\u003e\u003c\/p\u003e \u003cp\u003e7.1 Special Singular Solutions \u003ci\u003e99\u003c\/i\u003e\u003c\/p\u003e \u003cp\u003e(i) The Source Flow \u003ci\u003e99\u003c\/i\u003e\u003c\/p\u003e \u003cp\u003e(ii) The Doublet Flow \u003ci\u003e101\u003c\/i\u003e\u003c\/p\u003e \u003cp\u003e7.2 d’Alembert’s Paradox \u003ci\u003e104\u003c\/i\u003e\u003c\/p\u003e \u003cp\u003e7.3 Image of a Source in a Sphere \u003ci\u003e105\u003c\/i\u003e\u003c\/p\u003e \u003cp\u003e7.4 Flow Past an Arbitrary Body \u003ci\u003e107\u003c\/i\u003e\u003c\/p\u003e \u003cp\u003e7.5 Unsteady Flows \u003ci\u003e109\u003c\/i\u003e\u003c\/p\u003e \u003cp\u003e7.6 Renormalized (or Added) Mass of Bodies Moving through a Fluid \u003ci\u003e111\u003c\/i\u003e\u003c\/p\u003e \u003cp\u003e\u003cb\u003e8 Vortex Flows \u003c\/b\u003e\u003ci\u003e115\u003c\/i\u003e\u003c\/p\u003e \u003cp\u003e8.1 Vortex Tubes \u003ci\u003e115\u003c\/i\u003e\u003c\/p\u003e \u003cp\u003e8.2 Induced Velocity Field \u003ci\u003e117\u003c\/i\u003e\u003c\/p\u003e \u003cp\u003e8.3 Biot-Savart’s Law \u003ci\u003e117\u003c\/i\u003e\u003c\/p\u003e \u003cp\u003e8.4 von Kármán Vortex Street \u003ci\u003e121\u003c\/i\u003e\u003c\/p\u003e \u003cp\u003e8.5 Vortex Ring \u003ci\u003e124\u003c\/i\u003e\u003c\/p\u003e \u003cp\u003e8.6 Hill’s Spherical Vortex \u003ci\u003e129\u003c\/i\u003e\u003c\/p\u003e \u003cp\u003e8.7 Vortex Sheet \u003ci\u003e131\u003c\/i\u003e\u003c\/p\u003e \u003cp\u003e8.8 Vortex Breakdown: Brooke Benjamin’s Theory \u003ci\u003e135\u003c\/i\u003e\u003c\/p\u003e \u003cp\u003e\u003cb\u003e9 Rotating Flows \u003c\/b\u003e\u003ci\u003e143\u003c\/i\u003e\u003c\/p\u003e \u003cp\u003e9.1 Governing Equations and Elementary Results \u003ci\u003e143\u003c\/i\u003e\u003c\/p\u003e \u003cp\u003e9.2 Taylor-Proudman Theorem \u003ci\u003e144\u003c\/i\u003e\u003c\/p\u003e \u003cp\u003e9.3 Propagation of Inertial Waves in a Rotating Fluid \u003ci\u003e146\u003c\/i\u003e\u003c\/p\u003e \u003cp\u003e9.4 Plane Inertial Waves \u003ci\u003e147\u003c\/i\u003e\u003c\/p\u003e \u003cp\u003e9.5 Forced Wavemotion in a Rotating Fluid \u003ci\u003e150\u003c\/i\u003e\u003c\/p\u003e \u003cp\u003e(i) The Elliptic Case \u003ci\u003e153\u003c\/i\u003e\u003c\/p\u003e \u003cp\u003e(ii) The Hyperbolic Case \u003ci\u003e154\u003c\/i\u003e\u003c\/p\u003e \u003cp\u003e9.6 Slow Motion along the Axis of Rotation \u003ci\u003e155\u003c\/i\u003e\u003c\/p\u003e \u003cp\u003e9.7 Rossby Waves \u003ci\u003e160\u003c\/i\u003e\u003c\/p\u003e \u003cp\u003e\u003cb\u003e10 Water Waves \u003c\/b\u003e\u003ci\u003e167\u003c\/i\u003e\u003c\/p\u003e \u003cp\u003e10.1 Governing Equations \u003ci\u003e168\u003c\/i\u003e\u003c\/p\u003e \u003cp\u003e10.2 A Variational Principle for Surface Waves \u003ci\u003e169\u003c\/i\u003e\u003c\/p\u003e \u003cp\u003e10.3 Water Waves in a Semi-Infinite Fluid \u003ci\u003e171\u003c\/i\u003e\u003c\/p\u003e \u003cp\u003e10.4 Water Waves in a Fluid Layer of Finite Depth \u003ci\u003e172\u003c\/i\u003e\u003c\/p\u003e \u003cp\u003e10.5 Shallow-Water Waves \u003ci\u003e174\u003c\/i\u003e\u003c\/p\u003e \u003cp\u003e(i) Analogy with Gas Dynamics \u003ci\u003e175\u003c\/i\u003e\u003c\/p\u003e \u003cp\u003e(ii) Breaking of Waves \u003ci\u003e176\u003c\/i\u003e\u003c\/p\u003e \u003cp\u003e10.6 Water Waves Generated by an Initial Displacement over a Localized Region \u003ci\u003e176\u003c\/i\u003e\u003c\/p\u003e \u003cp\u003e10.7 Waves on a Steady Stream \u003ci\u003e182\u003c\/i\u003e\u003c\/p\u003e \u003cp\u003e(i) One-Dimensional Gravity Waves \u003ci\u003e183\u003c\/i\u003e\u003c\/p\u003e \u003cp\u003e(ii) One-Dimensional Capillary-Gravity Waves \u003ci\u003e184\u003c\/i\u003e\u003c\/p\u003e \u003cp\u003e(iii) Ship Waves \u003ci\u003e185\u003c\/i\u003e\u003c\/p\u003e \u003cp\u003e10.8 Gravity Waves in a Rotating Fluid \u003ci\u003e188\u003c\/i\u003e\u003c\/p\u003e \u003cp\u003e10.9 Theory of Tides \u003ci\u003e193\u003c\/i\u003e\u003c\/p\u003e \u003cp\u003e10.10 Hydraulic Jump \u003ci\u003e195\u003c\/i\u003e\u003c\/p\u003e \u003cp\u003e(i) Tidal Bores \u003ci\u003e195\u003c\/i\u003e\u003c\/p\u003e \u003cp\u003e(ii) The Dam-Break Problem \u003ci\u003e199\u003c\/i\u003e\u003c\/p\u003e \u003cp\u003e10.11 Nonlinear Shallow-Water Waves \u003ci\u003e202\u003c\/i\u003e\u003c\/p\u003e \u003cp\u003e (i) Solitary Waves \u003ci\u003e206\u003c\/i\u003e\u003c\/p\u003e \u003cp\u003e(ii) Periodic Cnoidal Waves \u003ci\u003e208\u003c\/i\u003e\u003c\/p\u003e \u003cp\u003e(iii) Interacting Solitary Waves \u003ci\u003e214\u003c\/i\u003e\u003c\/p\u003e \u003cp\u003e(iv) Stokes Waves \u003ci\u003e219\u003c\/i\u003e\u003c\/p\u003e \u003cp\u003e(v) Modulational Instability and Envelope Solutions \u003ci\u003e220\u003c\/i\u003e\u003c\/p\u003e \u003cp\u003e10.12 Nonlinear Capillary-Gravity Waves \u003ci\u003e230\u003c\/i\u003e\u003c\/p\u003e \u003cp\u003e(i) Resonant Three-Wave Interactions \u003ci\u003e230\u003c\/i\u003e\u003c\/p\u003e \u003cp\u003e(ii) Second-Harmonic Resonance \u003ci\u003e235\u003c\/i\u003e\u003c\/p\u003e \u003cp\u003e\u003cb\u003e11 Applications to Aerodynamics \u003c\/b\u003e\u003ci\u003e241\u003c\/i\u003e\u003c\/p\u003e \u003cp\u003e11.1 Airfoil Theory: Method of Complex Variables \u003ci\u003e242\u003c\/i\u003e\u003c\/p\u003e \u003cp\u003e(i) Force and Moments on an Arbitrary Body \u003ci\u003e242\u003c\/i\u003e\u003c\/p\u003e \u003cp\u003e(ii) Flow Past an Arbitrary Cylinder \u003ci\u003e245\u003c\/i\u003e\u003c\/p\u003e \u003cp\u003e(iii) Flow Around a Flat Plate \u003ci\u003e248\u003c\/i\u003e\u003c\/p\u003e \u003cp\u003e(iv) Flow Past an Airfoil \u003ci\u003e250\u003c\/i\u003e\u003c\/p\u003e \u003cp\u003e(v) The Joukowski Transformation \u003ci\u003e253\u003c\/i\u003e\u003c\/p\u003e \u003cp\u003e11.2 Thin Airfoil Theory \u003ci\u003e259\u003c\/i\u003e\u003c\/p\u003e \u003cp\u003e(i) Thickness Problem \u003ci\u003e262\u003c\/i\u003e\u003c\/p\u003e \u003cp\u003e(ii) Camber Problem  \u003ci\u003e264\u003c\/i\u003e\u003c\/p\u003e \u003cp\u003e(iii) Flat Plate at an Angle of Attack \u003ci\u003e269\u003c\/i\u003e\u003c\/p\u003e \u003cp\u003e(iv) Combined Aerodynamic Characteristics  \u003ci\u003e271\u003c\/i\u003e\u003c\/p\u003e \u003cp\u003e(v) The Leading-Edge Problem of a Thin Airfoil  \u003ci\u003e271\u003c\/i\u003e\u003c\/p\u003e \u003cp\u003e11.3 Slender-Body Theory \u003ci\u003e275\u003c\/i\u003e\u003c\/p\u003e \u003cp\u003e11.4 Prandtl’s Lifting-Line Theory for Wings \u003ci\u003e277\u003c\/i\u003e\u003c\/p\u003e \u003cp\u003e11.5 Oscillating Thin-Airfoil Problem: Theodorsen’s Theory \u003ci\u003e282\u003c\/i\u003e\u003c\/p\u003e \u003cp\u003e\u003cb\u003ePart III Dynamics of Compressible Fluid Flows \u003c\/b\u003e\u003ci\u003e297\u003c\/i\u003e\u003c\/p\u003e \u003cp\u003e\u003cb\u003e12 Review of Thermodynamics \u003c\/b\u003e\u003ci\u003e299\u003c\/i\u003e\u003c\/p\u003e \u003cp\u003e12.1 Thermodynamic System and Variables of State \u003ci\u003e299\u003c\/i\u003e\u003c\/p\u003e \u003cp\u003e12.2 The First Law of Thermodynamics and Reversible and Irreversible Processes \u003ci\u003e300\u003c\/i\u003e\u003c\/p\u003e \u003cp\u003e12.3 The Second Law of Thermodynamics \u003ci\u003e303\u003c\/i\u003e\u003c\/p\u003e \u003cp\u003e12.4 Entropy \u003ci\u003e304\u003c\/i\u003e\u003c\/p\u003e \u003cp\u003e12.5 Liquid and Gaseous Phases \u003ci\u003e307\u003c\/i\u003e\u003c\/p\u003e \u003cp\u003e\u003cb\u003e13 Isentropic Fluid Flows  \u003c\/b\u003e\u003ci\u003e309\u003c\/i\u003e\u003c\/p\u003e \u003cp\u003e13.1 Applications of Thermodynamics to Fluid Flows \u003ci\u003e309\u003c\/i\u003e\u003c\/p\u003e \u003cp\u003e13.2 Linear Sound Wave Propagation \u003ci\u003e310\u003c\/i\u003e\u003c\/p\u003e \u003cp\u003e13.3 The Energy Equation \u003ci\u003e310\u003c\/i\u003e\u003c\/p\u003e \u003cp\u003e13.4 Stream-Tube Area and Flow Velocity Relations \u003ci\u003e312\u003c\/i\u003e\u003c\/p\u003e \u003cp\u003e\u003cb\u003e14 Potential Flows \u003c\/b\u003e\u003ci\u003e317\u003c\/i\u003e\u003c\/p\u003e \u003cp\u003e14.1 Governing Equations \u003ci\u003e317\u003c\/i\u003e\u003c\/p\u003e \u003cp\u003e14.2 Streamline Coordinates \u003ci\u003e319\u003c\/i\u003e\u003c\/p\u003e \u003cp\u003e14.3 Conical Flows: Prandtl-Meyer Flow \u003ci\u003e320\u003c\/i\u003e\u003c\/p\u003e \u003cp\u003e14.4 Small Perturbation Theory \u003ci\u003e324\u003c\/i\u003e\u003c\/p\u003e \u003cp\u003e14.5 Characteristics \u003ci\u003e326\u003c\/i\u003e\u003c\/p\u003e \u003cp\u003e(i) Compatibility Conditions in Streamline Coordinates \u003ci\u003e328\u003c\/i\u003e\u003c\/p\u003e \u003cp\u003e(ii) A Singular-Perturbation Problem for Hyperbolic Systems \u003ci\u003e331\u003c\/i\u003e\u003c\/p\u003e \u003cp\u003e\u003cb\u003e15 Nonlinear Theory of Plane Sound Waves \u003c\/b\u003e\u003ci\u003e343\u003c\/i\u003e\u003c\/p\u003e \u003cp\u003e15.1 Riemann Invariants \u003ci\u003e343\u003c\/i\u003e\u003c\/p\u003e \u003cp\u003e15.2 Simple Wave Solutions \u003ci\u003e344\u003c\/i\u003e\u003c\/p\u003e \u003cp\u003e15.3 Nonlinear Propagation of a Sound Wave \u003ci\u003e352\u003c\/i\u003e\u003c\/p\u003e \u003cp\u003e15.4 Nonlinear Resonant Three-Wave Interactions of Sound Waves \u003ci\u003e355\u003c\/i\u003e\u003c\/p\u003e \u003cp\u003e15.5 Burgers Equation \u003ci\u003e361\u003c\/i\u003e\u003c\/p\u003e \u003cp\u003e\u003cb\u003e16 Shock Waves \u003c\/b\u003e\u003ci\u003e371\u003c\/i\u003e\u003c\/p\u003e \u003cp\u003e16.1 The Normal Shock Wave \u003ci\u003e371\u003c\/i\u003e\u003c\/p\u003e \u003cp\u003e16.2 The Oblique Shock Wave \u003ci\u003e384\u003c\/i\u003e\u003c\/p\u003e \u003cp\u003e16.3 Blast Waves: Taylor’s Self-similarity and Sedov’s Exact Solution \u003ci\u003e387\u003c\/i\u003e\u003c\/p\u003e \u003cp\u003e\u003cb\u003e17 The Hodograph Method \u003c\/b\u003e\u003ci\u003e393\u003c\/i\u003e\u003c\/p\u003e \u003cp\u003e17.1 The Hodograph Transformation of Potential Flow Equations \u003ci\u003e393\u003c\/i\u003e\u003c\/p\u003e \u003cp\u003e17.2 The Chaplygin Equation \u003ci\u003e394\u003c\/i\u003e\u003c\/p\u003e \u003cp\u003e17.3 The Tangent-Gas Approximation \u003ci\u003e396\u003c\/i\u003e\u003c\/p\u003e \u003cp\u003e17.4 The Lost Solution \u003ci\u003e401\u003c\/i\u003e\u003c\/p\u003e \u003cp\u003e17.5 The Limit Line \u003ci\u003e402\u003c\/i\u003e\u003c\/p\u003e \u003cp\u003e\u003cb\u003e18 Applications to Aerodynamics \u003c\/b\u003e\u003ci\u003e411\u003c\/i\u003e\u003c\/p\u003e \u003cp\u003e18.1 Thin Airfoil Theory \u003ci\u003e411\u003c\/i\u003e\u003c\/p\u003e \u003cp\u003e(i) Thin Airfoil in Linearized Supersonic Flows \u003ci\u003e411\u003c\/i\u003e\u003c\/p\u003e \u003cp\u003e(ii) Far-Field Behavior of Supersonic Flow Past a Thin Airfoil \u003ci\u003e414\u003c\/i\u003e\u003c\/p\u003e \u003cp\u003e(iii) Thin Airfoil in Transonic Flows \u003ci\u003e417\u003c\/i\u003e\u003c\/p\u003e \u003cp\u003e18.2 Slender Bodies of Revolution \u003ci\u003e420\u003c\/i\u003e\u003c\/p\u003e \u003cp\u003e18.3 Oscillating Thin Airfoil in Subsonic Flows: Possio’s Theory \u003ci\u003e427\u003c\/i\u003e\u003c\/p\u003e \u003cp\u003e18.4 Oscillating Thin Airfoils in Supersonic Flows: Stewartson’s Theory \u003ci\u003e435\u003c\/i\u003e\u003c\/p\u003e \u003cp\u003e\u003cb\u003ePart IV Dynamics of Viscous Fluid Flows \u003c\/b\u003e\u003ci\u003e439\u003c\/i\u003e\u003c\/p\u003e \u003cp\u003e\u003cb\u003e19 Exact Solutions to Equations of Viscous Fluid Flows \u003c\/b\u003e\u003ci\u003e441\u003c\/i\u003e\u003c\/p\u003e \u003cp\u003e19.1 Channel Flows  \u003ci\u003e442\u003c\/i\u003e\u003c\/p\u003e \u003cp\u003e19.2 Decay of a Line Vortex: The Lamb-Oseen Vortex  \u003ci\u003e443\u003c\/i\u003e\u003c\/p\u003e \u003cp\u003e19.3 Line Vortex in a Uniform Stream \u003ci\u003e446\u003c\/i\u003e\u003c\/p\u003e \u003cp\u003e19.4 Diffusion of a Localized Vorticity Distribution \u003ci\u003e446\u003c\/i\u003e\u003c\/p\u003e \u003cp\u003e19.5 Burgers Vortex  \u003ci\u003e451\u003c\/i\u003e\u003c\/p\u003e \u003cp\u003e19.6 Flow Due to a Suddenly Accelerated Plane  \u003ci\u003e453\u003c\/i\u003e\u003c\/p\u003e \u003cp\u003e19.7 The Round Laminar Jet: Landau-Squire Solution \u003ci\u003e456\u003c\/i\u003e\u003c\/p\u003e \u003cp\u003e19.8 Ekman Layer at a Free Surface in a Rotating Fluid \u003ci\u003e459\u003c\/i\u003e\u003c\/p\u003e \u003cp\u003e19.9 Centrifugal Flow Due to a Rotating Disk: von Kármán Solution \u003ci\u003e462\u003c\/i\u003e\u003c\/p\u003e \u003cp\u003e19.10 Shock Structure: Becker’s Solution \u003ci\u003e464\u003c\/i\u003e\u003c\/p\u003e \u003cp\u003e19.11 Couette Flow of a Gas \u003ci\u003e467\u003c\/i\u003e\u003c\/p\u003e \u003cp\u003e\u003cb\u003e20 Flows at Low Reynolds Numbers \u003c\/b\u003e\u003ci\u003e469\u003c\/i\u003e\u003c\/p\u003e \u003cp\u003e20.1 Dimensional Analysis \u003ci\u003e469\u003c\/i\u003e\u003c\/p\u003e \u003cp\u003e20.2 Stokes’ Flow Past a Rigid Sphere: Stokes’ Formula \u003ci\u003e470\u003c\/i\u003e\u003c\/p\u003e \u003cp\u003e20.3 Stokes’ Flow Past a Spherical Drop \u003ci\u003e474\u003c\/i\u003e\u003c\/p\u003e \u003cp\u003e20.4 Stokes’ Flow Past a Rigid Circular Cylinder: Stokes’ Paradox \u003ci\u003e478\u003c\/i\u003e\u003c\/p\u003e \u003cp\u003e20.5 Oseen’s Flow Past a Rigid Sphere \u003ci\u003e479\u003c\/i\u003e\u003c\/p\u003e \u003cp\u003e20.6 Oseen’s Approximation for Periodically Oscillating Wakes \u003ci\u003e483\u003c\/i\u003e\u003c\/p\u003e \u003cp\u003e\u003cb\u003e21 Flows at High Reynolds Numbers \u003c\/b\u003e\u003ci\u003e489\u003c\/i\u003e\u003c\/p\u003e \u003cp\u003e21.1 Prandtl’s Boundary-Layer Concept  \u003ci\u003e489\u003c\/i\u003e\u003c\/p\u003e \u003cp\u003e21.2 The Method of Matched Asymptotic Expansions \u003ci\u003e490\u003c\/i\u003e\u003c\/p\u003e \u003cp\u003e21.3 Location and Nature of the Boundary Layers \u003ci\u003e497\u003c\/i\u003e\u003c\/p\u003e \u003cp\u003e21.4 Incompressible Flow Past a Flat Plate  \u003ci\u003e500\u003c\/i\u003e\u003c\/p\u003e \u003cp\u003e(i) The Outer Expansion  \u003ci\u003e501\u003c\/i\u003e\u003c\/p\u003e \u003cp\u003e(ii) The Inner Expansion \u003ci\u003e502\u003c\/i\u003e\u003c\/p\u003e \u003cp\u003e(iii) Flow Due to Displacement Thickness \u003ci\u003e507\u003c\/i\u003e\u003c\/p\u003e \u003cp\u003e21.5 Separation of Flow in a Boundary Layer: Landau’s Theory \u003ci\u003e509\u003c\/i\u003e\u003c\/p\u003e \u003cp\u003e21.6 Boundary Layers in Compressible Flows \u003ci\u003e512\u003c\/i\u003e\u003c\/p\u003e \u003cp\u003e(i) Crocco’s Integral \u003ci\u003e514\u003c\/i\u003e\u003c\/p\u003e \u003cp\u003e(ii) Flow Past a Flat Plate: Howarth-Dorodnitsyn Transformation \u003ci\u003e516\u003c\/i\u003e\u003c\/p\u003e \u003cp\u003e21.7 Flow in a Mixing Layer between Two Parallel Streams \u003ci\u003e517\u003c\/i\u003e\u003c\/p\u003e \u003cp\u003e(i) Geometrical Characteristics of the Mixing Flow \u003ci\u003e520\u003c\/i\u003e\u003c\/p\u003e \u003cp\u003e21.8 Narrow Jet: Bickley’s Solution  \u003ci\u003e521\u003c\/i\u003e\u003c\/p\u003e \u003cp\u003e21.9 Wakes  \u003ci\u003e524\u003c\/i\u003e\u003c\/p\u003e \u003cp\u003e21.10 Periodic Boundary Layer Flows \u003ci\u003e524\u003c\/i\u003e\u003c\/p\u003e \u003cp\u003e\u003cb\u003e22 Jeffrey-Hamel Flow  \u003c\/b\u003e\u003ci\u003e529\u003c\/i\u003e\u003c\/p\u003e \u003cp\u003e22.1 The Exact Solution \u003ci\u003e529\u003c\/i\u003e\u003c\/p\u003e \u003cp\u003e(i) Only 𝑒\u003csub\u003e1\u003c\/sub\u003e Is Real and Positive \u003ci\u003e531\u003c\/i\u003e\u003c\/p\u003e \u003cp\u003e(ii) 𝑒\u003csub\u003e1\u003c\/sub\u003e, 𝑒\u003csub\u003e2\u003c\/sub\u003e, and 𝑒\u003csub\u003e3\u003c\/sub\u003e Are Real and Distinct  \u003ci\u003e532\u003c\/i\u003e\u003c\/p\u003e \u003cp\u003e22.2 Flows at Low Reynolds Numbers \u003ci\u003e535\u003c\/i\u003e\u003c\/p\u003e \u003cp\u003e22.3 Flows at High Reynolds Numbers \u003ci\u003e541\u003c\/i\u003e\u003c\/p\u003e \u003cp\u003e\u003cb\u003eReferences \u003c\/b\u003e\u003ci\u003e545\u003c\/i\u003e\u003c\/p\u003e \u003cp\u003e\u003cb\u003eBibliography \u003c\/b\u003e\u003ci\u003e549\u003c\/i\u003e\u003c\/p\u003e \u003cp\u003e\u003cb\u003eIndex \u003c\/b\u003e\u003ci\u003e551\u003c\/i\u003e\u003c\/p\u003e \u003cp\u003e\u003cb\u003eBhimsen K. Shivamoggi, PhD, \u003c\/b\u003eis 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.\u003c\/p\u003e  \u003cp\u003e\u003cb\u003eA practical treatment of mathematical fluid dynamics\u003c\/b\u003e\u003c\/p\u003e \u003cp\u003eIn \u003ci\u003eIntroduction to Theoretical and Mathematical Fluid Dynamics\u003c\/i\u003e, distinguished researcher Dr. Bhimsen K. Shivamoggi delivers a comprehensive and insightful exploration of fluid dynamics from a mathematical point of view. The book introduces readers to the mathematical study of fluid behavior and highlights areas of active research in fluid dynamics. With coverage of advances in the field over the last 15 years, this book provides in-depth examinations of theoretical and mathematical fluid dynamics with a particular focus on incompressible and compressible fluid flows. \u003c\/p\u003e\u003cp\u003e\u003ci\u003eIntroduction to Theoretical and Mathematical Fluid Dynamics\u003c\/i\u003e includes practical applications and exercises to illustrate the concepts discussed within, and real-world examples are explained throughout the text. Clear and explanatory material accompanies the rigorous mathematics, making the book perfect for students seeking to learn and retain this complex subject. \u003c\/p\u003e\u003cp\u003eThe book also offers: \u003c\/p\u003e\u003cul\u003e\n\u003cli\u003eA thorough introduction to the basic concepts and equations of fluid dynamics, including an introduction to the fluid model, the equations of fluid flows, and surface tension effects\u003c\/li\u003e \u003cli\u003eComprehensive explorations of the dynamics of incompressible fluid flows, fluid kinematics and dynamics, the complex-variable method, and three-dimensional irrotational flows\u003c\/li\u003e \u003cli\u003ePractical discussions of the dynamics of compressible fluid flows, including a review of thermodynamics, isentropic fluid flows, potential flows, and nonlinear theory of plane sound waves\u003c\/li\u003e\n\u003c\/ul\u003e \u003cp\u003eIdeal for graduate-level students taking courses on mathematical fluid dynamics as part of a program in mathematics, engineering, or physics, \u003ci\u003eIntroduction to Theoretical and Mathematical Fluid Dynamics\u003c\/i\u003e is also an indispensable resource for practicing applied mathematicians, engineers, and physicists.\u003c\/p\u003e","brand":"Wiley","offers":[{"title":"Default Title","offer_id":47989468594405,"sku":"NP9781119101505","price":135.0,"currency_code":"USD","in_stock":false}],"thumbnail_url":"\/\/cdn.shopify.com\/s\/files\/1\/1842\/7735\/files\/9781119101505.jpg?v=1761784222","url":"https:\/\/k12savings.com\/es\/products\/introduction-to-theoretical-and-mathematical-fluid-dynamics-isbn-9781119101505","provider":"K12savings","version":"1.0","type":"link"}