Bhimsen K. Shivamoggi

Introduction to Theoretical and Mathematical Fluid Dynamics (eBook, PDF)

• Format: PDF

Produktbeschreibung

INTRODUCTION TO THEORETICAL AND MATHEMATICAL FLUID DYNAMICS A practical treatment of mathematical fluid dynamics In Introduction to Theoretical and Mathematical Fluid Dynamics, 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. Introduction to Theoretical and Mathematical Fluid Dynamics 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. The book also offers: * A 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 * Comprehensive explorations of the dynamics of incompressible fluid flows, fluid kinematics and dynamics, the complex-variable method, and three-dimensional irrotational flows * Detailed 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 * Systematic discussions of the dynamics of viscous fluid flows, including shear-layer flow, jet flow and wake flow. Ideal for graduate-level students taking courses on mathematical fluid dynamics as part of a program in mathematics, engineering, or physics, Introduction to Theoretical and Mathematical Fluid Dynamics is also an indispensable resource for practicing applied mathematicians, engineers, and physicists.

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Produktdetails

• Verlag: John Wiley & Sons
• Seitenzahl: 576
• Erscheinungstermin: 16. September 2022
• Englisch
• ISBN-13: 9781119101512
• Artikelnr.: 66253626

Autorenporträt

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.

Inhaltsangabe

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 Dynam