Inviscid Incompressible Flow

by Marshall, Jeffrey S.

• ISBN13: 9780471375661
• ISBN10: 0471375667
• Edition: 1st
• Format: Hardcover
• Copyright: 2001-06-25
• Publisher: Wiley-Interscience

Summary

A comprehensive, modern account of the flow of inviscid incompressible fluids This one-stop resource for students, instructors, and professionals goes beyond analytical solutions for irrotational fluids to provide practical answers to real-world problems involving complex boundaries. It offers extensive coverage of vorticity transport as well as computational methods for inviscid flows, and it provides a solid foundation for further studies in fluid dynamics. Inviscid Incompressible Flow supplies a rigorous introduction to the continuum mechanics of fluid flows. It derives vector representation theorems, develops the vorticity transport theorem and related integral invariants, and presents theorems associated with the pressure field. This self-contained sourcebook describes both solution methods unique to two-dimensional flows and methods for axisymmetric and three-dimensional flows, many of which can be applied to two-dimensional flows as a special case. Finally, it examines perturbations of equilibrium solutions and ensuing stability issues. Important features of this powerful, timely volume include: * Focused, comprehensive coverage of inviscid incompressible fluids * Four entire chapters devoted to vorticity transport and solution of vortical flows * Theorems and computational methods for two-dimensional, axisymmetric, and three-dimensional flows * A companion Web site containing subroutines for calculations in the book * Clear, easy-to-follow presentation Inviscid Incompressible Flow, the only all-in-one presentation available on this topic, is a first-rate teaching and learning tool for graduate- and senior undergraduate-level courses in inviscid fluid dynamics. It is also an excellent reference for professionals and researchers in engineering, physics, and applied mathematics.

Author Biography

JEFFREY S. MARSHALL, PhD, is a professor in the Department of Mechanical Engineering and a research engineer at the Iowa Institute of Hydraulic Research at the University of Iowa, Iowa City.

Table of Contents

Preface	xi
Introduction	1	(8)
Role of Viscosity in High-Reynolds-Number Flows	3	(3)
Inviscid Flows	6	(3)
Bibliography	7	(2)
Vectors and Tensors	9	(15)
Cartesian Index Notation	9	(2)
Kronecker Delta and Permutation Tensor	11	(1)
Vector and Tensor Operations	12	(2)
Vector and Tensor Transformations	14	(1)
Symmetric and Skew-Symmetric Tensors	15	(1)
Vector Identities	16	(2)
Integral Identities	18	(6)
Bibliography	22	(1)
Problems	23	(1)
Kinematics of Fluid Motion	24	(20)
Descriptions of Fluid Motion	24	(4)
Deformation Measures	28	(1)
Stretch Rate and Vorticity	29	(4)
Dilatation	33	(3)
Pathlines, Streaklines, Streamlines, and Vortex Lines	36	(4)
Transport Theorem	40	(4)
Bibliography	42	(1)
Problems	42	(2)
Laws of Fluid Dynamics	44	(19)
Mass Conservation	44	(2)
Momentum Conservation	46	(3)
Moment of Momentum Conservation	49	(2)
Kinetic Energy Transport Theorem	51	(2)
Constraint of Incompressibility	53	(2)
Navier-Stokes Equation and Some Simple Solutions	55	(8)
Bibliography	59	(1)
Problems	59	(4)
Dynamics of Discontinuity Surfaces	63	(13)
Extended Transport Theorem for a Region Containing a Discontinuity Surface	63	(3)
Jump Conditions across a Surface of Discontinuity	66	(2)
Surface Tension	68	(5)
Boundary Conditions for Fluid Flow	73	(3)
Bibliography	74	(1)
Problems	75	(1)
Velocity Representations And Associated Theorems	76	(16)
Irrotational (Lamellar) and Related Flows	76	(3)
Incompressible (Solenoidal) Flows	79	(2)
Flows That Are Both Incompressible and Irrotational	81	(2)
Helmholtz Representation Theorem	83	(3)
Biot-Savart Law	86	(2)
Far-Field Asymptotic Form for Velocity in a Flow Extending to Infinity	88	(4)
Bibliography	90	(1)
Problems	90	(2)
Vorticity Transport Theorems	92	(22)
Vorticity Transport Equation	92	(3)
Motion of Vortex Lines	95	(2)
Preservation of Circulation	97	(1)
Vorticity Measures and Invariants	98	(7)
Vorticity Invariants in Two-Dimensional Flows	105	(2)
Vorticity Transport and Invariants in Viscous Flows	107	(7)
Bibliography	109	(1)
Problems	110	(4)
Pressure Theorems	114	(8)
Pressure Poisson Equation	114	(1)
Bernoulli Theorem	115	(1)
Boundary Integral Equation for Pressure	116	(3)
Special Results for Steady, Two-Dimensional Flows	119	(3)
Bibliography	120	(1)
Problems	120	(2)
Two-Dimensional Potential Flows	122	(44)
Analogy between Potential Flows and Analytic Functions of a Complex Variable	122	(2)
Some Basic Potential Flows	124	(4)
Superposition of Basic Flows	128	(5)
Circle Theorem	133	(3)
Method of Images	136	(3)
Conformal Transformation of Fluid Flows	139	(5)
Transformation ξ = zn	144	(4)
Joukowski Transformation	148	(3)
Schwarz-Christoffel Equation	151	(6)
Free-Streamline Theory	157	(9)
Bibliography	162	(1)
Problems	163	(3)
Forces on Bodies in Two-Dimensional Flows	166	(17)
Integration in the Complex Plane	166	(2)
Blasius Force and Moment Laws	168	(4)
Lagally's Theorem	172	(1)
D' Alembert's Paradox and the Kutta-Joukowski Lift Law	173	(2)
Application to Two-Dimensional Airfoils	175	(8)
Bibliography	180	(1)
Problems	180	(3)
Two-Dimensional Flows With Vorticity	183	(36)
Systems of Point Vortices	183	(3)
Conformal Transformation of Uniform-Vorticity Patches	186	(5)
Contour Integration Method for Uniform-Vorticity Patches	191	(2)
Discrete-Vortex Numerical Method: Basic Method	193	(4)
Discrete-Vortex Numerical Method: Acceleration Techniques	197	(6)
Vortex Sheets	203	(6)
Vortex Sheet Representation of Flat-Plate Airfoils	209	(3)
Flow with Uniform Background Vorticity	212	(7)
Bibliography	215	(1)
Problems	216	(2)
Computational Projects	218	(1)
Three-Dimensional Potential Flows	219	(41)
Governing Equations	219	(2)
Basic Potential Flows	221	(4)
Some Axisymmetric Flows with Immersed Bodies	225	(6)
Sphere Theorems	231	(4)
Slender-Body Theory	235	(3)
Source and Doublet Sheet Boundary-Integral Methods	238	(5)
Vortex Sheet Boundary-Integral Method	243	(3)
Forces Induced by Singularities	246	(3)
Added Mass and Buoyancy Forces	249	(11)
Bibliography	255	(1)
Problems	256	(2)
Computational Projects	258	(2)
Axisymmetric Vortex Flows	260	(36)
General Theory	260	(5)
Thin-Core Vortex Rings	265	(6)
Hill's Spherical Vortex	271	(2)
Axisymmetric Contour Dynamics	273	(4)
Steady Axisymmetric Flows	277	(2)
Waves of Variable Core Area	279	(4)
Plug-Flow Model	283	(5)
Axisymmetric Discrete-Vortex Method	288	(8)
Bibliography	292	(1)
Problems	293	(2)
Computational Projects	295	(1)
Vortex Tubes	296	(18)
Velocity Field Induced by a Curved Vortex Filament	297	(1)
Cut-Off Model for a Vortex Tube	298	(5)
Local-Induction Approximation	303	(3)
Bending Waves on a Vortex Tube	306	(8)
Bibliography	311	(1)
Problems	312	(1)
Computational Projects	313	(1)
Interfacial Wave Motion	314	(16)
Internal Waves in Layered Media	314	(2)
Linear Wave Theory	316	(3)
Capillary and Gravity Waves	319	(1)
Particle Displacement in a Wave Field	320	(2)
Wave Energy and Group Velocity	322	(3)
Boundary-Integral Method for Nonlinear Interfacial Waves	325	(5)
Bibliography	327	(1)
Problems	327	(3)
Stability of Fluid Flows	330	(37)
General Concepts	331	(1)
Stability of an Elliptical Vortex Patch in a Straining Flow	332	(5)
Stability of Two-Dimensional Point Vortex Arrays	337	(6)
Interfacial Instabilities	343	(3)
Capillary Instability of a Liquid Jet	346	(2)
Centrifugal Instability	348	(4)
Stability of Parallel Shear Flows	352	(6)
Three-Dimensional Instability of a Vortex Pair	358	(9)
Bibliography	361	(2)
Problems	363	(4)
Appendix A Common Expressions in Orthogonal Curvilinear Coordinate Systems	367	(6)
Index	373