Saffman P.G. Vortex Dynamics

Cambridge University Press, 1992. — 321 p. — ISBN 0-521-42058-X.The discovery of coherent structures in turbulence has fostered the hope that the study of vortices will lead to models and an understanding of turbulent flow, thereby solving or at least making less mysterious one of the great unsolved problems of classical physics. Vortex dynamics is a natural paradigm for the field of chaotic motion and modern dynamical system theory. The emphasis in this monograph is on the classical theory of inviscid incompressible fluids containing finite regions of vorticity. The effects of viscosity, compressibility, inhomogeneity and stratification are enormously important in many fields of application, from hypersonic flight to global environmental fluid mechanics. However, this volume focuses on those aspects of fluid motion which are primarily controlled by the vorticity and are such that the effects of the other fluid properties are secondaryPreface page
Fundamental properties of vorticity
Relation between velocity and vorticity
Vorlicity and rotation
Circulation
Vortex lines and tubes
The laws of vortex motion
Kelvin's circulation theorem
Cauchy's equations
lrrotational flow
Bernoulli's equation
Singular distributions of vortieitv
Vortex jumps
Vortex sheets
Line vortices
Image vorticity
Vortex momentum
Vortex force and hound vorticily
Hydrodynamic impulse
Impulsive generation from rest
Effect of compressibility
Angular impulse
Effect of viscosity
Impulse of isolated vortices
Impulse of a line vortex
Vortex centroid
MO Impulse in two dimensions
Kinetic energy of vortices
Helicity
Axisymmetric motion with swirl
Motion with surfaces
Virtual momentum of a moving body
Virtual momentum and impulse
Virtual angular momentum
Two-dimensional motion with circulation
Some applications
Virtual mass
Attraction of vortices or bodies to walls
Force on a body in a non-uniform stream
Force on a body in an accelerated irrotational stream
Rotating bodies
Torque on a body in a non-uniform stream
Self-propulsion of a deformable body
Buoyant vortex rings
Creation of vorticity
Formation of a vortex sheet
Leading edge suction on the sheet
Approximate development of the sheet into a vortex pair
Formation of a vortex ring
Creation of circulation about a body
Generation of vorticity by flow separation
Accelerated flow past a wing
Dynamics of line vortices in two-dimensional flow
Stability of a polygonal array
Vortices near walls
Kirchhoff-Routh path function
Conformal mapping and the Kirchhoff-Routh path function
Stability of infinite periodic arrays
The Karman vortex street
Statistical mechanics of assemblies of line vortices
Vortex sheets in two dimensions
The Birkhoff-Rott equation
Kelvin-Helmholtz instability
The ill-posedness of vortex sheets Roll-up of a semi-infinite vortex sheet: The Kaden spiral
General similarity solutions, single and multibranched spirals
Dynamics of two-dimensional vortex patches
Vortex sheets of finite thickness
Contour dynamics and Schwarz functions
The Kirchhoff vortex and elliptical patches in uniform strain
Equilibrium configurations for single patches
Filamentation
Vortex pairs
Arrays of vortex patches
Axisymmetric vortex rings
Formulation
Thin cored rings
Lamb's transformation and general core structure
Canonical co-ordinates for thin rings
Dynamics of vortex filaments
Local induction approximation
The cut-off method
Kelvin waves on a filament
Justification of the cut-off and higher-order approximations
Three-dimensional vortex instability
Oscillations of a vortex column
Long-wave co-operative instabilities
Short-wave co-operative instability
Ultra short-wave co-operative instability
Effects of viscosity
Viscous cores
Decay of trailing vortices
Burgers vortices
Miscellaneous topics
Minimum induced drag
Kelvin's variational principle
Hamiltonian dynamics of vortex patch moments
Vortex breakdown
Epilogue