Cambridge University Press, 1992. 321 p. — ISBN:0-521-42058-X hardbackThe 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 secondaryContents Preface 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 References Index
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4 Edition. — Academic Press, 2007. — 904 p. — ISBN: 0123737354
Fluid mechanics, the study of how fluids behave and interact under various forces and in various applied situations-whether in the liquid or gaseous state or both-is introduced and comprehensively covered in this widely adopted text. Fully revised and updated with the addition of a new chapter on biofluid...