Divi sion of En gineering, Brown Un iver sity, Providence, Rh ode Is land 02912It is indeed rather astonishing how little practical value scientific knowledge has for ordinary men, how dull and commonplace such of it as has value is, and how its value seems almost to vary inversely to its reputed utility.
G. H. Hardy, A Mathematician's Apology
INTRODUCTORY REMARKSVortex dynamic s would appear to be exempt from Hardy 's pe ssimi stic verdict. On one hand, the evolution of vorticity, and thu s the motion s of vortice s, are esse ntial ingredients of virtually any real flow. He nce vortex dynamic s is of profound practical importance. On the other hand, vortex motion ha s alway s con stituted a mathematically so phi sticated branch of fluid mechanics that continue s to invite the application of novel analyti cal technique s. Indeed it is ne it her dull nor co mmonplace .Thi s central role of vorticity in fluid mechanic s is not difficult to understand. As we know, any velocity field, v, can be sp lit into a su m of two field s, one with the sa me divergence as v, and no curl, and one with the sa me cu rl as v and vani shing divergence. Th is important re sult is due to Stoke s and to Helmholtz (1858; se e Sommerfeld 1964). In incompre ssi ble flow , as we deal with exclu si vely here, the fir st part is irrotational and diver gence-free and thu s lead s to the linear problem of po tential flow. , The se cond part, however , derive s directly from the vorticity of the field ' v. In the dynamic s of thi s part lie s the esse nce of the problem. 345 0066-4189/8 3/011 5-03 45$ 02.00 Annu. Rev. Fluid Mech. 1983.15:345-389. Downloaded from www.annualreviews.org by NORTH CAROLINA STATE UNIVERSITY on 10/20/12. For personal use only. Quick links to online content Further ANNUAL REVIEWS