In 1858 Hermann von Helmholtz published his seminal paper "Über Integrale der hydrodynamischen Gleichungen, welche den Wirbelbewegungen entsprechen," in Journal für die reine und angewandte Mathematik, vol. 55, pp. 25–55. So important was the paper that a few years later P. G. Tait published an English translation, "On integrals of the hydrodynamical equations which express vortex motion", in Philosophical Magazine, vol. 33, pp. 485–512 (1867). In his paper Helmholtz established his three "laws of vortex motion" in much the same way one finds them in any advanced textbook of fluid mechanics today. This work established the significance of vorticity to fluid mechanics and science in general.
For the next century or so vortex dynamics matured as a subfield of fluid mechanics, always commanding at least a major chapter in treatises on the subject. Thus, H. Lambs well known Hydrodynamics (6th ed., 1932) devotes a full chapter to vorticity and vortex dynamics as does G. K. Batchelors [https://archive.today/20130112165003/http://www.cambridge.org/uk/series/sSeries.asp?code=CML&srt=T Introduction to Fluid Dynamics] (1967). In due course entire treatises were devoted to vortex motion. H. Poincarés Théorie des Tourbillons (1893), [http://genealogy.math.ndsu.nodak.edu/html/id.phtml?id=80970 H. Villats] Leçons sur la Théorie des Tourbillons (1930), C. Truesdells The Kinematics of Vorticity (1954), and P. G. Saffmans [https://web.archive.org/web/20070314022441/http://www.cambridge.org/us/catalogue/email.asp?isbn=0521477395 Vortex Dynamics] (1992) may be mentioned. Early on individual sessions at scientific conferences were devoted to vortices, vortex motion, vortex dynamics and vortex flows. Later, entire meetings were devoted to the subject.
The range of applicability of Helmholtz's work grew to encompass atmospheric and oceanographic flows, to all branches of engineering and applied science and, ultimately, to superfluids (today including Bose–Einstein condensates). In modern fluid mechanics the role of vortex dynamics in explaining flow phenomena is firmly established. Well known vortices have acquired names and are regularly depicted in the popular media: hurricanes, tornadoes, waterspouts, aircraft trailing vortices (e.g., wingtip vortices), drainhole vortices (including the bathtub vortex), smoke rings, underwater bubble air rings, cavitation vortices behind ship propellers, and so on. In the technical literature a number of vortices that arise under special conditions also have names: the Kármán vortex street wake behind a bluff body, Taylor vortices between rotating cylinders, Görtler vortices in flow along a curved wall, etc.