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INTRODUCTION
All real fluid motions are rotational. Even in nearly irrotational flows the relatively small amount of vorticity present may be of central importance in determining major flow characteristics, and even some of those whose interest in fluid dynamics is only of the practical sort are now beginning to learn that the hitherto largely neglected questions of vorticity must at last be faced.
The more deeply one penetrates the general character of fluid motions, the more apparent it becomes that the dynamical properties of fluids in the main are but names, interpretations, and methods of measuring purely kinematical quantities, and that in general the flow of a fluid, whether perfect or viscous, may be defined by purely kinematical conditions. It is no accident that the greatest contributions to practical fluid dynamics were preceded by kinematical analyses which in themselves belong to pure mathematics rather than to mechanics or physics; while the work of Stokes, Helmholtz, and Kelvin is familiar, it is less well known that Euler headed his several successive presentations of the general equations of perfect fluids by increasingly detailed and accurate investigations of the possible motions of any deformable continuum, and that the same Zhukovski who discovered the artifice by which perfect fluid theory can be turned to practical use in plane wing theory began his career with a long memoir on the kinematics of continuous media.
In the realization that the kinematics of rotational motions contains the essence of fluid dynamics the present essay was conceived. Many a theorem generally regarded as dynamical will here be found in a purer form, presented at its proper station in a consecutive development. In particular, classical hydrodynamics may be characterized by the kinematical statement of Kelvin's circulation theorem, and in this way all the general properties of baro tropic flows of in viscid fluids subject to conservative extraneous force (properties which necessarily hold equally for a special class of flows of viscous liquids) will appear as special cases of certain purely kinematical theorems valid for arbitrary media. Let no one contend, however, that I have merely derived the old results in a new way. Rather, circulation-preserving motions afford but the simplest and most elegant applications of some parts of the general theory, a theory constructed in the hope that it will prove useful in understanding the behavior of complicated media whose dynamical response is more elaborate than that represented by the classical laws of viscosity. All dynamical statements I have relegated to parenthetical sections, appendices, or footnotes, not in a foolish attempt to diminish their physical importance, but rather to let the argument course freely, uninterrupted by merely interpretative remarks, and to leave the propositions free for application to such special dynamical situations as may be of interest either now or in the future — for I cannot too strongly urge that a kinematical result is a result valid forever, no matter how time and fashion may change the "laws" of physics.
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Excerpted from "The Kinematics of Vorticity"
by .
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