Summary
The problem of defining a vortex in a real fluid is discussed. The definition and identification of a vortex in unsteady motions is difficult since streamlines and pathlines are not invariant with respect to Galilean and rotational transformations. Recirculatory streamline patterns at a certain instant in time do not necessarily represent vortex motions in which fluid particles are moving around a common axis. Thus, instantaneous streamline patterns do not provide enough information to be used for the definition of a vortex. Extremal properties of the vorticity field are not helpful either, since a local extremum in the vorticity is not necessary for the existence of a vortex. A proposal for a definition based on pathlines is presented.
Zusammenfassung
Das Problem wird erörtert, Wirbel in einer realen Flüssigkeit zu definieren. In instationären Strömungen ist die Definition und Identifizierung eines Wirbels schwierig, weil Stromlinien und Teilchenbahnen nicht invariant hinsichtlich Galilei-Transformationen und Rotationen sind. Kreisförmige Stromlinienbilder zu einer bestimmten Zeit repräsentieren nicht notwendigerweise Wirbelbewegungen, in denen sich die Flüssigkeits-teilchen um eine gemeinsame Achse bewegen. Augenblickliche Stromlinienbilder geben daher nicht genügend Information zur Definition eines Wirbels. Extremaleigenschaften des Vorticityfeldes helfen ebenfalls nicht, da ein lokales Extremum der Vorticity nicht notwendig für die Existenz eines Wirbels ist. Ein Vorschlag für eine Definition auf der Basis von Teilchenbahnen wird gemacht.
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Lugt, H.J. (1979). The Dilemma of Defining a Vortex. In: Müller, U., Roesner, K.G., Schmidt, B. (eds) Recent Developments in Theoretical and Experimental Fluid Mechanics. Springer, Berlin, Heidelberg. https://doi.org/10.1007/978-3-642-67220-0_32
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DOI: https://doi.org/10.1007/978-3-642-67220-0_32
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