Exact Magnus-Force Formula for Three-Dimensional Fluid-Core Vortices
- 1 February 1970
- journal article
- research article
- Published by American Physical Society (APS) in Physical Review A
- Vol. 1 (2), 327-331
- https://doi.org/10.1103/physreva.1.327
Abstract
The two-dimensional Magnus formula can be extended to three-dimensional fluid-core vortices of arbitrary core structure by a precise redefinition of the stream velocity vector , vortex velocity vector , and circulation vector . For example, becomes the velocity, in a plane slicing the vortex core, of the "center of mass" of the vorticity. The exact three-dimensional formula is derived by analyzing the motion of vorticity relative to the fluid particles - a relative motion caused by the action of nonconservative forces on the vortex core (e.g., the electric force on a charged vortex ring in superfluid helium). The analysis deals with the vorticity field and, thus, can lead to simple formulas and insights in cases where the velocity field may be impossibly complicated. Examples introduced are (i) the concept of a "conserved vorticity current," (ii) a possible classical mechanism for the creation or destruction of vortex lines in superfluid helium, and (iii) a simple technique for analyzing the effect of viscosity on the structure of a vortex core.
Keywords
This publication has 4 references indexed in Scilit:
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- Growth of Pinned Quantized Vortex Lines in Helium IIPhysical Review B, 1966
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- The rotation of liquid helium II II. The theory of mutual friction in uniformly rotating helium IIProceedings of the Royal Society of London. Series A. Mathematical and Physical Sciences, 1956