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Helmholtz's vortex theorems require that a vortex filament

  • A.Must always lie along the free-stream direction
  • B.Loses strength steadily as it moves downstream in inviscid flow
  • C.Can begin and end anywhere within the fluid
  • D.Cannot end in the fluid, but must extend to a boundary or form a closed loop

Answer: D

Helmholtz showed that the strength of a vortex filament is constant along its length and that the filament cannot simply stop in the fluid. This is precisely why the bound vortex on a wing must continue as trailing vortices and close through the starting vortex, giving the closed vortex system that lifting-line theory assumes.

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