A Uniqueness Theorem for Incompressible Fluid Flows with Straight Streamlines

  title={A Uniqueness Theorem for Incompressible Fluid Flows with Straight Streamlines},
  author={Brendan Guilfoyle},
  journal={Journal of Mathematical Fluid Mechanics},
  • B. Guilfoyle
  • Published 8 January 2022
  • Mathematics
  • Journal of Mathematical Fluid Mechanics
It is proven that the only incompressible Euler fluid flows with fixed straight streamlines are those generated by the normal lines to a round sphere, a circular cylinder or a flat plane, the fluid flow being that of a point source, a line source or a plane source at infinity, respectively. The proof uses the local differential geometry of oriented line congruences to integrate the Euler equations explicitly. 


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  • 1967