A Uniqueness Theorem for Incompressible Fluid Flows with Straight Streamlines

Authors

Brendan Guilfoyle, School of STEM, Munster Technological University, Tralee, Co. Kerry, IrelandFollow

ORCID

https://orcid.org/0000-0002-7437-5046

Document Type

Article

Creative Commons License

This work is licensed under a Creative Commons Attribution 4.0 International License.

Disciplines

Mathematics | Physical Sciences and Mathematics

Publication Details

Journal of Mathematical Fluid Mechanics, vol. 24, no. 90. © 2024 The Authors.

Abstract

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.

Recommended Citation

Guilfoyle, B. A Uniqueness Theorem for Incompressible Fluid Flows with Straight Streamlines. J. Math. Fluid Mech. 24, 90 (2022). https://doi.org/10.1007/s00021-022-00725-z