Abstract
It is well known that the circulation of the velocity field of a fluid along a closed material curve is conserved for any solution of the Euler equation. We offer a slightly more explicit proof of that fact than that generally found in the literature. We then rewrite that property in terms of the rescaled variables and functions leading to the Euler-Leray equations and that are appropriate for studying self-similar solutions. We end up by discussing the implications of the conservation of circulation on the existence of such solutions.
- Received 5 April 2019
DOI:https://doi.org/10.1103/PhysRevFluids.4.084401
©2019 American Physical Society
Physics Subject Headings (PhySH)
Fluid DynamicsNonlinear Dynamics