Abstract
It is proved that a model of a turbulent swirling vortex near a plane, which was studied by Wu ( Proc. R. Soc. Lond . A 403, 235–268 (1986)), is inconsistent. There is no regular solution for a swirling downward flow satisfying the adherence condition at the surface. If the flow is upward the solution existence is not excluded but it cannot appear owing to a bifurcation, because an initial solution for a non-swirling conically similar jet emerging from an origin on the plane does not satisfy the adherence condition for any angular distribution of viscosity that is physically meaningful. On the other hand, if a jet in an ambient medium is induced by a convergent motion of the plane matter then, firstly, the laminar solution ceases to exist when the Reynolds number exceeds a finite critical value, so the flow must become turbulent; and, secondly, for a jet flow with a turbulent core a supercritical bifurcation takes place if the rotation friction on the plane is zero. As a result, a self-swirling jet flow is developed together with a spiral motion of the plane matter. Such a scenario may serve as a simple hydrodynamical model for some astrophysical and geophysical phenomena.
Sign-in/Register to access full text options 
Talk to us
Join us for a 30 min session where you can share your feedback and ask us any queries you have
Schedule a callMore From: Proceedings of the Royal Society of London. A. Mathematical and Physical Sciences
Disclaimer: All third-party content on this website/platform is and will remain the property of their respective owners and is provided on "as is" basis without any warranties, express or implied. Use of third-party content does not indicate any affiliation, sponsorship with or endorsement by them. Any references to third-party content is to identify the corresponding services and shall be considered fair use under The CopyrightLaw.
