Conical Flows of Fluid with Variable Viscosity
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, 235268 (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 nonswirling 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 selfswirling 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.
 Publication:

Proceedings of the Royal Society of London Series A
 Pub Date:
 September 1988
 DOI:
 10.1098/rspa.1988.0097
 Bibcode:
 1988RSPSA.419...91G
 Keywords:

 Conical Flow;
 Viscous Flow;
 Swirling;
 Turbulent Flow;
 Fluid Mechanics and Heat Transfer