Swirling flow induced by jets and plumes

Abstract

The interactions of the slow flow induced by the entrainment of axisymmetric jets and plumes with the surrounding geometry may result in the appearance of azimuthal swirling motion. This swirling flow evolves as it approaches the jet (or plume) as a result of the action of viscous forces on the solid surfaces bounding the fluid domain. When the initial size of the jet or plume a is much smaller than the characteristic radial distance $$R_\infty $$ at which the swirl is generated, the evolution of the flow leads to a self-similar description with weak swirling motion, valid at intermediate radial distances R such that $$a \ll R \ll R_\infty $$ and axial distances L from the source such that $$a \ll L \ll R_\infty $$ . In the present investigation of both laminar and turbulent jets and plumes, it is found that the circulation $$\varGamma $$ is described by a self-similar solution of the second kind, with the exponent $$\lambda $$ in the radial decay rate $$\varGamma \propto (R/R_\infty )^\lambda $$ obtained as an eigenvalue. The resulting azimuthal velocity distributions can find application in mathematical formulations of jet and plume problems involving interactions with ambient swirl, relevant in studies of dust devils and fire whirls.