Conical turbulent swirling vortex with variable eddy viscosity

In the one hundred years since Rankine suggested his well known two-dimensional vortex model with finite core, no one has ever found any exact vortex solutions of the Navier-Stokes equations that can satisfy a complete set of physical boundary conditions. In this paper a variable viscosity is introduced and the existence of conical turbulent vortex solutions of the Navier-Stokes equations is examined. It is found that for a class of deliberately chosen eddy viscosity function a steady turbulent vortex can, for the first time, satisfy both the regularity condition at the core and the adherence condition at the surface, except for a singularity at the origin inherent in all conical similarity solutions. In its asymptotic form, if the eddy viscosity only varies in a boundary layer near the surface or the core, outside the layer the solution given would approach one of the laminar solutions of Yih et al . ( Physics Fluids 25, 2147 (1982)) or that of Serrin ( Phil. Trans. R. Soc. Lond. A 271, 325 (1972)) respectively. These results reveal some remarkable relations between the behaviour, and even the existence, of a vortex and turbulence.

The development and structure of turbulent plane jets

The structure and development of turbulent plane jets in still air and moving streams are described. The nature of the small-scale turbulence cannot be accurately ascertained because of the difficulties inherent in the measurement of dissipation in highly turbulent flows. Although correlation measurements in a jet in still air indicate a large-scale structure which can best be described as ‘local flapping’, measurements in a jet in a moving stream do not reveal a similar structure. The development of the turbulence structure in a jet in a moving parallel stream is described and the properties of turbulent jets and wakes are shown to be reasonably well predicted by the use of a variable-eddy-viscosity formula together with the formal self-preserving properties of the equations of motion.