Modified Taylor vortices

Abstract

The classic problem reported by Taylor [Philos. Mag. 46, 671 (1923)] on the viscous decay of a planar vortex grid is here extended in three ways. First we present solutions for the vortex grid modulated in the direction normal to the grid. Second, we find a solution for viscous decay of vortices on a disk and its modulation along the axial direction. Finally, we provide solutions for the viscous decay of vortices on a cylindrical surface and its modulation along the radial direction. The exponentially decaying vortices in these modulated vortex systems represent exact unsteady three-dimensional solutions of the Navier-Stokes equations.