Note on a Class of Solutions of the Navier-Stokes Equations Representing Steady Rotationally-Symmetric Flow

This note describes one- and two-parameter families of solutions of steady rotationally-symmetric viscous flow. The solutions are such that the Navier-Stokes equations reduce to ordinary differential equations in a single position variable. The one-parameter family represents flow which is rigid-body rotation at infinity and over a plane through the origin; the solution given by von Kármán in 1921 is one member of this family. The two-parameter family represents flow which is rigid body rotation over each of two planes at a finite distance apart. The case of large Reynolds number is particularly interesting, since the two bounding planes are then separated by a region of rigid-body rotation and translation in which viscous effects are negligible.