On the Generation of Secondary Velocity Along a Vortex Line

Abstract

A general expression for the generation of secondary velocity along a vortex line is developed for the case of incompressible flow with uniform viscosity. The result is given with various degrees of specialization, i.e., for unsteady flows, unsteady circulation-preserving flows, flows with vanishing flexion, and steady inviscid flows. The formulation for the case of steady flow in which the direct action of viscosity is discounted is applied to the rationalization of experimentally observed secondary-flow phenomena at the convex wall for entrance flow in a curved channel of rectangular cross section.