Vortices, stability, and turbulence

Abstract

The transition process between laminar flow to turbulent flow is discussed in terms of a third state of fluid motion, vortical motion that is approximately periodic in space and/or time and displays symmetrical properties. The possibility that the transition from laminar to turbulent flow is accompanied by intermediate vortical states, with turbulence being an instability of the vortical states, is examined, with consideration given to the hypothesis that the turbulent state retains a memory of the vortex structures. Solutions are sought for the Navier-Stokes equations for a viscous liquid in a channel. Instances of inviscid vortical states and the presence of a three-dimensional instability are studied, demonstrating that transition phenomena can be explained qualitatively in terms of vortical state characteristics.