Analytical Model for Transition in Couette and Poiseuille Flows

Abstract

Transition to turbulence initiated by the linear transient growth mechanism is studied in plane Couette and plane Poiseuille flows. A novel analytical approximation of the linear transient growth mechanism enables us performing a secondary linear stability analysis of the modified base-flow. The predictions of the secondary stability analysis are verified by obtaining transition in a direct numerical simulation (DNS) initiated with the corresponding analytical expressions, which represent four streamwise vortices. The relatively small number of modes in the analytical approximation enables us to follow most of the process analytically using the multiple time scales approach. It is demonstrated that a similar mechanism of transition, via the creation of wall-normal inflection points, is present in both types of flow. While in Couette flow most of the disturbance energy is gained during the secondary instability phase, in Poiseuille flow, it is gained during the linear transient growth stage.