On the Stability and Transition of Time Periodic Pipe Flow

This computational study investigates the transition to turbulence of fluid in a pipe that is subjected to a sinusoidal oscillation. The problem is solved by separating the flow into a laminar base-flow and a linear infinitesimal perturbation. The energy of the perturbation is followed through time-stepper methods, with growth leading towards turbulence, and decay leading to a laminar state. The analysis demonstrates an exponential increase in transient growth of the perturbation as the flow control parameters are varied, a case normally only associated with separated shear flows. The driving mechanism is isolated to a new linear process involving the coordination of two known inviscid instabilities linked to the structure of the laminar base-flow.