The role of streamwise perturbations in pipe flow transition

Abstract

The phenomenon of subcritical transition in Hagen-Poiseuille or pipe flow is explored for a wide range of Reynolds numbers within the interval Re∊[2.5×103,1.26×104] by means of a computational method that numerically resolves the transitional dynamics with nearly 3.5×104 degrees of freedom on a medium aspect-ratio domain of length 32π∕5. The aim of this exploration is to provide a theoretical characterization of the basin of attraction of the basic regime by measuring the minimal amplitude of an initial global perturbation leading to transition. The analysis is based on a particular theoretical scenario that considers streamwise-independent finite amplitude initial vortical perturbations that trigger global transition via optimal inflectional instabilities of streamwise-dependent modes with selected axial wave numbers. Disturbances consisting of 1, 2, and 3 pairs of vortices are investigated. Special attention is given to relaminarization phenomena that is frequently observed for low Reynolds numbers. Long lasting turbulent regimes and relaminarized flows are distinguished by means of time integrations of suitable length between Tmin=600 and Tmax=1000 advective time units. Some transitional runs are specifically analyzed to exemplify the transition scenario under investigation and its independence of pipe length is verified with a few computations on a longer pipe of length 32π (1.4×105 degrees of freedom). For large values of the Reynolds number, a theoretical scaling law for the threshold amplitude of a perturbation required to trigger transition is provided. Different types of perturbations seem to respond to different scaling laws.