Linear Stability Analysis and Transient Growth in Steady and Pulsatile Flows in a Constricted Channel

Abstract

A three-dimensional direct stability analysis of the flow in a straight channel with a smooth constriction with 50% occlusion is performed. Two-dimensional steady and long-period pulsatile flows are investigated with respect to instabilities and transition to turbulence. The steady base flow is asymmetric for the Reynolds number range considered in this work, with critical value for linear instability of Re = 558.7 to three-dimensional perturbations. Although the steady flow is linearly stable for two-dimensional perturbations at Re = 700, it presents a maximum transient energy growth of the order of 107. The pulsatile flow becomes linearly unstable at Re = 249.7 to three-dimensional perturbations. The optimal initial condition that triggers the maximum growth of a two-dimensional perturbation occurs for a disturbance applied shortly after the peak velocity of the pulse for Re = 200 with a growth of the order of 103, the same order found for Re = 400, but applying the perturbation in the beginning of the pulse.