Linear instability of pipe flow at small rotation number

• Published in: Indian journal of physics 2022-07, Vol.96 (8), p.2415-2425
• Main Authors: Nkengmené, H. Ségning, Hinvi, L. A., Monwanou, V. A., Orou, J. B. Chabi
• Format: Article
• Language: English
• Subjects: Amplitudes; Astrophysics and Astroparticles; Flow stability; Fluid flow; Original Paper; Perturbation; Physics; Physics and Astronomy; Pipe flow; Reynolds number; Rotation
• ISSN: 0973-1458; 0974-9845
• DOI: 10.1007/s12648-021-02165-3

This paper studies the transition to turbulence of pipe flow for a system rotating about the streamwise direction. The linearized Navier–Stokes equations are numerically solved using the Petrov–Galerkin discretization. Both destabilizing and stabilizing effects of the rotation are highlighted. We show that in comparison to the linear stability situation at the Reynolds number going up to 10 7 , for the non-rotating case, pipe flow is linearly unstable to infinitesimal perturbations at low rotation numbers. By fixing the Reynolds numbers, small rotation numbers increase the amplitude of perturbations, which attain the maximum values in the region of the unstable modes. As they exceed their maximum values, these perturbations are attenuated. When the rotation number is increased further, perturbations are progressively damped until a critical value above which the flow becomes linearly stable. We determine the region in perturbation amplitude which separates perturbations that trigger instabilities and perturbations that decay toward the laminar profile. This study also reveals that the large values of rotation numbers cause a symmetric structure onto the flow, in a domain that is periodically continued in the axial direction.