Linear stability of the flow in a toroidal pipe

Authors: Canton, J.C., Schlatter, P., Örlü, R.
Document Type: Conference
Pubstate: Published
Journal: Proc. 9th Turbulence Shear Flow Phenomena (TSFP-9), June 30 - July 3, 2015, The University of Melbourne, Australia
Volume: 1  
Year: 2015


While hydrodynamic stability and transition to turbulence in straight pipes — being one of the most fundamental problems in fluid mechanics — has been studied extensively, the stability of curved pipes has received less attention. In the present work, the first (linear) instability of the canonical flow inside a toroidal pipe is investigated as a first step in the study of the related laminar-turbulent transition process. The impact of the curvature of the pipe, in the range 0.002 < delta < 1, on the stability properties of the flow is studied in the framework of linear stability analysis. Results show that the flow is indeed modally unstable for all curvatures investigated and that the wave number corresponding to the critical mode depends on the curvature, as do several other features of this problem. The critical modes are mainly located in the region of the Dean vortices, and are characterised by oscillations which are symmetric or anti-symmetric as a function of the curvature. The neutral curve associated with the first bifurcation is the result of a complex interaction between isolated modes and branches composed by several modes characterised by a common structure. This behaviour is in obvious contrast to that of straight pipes, which are linearly stable for all Reynolds numbers.