Abstract
The onset of turbulence in subcritical shear flows is one of the most puzzling manifestations of critical phenomena in fluid dynamics. The present study focuses on the Couette flow inside an infinitely long annular geometry where the inner rod moves with constant velocity and entrains fluid, by means of direct numerical simulation. Although for a radius ratio close to unity the system is similar to plane Couette flow, a qualitatively novel regime is identified for small radius ratio, featuring no oblique bands. An analysis of finite-size effects is carried out based on an artificial increase of the perimeter. Statistics of the turbulent fraction and of the laminar gap distributions are shown both with and without such confinement effects. For the wider domains, they display a cross-over from exponential to algebraic scaling. The data suggest that the onset of the original regime is consistent with the dynamics of one-dimensional directed percolation at onset, yet with additional frustration due to azimuthal confinement effects.
Highlights
The dynamics at the onset of turbulent fluid flow, as the parameters are varied, is one of the most puzzling issues of hydrodynamics
As the Reynolds number is varied, this competition takes the form of laminar-turbulent coexistence featuring some interesting analogies with phase transitions in thermodynamics
The statistical post-processing protocol for spatiotemporal intermittency (STI) is vastly similar to that used by other authors: the first step is to monitor the decay in the time of the turbulence fraction Ft (t) when the system is initiated with turbulence everywhere
Summary
The dynamics at the onset of turbulent fluid flow, as the parameters are varied, is one of the most puzzling issues of hydrodynamics. As the Reynolds number (their main control parameter) is varied, this competition takes the form of laminar-turbulent coexistence featuring some interesting analogies with phase transitions in thermodynamics The onset of this coexistence in wall-bounded shear flows has been speculated to follow a statistical scenario called directed percolation (DP). We revisit transition in annular Couette flow (aCf) in the light of critical scaling This flow has a geometry similar to cylindrical pipe flow, with a solid cylinder at its centerline. The geometry is determined by the radius ratio η between the radius of the outer pipe and that of the inner one This flow supports both turbulence [31] as well as a linearly stable base flow for all Reynolds number of interest, transition has to be of the subcritical type.
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