Scale invariance at the onset of turbulence in Couette flow

TL;DR

This paper demonstrates scale invariance at the critical point of turbulence onset in Couette flow through direct numerical simulations, revealing that turbulence transitions from transient to sustained at a specific threshold.

Contribution

It provides the first evidence of scale invariance at the transition to turbulence in Couette flow by analyzing size distributions near criticality.

Findings

Turbulent stripes are transient below criticality.

Turbulence becomes sustained beyond a critical point.

Scale invariance is observed at the onset of turbulence.

Abstract

Laminar-turbulent intermittency is intrinsic to the transitional regime of a wide range of fluid flows including pipe, channel, boundary layer and Couette flow. In the latter turbulent spots can grow and form continuous stripes, yet in the stripe-normal direction they remain interspersed by laminar fluid. We carry out direct numerical simulations in a long narrow domain and observe that individual turbulent stripes are transient. In agreement with recent observations in pipe flow we find that turbulence becomes sustained at a distinct critical point once the spatial proliferation outweighs the inherent decaying process. By resolving the asymptotic size distributions close to criticality we can for the first time demonstrate scale invariance at the onset of turbulence.