Reply to Comment on 'Critical behaviour in the relaminarization of localized turbulence in pipe flow'

Abstract

This is a Reply to Comment arXiv:0707.2642 by Hof et al. on Letter arXiv:physics/0608292 which was subsequently published in Phys Rev Lett, 98, 014501 (2007). In our letter it was reported that in pipe flow the median time $\tau$ for relaminarisation of localised turbulent disturbances closely follows the scaling $\tau \sim 1/(R{e}_c-Re)$. This conclusion was based on data from collections of 40 to 60 independent simulations at each of six different Reynolds numbers, Re. In the Comment, Hof et al. estimate $\tau$ differently for the point at lowest Re. Although this point is the most uncertain, it forms the basis for their assertion that the data might then fit an exponential scaling $\tau \sim \exp (ARe)$, for some constant A, supporting Hof et al. (2006) Nature, 443, 59. The most certain point (at largest Re) does not fit their conclusion and is rejected. We clarify why their argument for rejecting this point is flawed. The median $\tau$ is estimated from the distribution of observations, and it is shown that the correct part of the distribution is used. The data is sufficiently well determined to show that the exponential scaling cannot be fit to the data over this range of Re, whereas the $\tau \sim 1/(R{e}_c-Re)$ fit is excellent, indicating critical behaviour and supporting experiments by Peixinho & Mullin 2006.

1 page, 1 figure

References in corpus (3)

• Travelling waves in pipe flow
• Scaling of the turbulence transition threshold in a pipe
• Sensitive dependence on initial conditions in transition to turbulence in pipe flow

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• Relative periodic orbits in transitional pipe flow
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• Transient Turbulence in Taylor-Couette Flow
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• Directed percolation describes lifetime and growth of turbulent puffs and slugs
• The critical point of the transition to turbulence in pipe flow
• Extreme fluctuations and the finite lifetime of the turbulent state
• Statistical transition to turbulence in plane channel flow
• Modeling transitional plane Couette flow
• Lifetime statistics in transitional pipe flow
• Increasing lifetimes and the growing saddles of shear flow turbulence
• Extreme events in transitional turbulence
• Supertransient magnetohydrodynamic turbulence in Keplerian shear flows
• A novel type of intermittency in a nonlinear dynamo in a compressible flow
• Modeling the transition to turbulence in shear flows
• Turbulent dynamics of pipe flow captured in a reduced model: puff relaminarisation and localised `edge' states
• Understanding the sub-critical transition to turbulence in wall flows
• Structure interactions in a reduced-order model for wall-bounded turbulence
• How does flow in a pipe become turbulent?
• Method to measure efficiently rare fluctuations of turbulence intensity for turbulent-laminar transitions in pipe flows
• Turbulence lifetimes: what we can learn from the physics of glasses
• Deterministic and stochastic aspects of the transition to turbulence
• Dynamics of spatially localized states in transitional plane Couette flow
• Pattern preservation during the decay and growth of localized wave packet in two-dimensional channel flow
• Aging and memory of transitional turbulence
• Modelling the transition from shear-driven turbulence to convective turbulence in a vertical heated pipe
• Turbulence phenomena for viscous fluids by a phase field model. Vorticies and instability