Method to measure efficiently rare fluctuations of turbulence intensity for turbulent-laminar transitions in pipe flows

TL;DR

This paper introduces a novel rare-event sampling method to efficiently measure fluctuations in turbulence intensity near the turbulent-laminar transition in pipe flows, enabling analysis of transition time-scales at high Reynolds numbers.

Contribution

The paper presents a new sampling technique combining typical and rare fluctuation measurements with feedback control of Reynolds number, applicable to experiments.

Findings

Turbulence decay time-scale increases super-exponentially with Reynolds number.

The method effectively captures rare fluctuations in turbulence intensity.

Application to a chaotic model confirms the method's ability to analyze high-Re regimes.

Abstract

The fluctuations of turbulence intensity in a pipe flow around the critical Reynolds number is difficult to study but important because they are related to turbulent-laminar transitions. We here propose a rare-event sampling method to study such fluctuations in order to measure the time-scale of the transition efficiently. The method is composed of two parts: (i) the measurement of typical fluctuations (the bulk part of an accumulative probability function) and (ii) the measurement of rare fluctuations (the tail part of the probability function) by employing dynamics where a feedback control of the Reynolds number is implemented. We apply this method to a chaotic model of turbulent puffs proposed by Barkley and confirm that the time-scale of turbulence decay increases super-exponentially even for high Reynolds numbers up to Re = 2500, where getting enough statistics by brute-force calculations is difficult. The method uses a simple procedure of changing Reynolds number that can be applied even to experiments.