Size-dependent transient nature of localized turbulence in transitional channel flow

TL;DR

This paper investigates the transient behavior of localized turbulent bands in transitional channel flow, revealing their stochastic lifetimes and size dependence, which impacts understanding of flow transition and universality classes.

Contribution

It demonstrates that turbulent bands are transient with size-dependent lifetimes, challenging the notion of sustained turbulence above a threshold Reynolds number.

Findings

Turbulent band lifetimes are exponentially distributed.

Mean lifetime increases with Reynolds number and band length.

Size dependence influences the flow transition and universality class interpretation.

Abstract

It has been reported that a fully localized turbulent band in channel flow becomes sustained when the Reynolds number is above a threshold. Here we show evidences that turbulent bands are of a transient nature instead. When the band length is controlled to be fixed, lifetimes of turbulent bands appear to be stochastic and exponentially distributed, a sign of a memoryless transient nature. Besides increasing with the Reynolds number, the mean lifetime also strongly increases with the band length. Given that the band length always changes over time in real channel flow, this size dependence may translate into a time dependence, which needs to be taken into account when clarifying the relationship between channel flow transition and the directed percolation universality class.