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

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 evidence that turbulent bands are of a transient nature instead. When the band length is controlled to be fixed, the lifetime of turbulent bands appears 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.