Puff dynamics in the azimuthally constrained pipe flow

Transition to turbulence in pipe flow is best understood as a nonequilibrium

phenomenon that takes place in the thermodynamic limit of infinite time and pipe

extent. In this framework, a critical Reynolds number is defined as one beyond

which the spatially localized turbulent structures known as puffs proliferate at

a rate higher than that of their decay, thus, sustaining turbulence

statistically. While the large-scale aspects of this description have been

strongly supported by laboratory and computer experiments, the topics of ongoing

debate are which physical processes give rise to puff phenomenology and how are

they connected to the Navier--Stokes equations that govern the dynamics. In

order to reduce the complexity of this problem, we study it in the direct

numerical simulations of pipe flow subjected to azimuthal symmetry constraints.

We show that the basic puff phenomenology, i.e. split and decay, is fully

captured in simulation domains that are doubly periodic and mirror-symmetric in

the azimuth. We argue that the reduced number of degrees of freedom in this 

symmetry-constrained domain allows for the systematic identification of causal 

relations between different flow structures.