Mean azimuthal flow of puff in pipe flow

The mean azimuthal flow of puff, a key structure of the subcritical transition in pipe flow, is studied numerically and theoretically in this Letter. It is revealed that the mean azimuthal velocities (MAVs) are governed by the least stable azimuthal modes at the far downstream and upstream, respectively. At the upstream near-wall region, the statistical period between the direction reversals of the area-averaged MAV becomes longer with the increase in the Reynolds number (Re), illustrating the same trend as the lifetime of puffs. At Re = 2300, the puff splitting is found to be inhibited when MAV is suppressed, and the facilitating mechanism of MAV on the puff splitting is explained in terms of the enhancement effect of MAV on the downstream disturbance kinetic energy: it elongates the central high-kinetic-energy region of puff, whose extended downstream part may grow further to generate a new puff.