State space analysis of minimal channel flow

Turbulence and edge states are investigated numerically in a plane Poiseuille flow driven by a fixed pressure gradient. Simulations are carried out within the minimal flow unit, a concept introduced by Jimenez and Moin (1991 J. Fluid Mech. 225 213-40) to unravel the dynamics of near-wall structures in the absence of outer large-scale motions. For both turbulent and edge regimes the activity appears to be localised near only one wall at a time, and the long term dynamics features abrupt reversals. The dynamics along one reversal is structured around the transient visit to a subspace of symmetric flow fields. An exact travelling wave solution is found to exist very close to this subspace. Additionally the self-similarity of the asymmetric states is addressed. Contrary to most studies focusing on symmetric solutions, the present study suggests that edge states, when localised near one wall, do not scale in outer units. The current study suggests a composite scaling.