State space analysis of minimal channel flow
Résumé
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 Jiménez and Moin (1991 J. Fluid
Mech. 225 21340) 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.