Journal of Fluid Mechanics


Large-scale secondary structures in duct flow

a1 DIASP, Politecnico di Torino, Corso Duca degli Abruzzi 24, 10129 Torino, Italy
a2 DIAM, Università di Genova, Via Montallegro 1, 16145, Genova, Italy

Article author query
galletti b   [Google Scholar] 
bottaro a   [Google Scholar] 


The spatial growth of small perturbations developing on a fully developed base flow in a duct with two inhomogeneous cross-flow directions is examined. For a laminar mean flow it is shown that optimally configured vortices at an upstream cross-section induce large transient amplification of a disturbance energy norm downstream. Such a linear growth is a likely initial stage of transition in ducts for which the cross-section is square or of moderate aspect ratio, asymptotically stable according to conventional eigen-analyis. With the increase of the cross-sectional aspect ratio the transient growth results of the plane channel flow case are approached. The optimization methodology is then employed to study the transient amplification of large-scale secondary structures developing in a square duct for which the unidirectional base motion has a turbulent-like profile. Under the hypothesis that fine-scale turbulence does not affect the growth of large-scale secondary flows, it is shown that cross-stream vortices are sustained by the mean flow and grow maximally over a streamwise distance of several thousand viscous units of length.

(Received March 12 2004)
(Revised May 5 2004)