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Direct numerical simulations of transitional flow in a rectangular duct of cross-sectional aspect ratio
being the duct half-span and half-height, respectively) have been performed in the Reynolds number range
being the bulk velocity and the kinematic viscosity, respectively) in order to investigate the dependence on the aspect ratio of spatially localized turbulence structures. It was observed that the lowest Reynolds number
, estimated in a specific way, for localized (transiently sustaining) turbulence decreases monotonically from
(square duct) with increasing aspect ratio, and for
it nearly attains a minimal value
that is consistent with the onset Reynolds number of turbulent spots in a plane channel (
). Turbulent states consist of localized structures that undergo a fundamental change around
is streamwise-localized similar to turbulent puffs in pipe flow, while for
–9 turbulence at
is also localized in the spanwise direction, similar to turbulent spots in plane channel flow. This structural change in turbulent states at
is attributed to the exclusion of turbulence from the vicinity of the duct sidewalls in the case of a wide duct with
: here the friction length on the sidewalls is so long that the size (around 100 times the friction length) of a self-sustaining minimal flow unit of streamwise vortices and streaks is larger than the duct height and, therefore, it cannot be accommodated.
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