Abstract
We employ a recently introduced structured input–output analysis (SIOA) approach to analyse streamwise and spanwise wavelengths of flow structures in stably stratified plane Couette flow. In the low-Reynolds-number (
$Re$
) low-bulk Richardson number (
$Ri_b$
) spatially intermittent regime, we demonstrate that SIOA predicts high amplification associated with wavelengths corresponding to the characteristic oblique turbulent bands in this regime. SIOA also identifies quasi-horizontal flow structures resembling the turbulent–laminar layers commonly observed in the high-
$Re$
high-
$Ri_b$
intermittent regime. An SIOA across a range of
$Ri_b$
and
$Re$
values suggests that the classical Miles–Howard stability criterion (
$Ri_b\leq 1/4$
) is associated with a change in the most amplified flow structures when the Prandtl number is close to one (
$Pr\approx 1$
). However, for
$Pr\ll 1$
, the most amplified flow structures are determined by the product
$PrRi_b$
. For
$Pr\gg 1$
, SIOA identifies another quasi-horizontal flow structure that we show is principally associated with density perturbations. We further demonstrate the dominance of this density-associated flow structure in the high
$Pr$
limit by constructing analytical scaling arguments for the amplification in terms of
$Re$
and
$Pr$
under the assumptions of unstratified flow (with
$Ri_b=0$
) and streamwise invariance.
Funder
National Science Foundation
Publisher
Cambridge University Press (CUP)
Subject
Mechanical Engineering,Mechanics of Materials,Condensed Matter Physics,Applied Mathematics
Cited by
3 articles.
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