Abstract
Whereas streamwise effective slope (
$ES_{x}$
) is accepted as a key topographical parameter in the context of rough-wall turbulent flows, the significance of its spanwise counterpart (
$ES_{y}$
) remains largely unexplored. Here, the response of turbulent channel flow over irregular, three-dimensional rough walls with systematically varied values of
$ES_{y}$
is studied using direct numerical simulation. All simulations were performed at a fixed friction Reynolds number 395, corresponding to a viscous-scaled roughness height
$k^{+}\approx 65.8$
(where
$k$
is the mean peak-to-valley height). A surface generation algorithm is used to synthesise a set of ten irregular surfaces with specified
$ES_{y}$
for three different values of
$ES_{x}$
. All surfaces share a common mean peak-to-valley height and are near-Gaussian, which allows this study to focus on the impact of varying
$ES_{y}$
, since roughness amplitude, skewness and
$ES_{x}$
can be eliminated simultaneously as parameters. Based on an analysis of first- and second-order velocity statistics, as well as turbulence co-spectra and the fractional contribution of pressure and viscous drag, the study shows that
$ES_{y}$
can strongly affect the roughness drag penalty – particularly for low-
$ES_{x}$
surfaces. A secondary observation is that particular low-
$ES_{y}$
surfaces in this study can lead to diminished levels of outer-layer similarity in both mean flow and turbulence statistics, which is attributed to insufficient scale separation between the outer length scale and the in-plane spanwise roughness wavelength.
Funder
Engineering and Physical Sciences Research Council
Publisher
Cambridge University Press (CUP)
Subject
Mechanical Engineering,Mechanics of Materials,Condensed Matter Physics,Applied Mathematics
Cited by
10 articles.
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