Highlyresolved, direct numerical simulations of turbulent channel flows with sub
Kolmogorov grid resolution are performed to investigate the characteristics of wallbounded turbulent flows in the presence of sinusoidal wall waviness. The wall waviness serves as a simplified model to study the effects of welldefined geometric parameters of roughness on the characteristics of wallbounded turbulent flows. In this study, a twodimensional wave profile with steepness ranging from 0.06 to 0.25 and wave amplitudes ranging from 9 to 36 wall units were considered. For the smooth and wavywall simulations, the Reynolds number based on the friction velocity was kept constant. To study the effects of wave amplitude and wavelength on turbulence, twodimensional time and spanwise averaged distributions of the mean flow, turbulent kinetic energy, and Reynolds stresses as well as turbulent kinetic energy production and dissipation are examined. Furthermore, in order to provide a more direct comparison
with the smoothwall turbulent channel flow onedimensional pro files of these quantities are computed by averaging them over one wavelength of the wave profile. A strong effect of the wallwaviness and, in particular, the wave amplitude and wavelength on the characteristics of the turbulence was obtained. Wall waviness mainly affected the inner flow region while all recorded turbulent statistics collapsed in the outer flow region. Significant reductions in turbulent kinetic energy, production and dissipation were obtained with increasing wave amplitudes when reported in inner scale. While production is lower for all wavy wall cases considered here in comparison to the smooth wall, reducing the wavelength caused an increase in production and a decrease in dissipation.
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Amplitude and wavelength scaling of sinusoidal roughness effects in turbulent channel flow at fixed
Direct numerical simulations are performed for incompressible, turbulent channel flow over a smooth wall and different sinusoidal wall roughness configurations at a constant $Re_\tau = 720$ . Sinusoidal walls are used to study the effects of welldefined geometric features of roughnessamplitude, $a$ , and wavelength, $\lambda$ , on the flow. The flow in the nearwall region is strongly influenced by both $a$ and $\lambda$ . Establishing appropriate scaling laws will aid in understanding the effects of roughness and identifying the relevant physical mechanisms. Using inner variables and the roughness function to scale the flow quantities provides support for Townsend's hypothesis, but inner scaling is unable to capture the flow physics in the nearwall region. We provide modified scaling relations considering the dynamics of the shear layer and its interaction with the roughness. Although not a particularly surprising observation, this study provides clear evidence of the dependence of flow features on both $a$ and $\lambda$ . With these relations, we are able to collapse and/or align peaks for some flow quantities and, thus, capture the effects of surface roughness on turbulent flows even in the nearwall region. The shearlayer scaling supports the hypothesis that the physical mechanisms responsible for turbulent kinetic energy production in turbulent flows over rough walls are greatly influenced by the shear layer and its interaction with the roughness elements. Finally, a semiempirical model is developed to predict the contribution of pressure and skin friction drag on the roughness element based purely on its geometric parameters and the corresponding shearlayer velocity scale.
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 Award ID(s):
 1706346
 NSFPAR ID:
 10317509
 Date Published:
 Journal Name:
 Journal of Fluid Mechanics
 Volume:
 937
 ISSN:
 00221120
 Format(s):
 Medium: X
 Sponsoring Org:
 National Science Foundation
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