Non-$k$-type behaviour of roughness when in-plane wavelength approaches the boundary layer thickness. (22nd January 2021)

• Record Type: Journal Article
• Authors: Nugroho, B.; Monty, J. P.; Utama, I. K. A. P.; Ganapathisubramani, B.; Hutchins, N.
• Is Part Of: Journal of fluid mechanics. Volume 911(2021)
• Publication Date: 2021-01-22
• Subjects: turbulent boundary layers; Fluid mechanics -- Periodicals; 532.005
• DOI: 10.1017/jfm.2020.875
• Languages: English
• ISSNs: 0022-1120

Abstract

Abstract: Abstract : A surface roughness from a recently cleaned and painted ship's hull was scanned, scaled and replicated for laboratory testing to systematically investigate the influence of the ratio of in-plane roughness wavelength, $\lambda$, with respect to the boundary layer thickness $\delta$ . The experiments were performed by geometrically scaling the surface which maintains a constant effective slope $ES_x$ and solidity $\varLambda$, while the ratio of $\lambda /\delta$ is varied. Here we scale the scanned roughness topography by a factor of 2.5 and 15, and measure the mean velocity profiles in the turbulent boundary layers developing over these surfaces at a range of free stream velocities and streamwise measurement locations. The results show that the $2.5\times$ scaled roughness, which has $\lambda /\delta \ll 1$, behaves in the expected $k$ -type manner, with a roughness function ${\rm \Delta} U^+$ that is proportional to the viscous-scaled roughness height. The $15\times$ surface, however, which has $\lambda /\delta \approx 1$, exhibits very different non- $k$ -type behaviour. This larger surface does not approach the fully rough asymptote and also exhibits a drag penalty that is comparable to the $2.5\times$ case despite the sixfold increase in the roughness height. Measurements on a spanwise–wall-normal plane reveal that the $15\times$ surface has introduced a large-scale spanwise variation in mean streamwise velocity (dispersive stresses) that extend far beyond the logarithmic region. Together this evidence suggests that a demarcation between $k$ -type and non- $k$ -type behaviour can occur in situations where the in-plane roughness wavelength approaches the boundary layer thickness. This finding has important implications to how we scale small-scale roughness from high Reynolds number ( Re ) large-scale applications for testing in low Re small-scale laboratory facilities or simulations.