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Revisiting Raupach’s Flow-Sheltering Paradigm

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Abstract

In this commentary, we revisit Raupach’s flow-sheltering paradigm that asserts reduced wall-shear stress behind a surface roughness element (MR Raupach in Boundary-Layer Meteorol, 60(4):375–395, 1992). Direct numerical simulations of a turbulent boundary layer over a wall-mounted rectangular roughness are conducted we consider roughness with three different aspect ratios and flows at two Reynolds numbers. A large computational domain is used to study the behaviours of the wall-shear stress in both the near-wake and the far-wake regions. Aside from a low wall-shear stress region in the near-wake as one would expect from the flow-sheltering paradigm, a high-stress region is found in the far-wake. The presence of such a high-stress region challenges the well-established flow sheltering paradigm and is also counter-intuitive. Detailed analysis of the vortical structures shows that the high wall-shear stress region is a consequence of the horse-shoe-vortex-induced downwash motion in the far-wake.

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References

  • Bose ST, Park GI (2018) Wall-modeled large-eddy simulation for complex turbulent flows. Ann Rev Fluid Mech 50:535–561

    Article  Google Scholar 

  • Castro IP, Robins AG (1977) The flow around a surface-mounted cube in uniform and turbulent streams. J Fluid Mech 79(2):307–335

    Article  Google Scholar 

  • Coceal O, Belcher S (2004) A canopy model of mean winds through urban areas. Q J R Meteorol Soc 130(599):1349–1372

    Article  Google Scholar 

  • Darcy H (1857) Recherches expérimentales relatives au mouvement de l’eau dans les tuyaux. Mallet-Bachelier, France

    Google Scholar 

  • Eitel-Amor G, Örlü R, Schlatter P (2014) Simulation and validation of a spatially evolving turbulent boundary layer up to Re\(_\theta \)= 8300. Int J Heat Fluid Flow 47:57–69

    Article  Google Scholar 

  • Flack KA, Schultz MP (2010) Review of hydraulic roughness scales in the fully rough regime. J Fluids Eng 132(4):041–203

    Article  Google Scholar 

  • Hagen GHL (1854) Über den einfluss der temperatur auf die bewegung des wassers in röhren. Druckerei der Königl. akademie der wissenschaften, Germany

    Google Scholar 

  • Hearst RJ, Gomit G, Ganapathisubramani B (2016) Effect of turbulence on the wake of a wall-mounted cube. J Fluid Mech 804:513–530

    Article  Google Scholar 

  • Hussein HJ, Martinuzzi R (1996) Energy balance for turbulent flow around a surface mounted cube placed in a channel. Phys Fluids 8(3):764–780

    Article  Google Scholar 

  • Hwang HG, Lee JH (2018) Secondary flows in turbulent boundary layers over longitudinal surface roughness. Phys Rev Fluids 3(1):014–608

    Article  Google Scholar 

  • Jiménez J (2004) Turbulent flows over rough walls. Annu Rev Fluid Mech 36:173–196

    Article  Google Scholar 

  • Kemler E (1933) A study of the data on the flow of fluids in pipes. Trans ASME 55(2):7–22

    Google Scholar 

  • Leonardi S, Castro IP (2010) Channel flow over large cube roughness: a direct numerical simulation study. J Fluid Mech 651:519–539

    Article  Google Scholar 

  • Leonardi S, Orlandi P, Smalley R, Djenidi L, Antonia R (2003) Direct numerical simulations of turbulent channel flow with transverse square bars on one wall. J Fluid Mech 491:229–238

    Article  Google Scholar 

  • Macdonald R, Griffiths R, Hall D (1998) An improved method for the estimation of surface roughness of obstacle arrays. Atmos Environ 32(11):1857–1864

    Article  Google Scholar 

  • MacDonald M, Chan L, Chung D, Hutchins N, Ooi A (2016) Turbulent flow over transitionally rough surfaces with varying roughness densities. J Fluid Mech 804:130–161

    Article  Google Scholar 

  • Martinuzzi R, Tropea C (1993) The flow around surface-mounted, prismatic obstacles placed in a fully developed channel flow. J Fluids Eng 115:85–92

    Article  Google Scholar 

  • Marusic I, Monty JP, Hultmark M, Smits AJ (2013) On the logarithmic region in wall turbulence. J Fluid Mech 716:R3

    Article  Google Scholar 

  • Millward-Hopkins JT, Tomlin AS, Ma L, Ingham D, Pourkashanian M (2011) Estimating aerodynamic parameters of urban-like surfaces with heterogeneous building heights. Boundary-Layer Meteorol 141(3):443–465

    Article  Google Scholar 

  • Moody LF (1944) Friction factors for pipe flow. Trans ASME 66:671–684

    Google Scholar 

  • Pigott RJS (1933) The flow of fluids in closed conduits. Mech Eng 55(8):497–515

    Google Scholar 

  • Raupach M (1992) Drag and drag partition on rough surfaces. Boundary-Layer Meteorol 60(4):375–395

    Article  Google Scholar 

  • Raupach MR, Antonia RA, Rajagopalan S (1991) Rough-wall turbulent boundary layers. Appl Mech Rev 44(1):1–25

    Article  Google Scholar 

  • Rouhi A, Chung D, Hutchins N (2019) Direct numerical simulation of open-channel flow over smooth-to-rough and rough-to-smooth step changes. J Fluid Mech 866:450–486

    Article  Google Scholar 

  • Rouse H (1943) Evaluation of boundary roughness. In: Proceedings Second Hydraulics Conference, Univ. of Iowa Studies in Engrg, Bulletin No. 27

  • Sadique J, Yang XIA, Meneveau C, Mittal R (2017) Aerodynamic properties of rough surfaces with high aspect-ratio roughness elements: effect of aspect ratio and arrangements. Boundary-Layer Meteorol 163(2):203–224

    Article  Google Scholar 

  • Schultz MP, Kavanagh CJ, Swain GW (1999) Hydrodynamic forces on barnacles: implications on detachment from fouling-release surfaces. Biofouling 13(4):323–335

    Article  Google Scholar 

  • Shao Y, Yang Y (2005) A scheme for drag partition over rough surfaces. Atmos Environ 39(38):7351–7361

    Article  Google Scholar 

  • Shao Y, Yang Y (2008) A theory for drag partition over rough surfaces. J Geophys Res Earth 113:F2

  • Stroh A, Schäfer K, Frohnapfel B, Forooghi P (2020) Rearrangement of secondary flow over spanwise heterogeneous roughness. J Fluid Mech 885:R5

    Article  Google Scholar 

  • Xie ZT, Castro IP (2008) Efficient generation of inflow conditions for large eddy simulation of street-scale flows. Flow Turbul Combust 81(3):449–470

    Article  Google Scholar 

  • Yang XIA, Meneveau C (2017) Modelling turbulent boundary layer flow over fractal-like multiscale terrain using large-eddy simulations and analytical tools. Philos Trans R Soc Lond Ser A 375(2091):20160098

    Google Scholar 

  • Yang Y, Shao Y (2005) Drag partition and its possible implications for dust emission. Water Air Soil Poll 5(3–6):251–259

    Article  Google Scholar 

  • Yang Y, Shao Y (2006) A scheme for scalar exchange in the urban boundary layer. Boundary-Layer Meteorol 120(1):111–132

    Article  Google Scholar 

  • Yang XIA, Sadique J, Mittal R, Meneveau C (2016) Exponential roughness layer and analytical model for turbulent boundary layer flow over rectangular-prism roughness elements. J Fluid Mech 789:127–165

    Article  Google Scholar 

  • Yang XIA, Xu H, Huang XLD, Ge MW (2019) Drag forces on sparsely packed cube arrays. J Fluid Mech 880:992–1019

    Article  Google Scholar 

Download references

Acknowledgements

This material is based upon work supported by the Department of Energy under Award Number(s) DE-FE0031280. Disclaimer: This report was prepared as an account of work sponsored by an agency of the United States Government. Neither the United States Government nor any agency thereof, nor any of their employees, makes any warranty, express or implied, or assumes any legal liability or responsibility for the accuracy, completeness, or usefulness of any information, apparatus, product, or process disclosed, or represents that its use would not infringe privately owned rights. Reference herein to any specific commercial product, process, or service by trade name, trademark, manufacturer, or otherwise does not necessarily constitute or imply its endorsement, recommendation, or favouring by the United States Government or any agency thereof. The views and opinions of authors expressed herein do not necessarily state or reflect those of the United States Government or any agency thereof. The DNSs are performed on XSEDE and ACI-ICS. MG thanks the support of National Natural Science Foundation of China (No. 11772128).

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Authors and Affiliations

  1. Mechanical Engineering, Pennsylvania State University, State College, PA, 16802, USA

    Xiang Yang

  2. State Key Laboratory of Alternate Electrical Power System with Renewable Energy Sources (NCEPU), Beijing, 102206, China

    Mingwei Ge

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  1. Xiang Yang
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  2. Mingwei Ge
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Correspondence to Xiang Yang.

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Yang, X., Ge, M. Revisiting Raupach’s Flow-Sheltering Paradigm. Boundary-Layer Meteorol 179, 313–323 (2021). https://doi.org/10.1007/s10546-020-00597-8

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