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Coherent structures and associated subgrid-scale energy transfer in a rough-wall turbulent channel flow

  • Jiarong Hong (a1), Joseph Katz (a1), Charles Meneveau (a1) and Michael P. Schultz (a2)

Abstract

This paper focuses on turbulence structure in a fully developed rough-wall channel flow and its role in subgrid-scale (SGS) energy transfer. Our previous work has shown that eddies of scale comparable to the roughness elements are generated near the wall, and are lifted up rapidly by large-scale coherent structures to flood the flow field well above the roughness sublayer. Utilizing high-resolution and time-resolved particle-image-velocimetry datasets obtained in an optically index-matched facility, we decompose the turbulence into large ( ${\gt }\lambda $ ), intermediate ( $3\text{{\ndash}} 6k$ ), roughness ( $1\text{{\ndash}} 3k$ ) and small ( ${\lt }k$ ) scales, where $k$ and $\lambda (\lambda / k= 6. 8)$ are roughness height and wavelength, respectively. With decreasing distance from the wall, there is a marked increase in the ‘non-local’ SGS energy flux directly from large to small scales and in the fraction of turbulence dissipated by roughness-scale eddies. Conditional averaging is used to show that a small fraction of the flow volume (e.g. 5 %), which contains the most intense SGS energy transfer events, is responsible for a substantial fraction (50 %) of the energy flux from resolved to subgrid scales. In streamwise wall-normal ( $x\text{{\ndash}} y$ ) planes, the averaged flow structure conditioned on high SGS energy flux exhibits a large inclined shear layer containing negative vorticity, bounded by an ejection below and a sweep above. Near the wall the sweep is dominant, while in the outer layer the ejection is stronger. The peaks of SGS flux and kinetic energy within the inclined layer are spatially displaced from the region of high resolved turbulent kinetic energy. Accordingly, some of the highest correlations occur between spatially displaced resolved velocity gradients and SGS stresses. In wall-parallel $x\text{{\ndash}} z$ planes, the conditional flow field exhibits two pairs of counter-rotating vortices that induce a contracting flow at the peak of SGS flux. Instantaneous realizations in the roughness sublayer show the presence of the counter-rotating vortex pairs at the intersection of two vortex trains, each containing multiple $\lambda $ -spaced vortices of the same sign. In the outer layer, the SGS flux peaks within isolated vortex trains that retain the roughness signature, and the distinct pattern of two counter-rotating vortex pairs disappears. To explain the planar signatures, we propose a flow consisting of U-shaped quasi-streamwise vortices that develop as spanwise vorticity is stretched in regions of high streamwise velocity between roughness elements. Flow induced by adjacent legs of the U-shaped structures causes powerful ejections, which lift these vortices away from the wall. As a sweep is transported downstream, its interaction with the roughness generates a series of such events, leading to the formation of inclined vortex trains.

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Corresponding author

Email address for correspondence: katz@jhu.edu

References

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Adrian, R. J., Meinhart, C. D. & Tomkins, C. D. 2000 Vortex organization in the outer region of the turbulent boundary layer. J. Fluid Mech. 422, 154.
Anderson, W. & Meneveau, C. 2010 A large-eddy simulation model for boundary-layer flow over surfaces with horizontally resolved but vertically unresolved roughness elements. Boundary-Layer Meteorol. 137, 119.
Antonia, R. A. 1981 Conditional sampling in turbulence measurement. Annu. Rev. Fluid Mech. 13, 131156.
Avissar, R. & Pielke, R. A. 1989 A parameterization of heterogeneous land surfaces for atmospheric numerical models and its impact on regional meteorology. Mon. Weath. Rev. 117, 21132136.
Bandyopadhyay, P. R. & Watson, R. D. 1988 Structure of rough wall turbulent boundary layers. Phys. Fluids 31, 18771883.
Bou-Zeid, E., Meneveau, C. & Parlange, M. B. 2004 Large-eddy simulation of neutral atmospheric boundary layer flow over heterogeneous surfaces: blending height and effective surface roughness. Water Resour. Res. 40, 118.
Carper, M. A. & Porté-Agel, F. 2004 The role of coherent structures in subfilter-scale dissipation of turbulence measured in the atmospheric surface layer. J. Turbul. 5, 124.
Chamecki, M., Meneveau, C. & Parlange, M. B. 2009 Large eddy simulation of pollen transport in the atmospheric boundary layer. J. Aero. Sci. 40, 241255.
Chen, J., Katz, J. & Meneveau, C. 2005 Implication of mismatch between stress and strain-rate in turbulence subjected to rapid straining and destraining on dynamic LES models. J. Fluids Engng 127, 840850.
Chung, D. & Pullin, D. I. 2009 Large-eddy simulation and wall modelling of turbulent channel flow. J. Fluid Mech. 631, 281309.
Djenidi, L., Antonia, R. A., Amielh, M. & Anselmet, F. 2008 A turbulent boundary layer over a two-dimensional rough wall. Exp. Fluids 44, 3747.
Doron, P., Bertuccioli, L., Katz, J. & Osborn, T. R. 2001 Turbulence characteristics and dissipation estimates in the coastal ocean bottom boundary layer from PIV data. J. Phys. Oceanogr. 31, 21082134.
Finnigan, J. J. 2000 Turbulence in plant canopies. Annu. Rev. Fluid Mech. 32, 519571.
Finnigan, J. J., Shaw, R. H. & Patton, E. G. 2009 Turbulence structure above a vegetation canopy. J. Fluid Mech. 637, 387424.
Flack, K. A., Schultz, M. P. & Shapiro, T. A. 2005 Experimental support for Townsend’s Reynolds number similarity hypothesis on rough walls. Phys. Fluids 17, 035102.
Germano, M., Piomelli, U., Moin, P. & Cabot, W. H. 1991 A dynamic subgrid scale eddy viscosity model. Phys. Fluids 3, 17601765.
Hackett, E. E., Luznik, L., Nayak, A. R., Katz, J. & Osborn, T. R. 2011 Field measurements of turbulence at an unstable interface between current and wave bottom boundary layers. J. Geophys. Res. 116, C02022.
Hong, J., Katz, J. & Schultz, M. P. 2011 Near-wall turbulence statistics and flow structures over three-dimensional roughness in a turbulent channel flow. J. Fluid Mech. 667, 137.
Ikeda, T. & Durbin, P. A. 2007 Direct simulations of a rough-wall channel flow. J. Fluid Mech. 571, 235263.
Jiménez, J. 2004 Turbulent flows over rough walls. Annu. Rev. Fluid Mech. 36, 173196.
Juneja, A. & Brasseur, J. G. 1999 Characteristics of subgrid-resolved-scale dynamics in anisotropic turbulence, with application to rough-wall boundary layers. Phys. Fluids 11, 30543068.
Keirsbulck, L., Labraga, L., Mazouz, A. & Tournier, C. 2002 Surface roughness effects on turbulent boundary layer structures. J. Fluids Engng 124, 127135.
Khanna, S. & Brasseur, J. G. 1998 Three-dimensional buoyancy- and shear-induced local structure of the atmospheric boundary layer. J. Atmos. Sci. 55, 710743.
Krogstad, P. Å. & Antonia, R. A. 1994 Structure of turbulent boundary layers on smooth and rough walls. J. Fluid Mech. 277, 122.
Krogstad, P. Å. & Antonia, R. A. 1999 Surface roughness effects in turbulent boundary layers. Exp. Fluids 27, 450460.
Krogstad, P. Å., Antonia, R. A. & Browne, L. W. B. 1992 Comparison between rough- and smooth-wall turbulent boundary layers. J. Fluid Mech. 245, 599-599.
Kunkel, G. J. & Marusic, I. 2006 Study of the near-wall-turbulent region of the high-Reynolds-number boundary layer using an atmospheric flow. J. Fluid Mech. 548, 375402.
Lee, J. H., Sung, H. J. & Krogstad, P. Å. 2011 Direct numerical simulation of the turbulent boundary layer over a cube-roughened wall. J. Fluid Mech. 669, 397431.
Lee, S. H. & Sung, H. J. 2007 Direct numerical simulation of the turbulent boundary layer over a rod-roughened wall. J. Fluid Mech. 584, 125146.
Lesieur, M. & Metais, O. 1996 New trends in large-eddy simulations of turbulence. Annu. Rev. Fluid Mech. 28, 4582.
Lilly, D. K. 1967 The representation of small-scale turbulence in numerical simulation experiments. In The IBM Scientific Computing Symposium on Environmental Sciences, pp. 195210.
Lilly, D. K. 1992 A proposed modification of the Germano subgrid scale closure method. Phys. Fluids 4, 633635.
Liu, S., Meneveau, C. & Katz, J. 1994 On the properties of similarity subgrid-scale models as deduced from measurements in a turbulent jet. J. Fluid Mech. 275, 83120.
Meneveau, C. 1994 Statistics of turbulence subgrid-scale stresses: necessary conditions and experimental tests. Phys. Fluids 6, 815833.
Meneveau, C. & Katz, J. 2000 Scale-invariance and turbulence models for large-eddy simulation. Annu. Rev. Fluid Mech. 32, 132.
Misra, A. & Pullin, D. I. 1997 A vortex-based subgrid stress model for large-eddy simulation. Phys. Fluids 9, 24432454.
Monin, A. S. & Obukhov, A. M. 1959 Basic laws of turbulent mixing in the surface layer of the atmosphere. Contrib. Geophys. Inst. Acad. Sci. USSR 24, 163187.
Natrajan, V. K. & Christensen, K. T. 2006 The role of coherent structures in subgrid-scale energy transfer within the log layer of wall turbulence. Phys. Fluids 18, 065104.
Pierrehumbert, R. & Widnall, S. 1982 The two- and three-dimensional instabilities of a spatially periodic shear layer. J. Fluid Mech. 114, 5982.
Piomelli, U. 1999 Large-eddy simulation: achievements and challenges. Prog. Aerosp. Sci. 35, 335362.
Piomelli, U. 2008 Wall-layer models for large-eddy simulations. Prog. Aerosp. Sci. 44, 437446.
Piomelli, U, Ferziger, J. H., Moin, P. & Kim, J. 1989 New approximate boundary conditions for large eddy simulations of wall-bounded flows. Phys. Fluids A 1, 10611068.
Piomelli, U., Yu, Y. & Adrian, R. J. 1996 Subgrid scale energy transfer and near wall turbulence structure. Phys. Fluids 8, 215224.
Pope, S. B. 2000 Turbulent Flows. Cambridge University Press.
Porté-Agel, F., Meneveau, C. & Parlange, M. B. 2000 A scale-dependent dynamic model for large-eddy simulation: application to a neutral atmospheric boundary layer. J. Fluid Mech. 415, 261284.
Raupach, M. R., Antonia, R. A. & Rajagopalan, S. 1991 Rough-wall turbulent boundary layers. Appl. Mech. Rev. 44, 125.
Rogallo, R. S. & Moin, P. 1984 Numerical simulation of turbulent flows. Annu. Rev. Fluid Mech. 16, 99137.
Schultz, M. P. & Flack, K. A. 2003 Turbulent boundary layers over surfaces smoothed by sanding. J. Fluids Engng 125, 863870.
Schultz, M. P. & Flack, K. A. 2007 The rough-wall turbulent boundary layer from the hydraulically smooth to the fully rough regime. J. Fluid Mech. 580, 381405.
Schultz, M. P. & Flack, K. A. 2009 Turbulent boundary layers on a systematically varied rough wall. Phys. Fluids 21, 015104.
Smagorinsky, J. 1963 General circulation experiments with the primitive equations. Mon. Weath. Rev. 91, 99164.
Tachie, M. F., Bergstrom, D. J. & Balachandar, R. 2000 Rough wall turbulent boundary layers in shallow open channel flow. J. Fluids Engng 122, 533541.
Tachie, M. F., Bergstrom, D. J. & Balachandar, R. 2003 Roughness effects in low- ${\mathit{Re}}_{\theta } $ open-channel turbulent boundary layers. Exp. Fluids 35, 338346.
Talapatra, S. & Katz, J. 2012 Coherent structures in the inner part of a rough wall boundary layer resolved using holographic PIV. J. Fluid Mech. (accepted).
Townsend, A. A. 1976 The Structure of Turbulent Shear Flow. Cambridge University Press.
Van Hout, R., Zhu, W., Luznik, L., Katz, J., Kleissl, J. & Parlange, M. 2007 PIV measurements in the atmospheric boundary layer within and above a mature corn canopy. Part 1. Statistics and energy flux. J. Atmos. Sci. 64, 28052824.
Volino, R. J., Schultz, M. P. & Flack, K. A. 2007 Turbulence structure in rough- and smooth-wall boundary layers. J. Fluid Mech. 592, 263293.
Volino, R. J., Schultz, M. P. & Flack, K. A. 2011 Turbulence structure in boundary layers over periodic two- and three-dimensional roughness. J. Fluid Mech. 676, 172190.
Wu, Y. & Christensen, K. T. 2006 Population trends of spanwise vortices in wall turbulence. J. Fluid Mech. 568, 5576.
Wu, Y. & Christensen, K. T. 2007 Outer-layer similarity in the presence of a practical rough-wall topography. Phys. Fluids 19, 085108.
Wu, Y. & Christensen, K. T. 2010 Spatial structure of a turbulent boundary layer with irregular surface roughness. J. Fluid Mech. 655, 380418.
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Coherent structures and associated subgrid-scale energy transfer in a rough-wall turbulent channel flow

  • Jiarong Hong (a1), Joseph Katz (a1), Charles Meneveau (a1) and Michael P. Schultz (a2)

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