Book contents
- Frontmatter
- Contents
- Contributors
- Prologue
- Part I Paradigms and Tools
- Part II Challenges
- 9 Transition to Turbulence
- 10 Wall-Bounded Turbulence
- 11 Scale-by-Scale Nonequilibrium in Turbulent Flows
- 12 Coarse-Graining in Multiphase Flows: From Micro to Meso to Macroscale for Euler–Lagrange and Euler–Euler Simulations
- 13 Coarse Graining for Thermal Flows
- 14 High-Order Simulations of Supersonic Combustion
- 15 Coarse-Graining Supersonic Combustion
- 16 Transition and Multiphysics in Inertial Confinement Fusion Capsules
- 17 Firestorms, Fallout, and Atmospheric Turbulence Induced by a Nuclear Detonation
- Epilogue
- Abbreviations
- Index
- References
10 - Wall-Bounded Turbulence
from Part II - Challenges
Published online by Cambridge University Press: 31 January 2025
Book contents
- Frontmatter
- Contents
- Contributors
- Prologue
- Part I Paradigms and Tools
- Part II Challenges
- 9 Transition to Turbulence
- 10 Wall-Bounded Turbulence
- 11 Scale-by-Scale Nonequilibrium in Turbulent Flows
- 12 Coarse-Graining in Multiphase Flows: From Micro to Meso to Macroscale for Euler–Lagrange and Euler–Euler Simulations
- 13 Coarse Graining for Thermal Flows
- 14 High-Order Simulations of Supersonic Combustion
- 15 Coarse-Graining Supersonic Combustion
- 16 Transition and Multiphysics in Inertial Confinement Fusion Capsules
- 17 Firestorms, Fallout, and Atmospheric Turbulence Induced by a Nuclear Detonation
- Epilogue
- Abbreviations
- Index
- References
Summary
We explore the treatment of near-wall turbulence in coarse-grained representations of wall-bounded turbulence. Such representations are complicated by the fact that at high Reynolds number the near-wall effects occur in an asymptotically thin layer. Because of this, many near-wall models are posed as effective boundary conditions, essentially eliminating the thin wall layer that is too thin to resolve. This is commonly referred to as wall-modeled large eddy simulation, and the viability of this approach is supported by the weakness of the interaction between the near-wall turbulence and that further away. Such models are generally informed by known characteristics of near-wall turbulence, such as the log-layer in the mean velocity and the so-called law-of-the-wall. In this chapter, we consider such coarse-grained near-wall models and the approximations implicit in their formulation from the perspective of thin-layer asymptotics.
- Type
- Chapter
- Information
- Coarse Graining TurbulenceModeling and Data-Driven Approaches and their Applications, pp. 306 - 332Publisher: Cambridge University PressPrint publication year: 2025
References
Afzal, N. 1996. Wake layer in a turbulent boundary layer with pressure gradient: A new approach. Pages 95–118 in IUTAM Symposium on Asymptotic Methods for Turbulent Shear Flows at High Reynolds Numbers, Gersten, K. (ed). Kluwer Academic Publishers.Google Scholar
Bae, H. J., Lozano-Durán, A., Bose, S. T., and Moin, P. 2019. Dynamic slip wall model for large-eddy simulation. Journal of Fluid Mechanics, 859, 400–432.CrossRefGoogle ScholarPubMed
Balaras, E., Benocci, C., and Piomelli, U. 1996. Two-layer approximate boundary conditions for large-eddy simulations. AIAA Journal, 34(6), 1111–1119.CrossRefGoogle Scholar
Bermejo-Moreno, I., Campo, L., Larsson, J., Bodart, J., Helmer, D., and Eaton, J. K. 2014. Confinement effects in shock wave/turbulent boundary layer interactions through wall-modelled large-eddy simulations. Journal of Fluid Mechanics, 758, 5–62.CrossRefGoogle Scholar
Bocquet, S., Sagaut, P., and Jouhaud, J. 2012. A compressible wall model for large-eddy simulation with application to prediction of aerothermal quantities. Physics of Fluids, 24(6), 065103.CrossRefGoogle Scholar
Bose, S., and Park, G. 2018. Wall-modeled large-eddy simulation for complex turbulent flows. Annual Review of Fluid Mechanics, 50, 531–561.CrossRefGoogle ScholarPubMed
Bose, S. T., and Moin, P. 2014. A dynamic slip boundary condition for wall-modeled large-eddy simulation. Physics of Fluids, 26(1), 015104.CrossRefGoogle Scholar
Cabot, W., and Moin, P. 2000. Approximate wall boundary conditions in the large-eddy simulation of high Reynolds number flow. Flow, Turbulence and Combustion, 63, 269–291.CrossRefGoogle Scholar
Carney, S. P., and Moser, R. D. 2023. Slow-growth approximation for near-wall patch representation of wall-bounded turbulence. Journal of Fluid Mechanics, 966, A45.CrossRefGoogle Scholar
Carney, S. P., Engquist, B., and Moser, R. D. 2020. Near-wall patch representation of wall-bounded turbulence. Journal of Fluid Mechanics, 903, A23.CrossRefGoogle Scholar
Chang, H. 2012. Modeling turbulence using optimal large eddy simulation. Ph.D. thesis, University of Texas at Austin.Google Scholar
Chapman, D. R. 1979. Computational aerodynamics development and outlook. AIAA Journal, 17(12), 1293–1313.CrossRefGoogle Scholar
Cheng, W., Pullin, D. I., and Samtaney, R. 2015. Large-eddy simulation of separation and reattachment of a flat plate turbulent boundary layer. Journal of Fluid Mechanics, 785, 78–108.CrossRefGoogle Scholar
Choi, H., and Moin, P. 2012. Grid-point requirements for large eddy simulation: Chapman’s estimates revisited. Physics of Fluids, 24(1), 011702.CrossRefGoogle Scholar
Chung, D., and Pullin, D. I. 2009. Large-eddy simulation and wall modelling of turbulent channel flow. Journal of Fluid Mechanics, 631, 281–309.CrossRefGoogle Scholar
Corrsin, S. 1958. Local isotropy in turbulent shear flow. National Advisory Committee for Aeronautics.Google Scholar
De Vanna, F., Cogo, M., Bernardini, M., Picano, F., and Benini, E. 2021. Unified wall-resolved and wall-modeled method for large-eddy simulations of compressible wall-bounded flows. Physical Review Fluids, 6(3), 034614.CrossRefGoogle Scholar
Deardorff, J. W. 1970. A numerical study of three-dimensional turbulent channel flow at large Reynolds numbers. Journal of Fluid Mechanics, 41(2), 453–480.CrossRefGoogle Scholar
Dong, S., Lozano-Durán, A., Sekimoto, A., and Jiménez, J. 2017. Coherent structures in statistically stationary homogeneous shear turbulence. Journal of Fluid Mechanics, 816, 167–208.CrossRefGoogle Scholar
Duprat, C., Balarac, G., Métais, O., Congedo, P. M., and Brugière, O. 2011. A wall-layer model for large-eddy simulations of turbulent flows with/out pressure gradient. Physics of Fluids, 23(1), 015101.CrossRefGoogle Scholar
Fowler, M., Zaki, T. A., and Meneveau, C. 2022. A Lagrangian relaxation towards equilibrium wall model for large eddy simulation. Journal of Fluid Mechanics, 934, A44.CrossRefGoogle Scholar
Fröhlich, J., and Von Terzi, D. 2008. Hybrid LES/RANS methods for the simulation of turbulent flows. Progress in Aerospace Sciences, 44(5), 349–377.CrossRefGoogle Scholar
Ghosal, S. 1996. An analysis of numerical errors in large-eddy simulations of turbulence. Journal of Computational Physics, 125(1), 187–206.CrossRefGoogle Scholar
Ghosal, S., and Moin, P. 1995. The basic equations for the large eddy simulation of turbulent flows in complex geometry. Journal of Computational Physics, 118(1), 24–37.CrossRefGoogle Scholar
Goc, K. A., Lehmkuhl, O., Park, G. I., Bose, S. T., and Moin, P. 2021. Large Eddy Simulation of Aircraft at Affordable Cost: a Milestone in Computational Fluid Dynamics. Flow, 1, E14.CrossRefGoogle Scholar
Grinstein, F. F., Margolin, L. G., and Rider, W. J. 2010. Implicit Large Eddy Simulation, Computing Turbulent Flow Dynamics. Cambridge University Press.Google Scholar
Haering, S., Lee, M., and Moser, R. D. 2019. Resolution-induced anisotropy in large-eddy simulations. Physical Review Fluids, 4(11), 114605.CrossRefGoogle Scholar
Haering, S. W., Oliver, T. A., and Moser, R. D. 2022. Active model split hybrid RANS/LES. Physical Review Fluids, 7(1), 014603.CrossRefGoogle Scholar
Hamilton, J. M., Kim, J., and Waleffe, F. 1995. Regeneration mechanisms of near-wall turbulence structures. Journal of Fluid Mechanics, 287, 317–348.CrossRefGoogle Scholar
Heinz, S. 2020. A review of hybrid RANS-LES methods for turbulent flows: Concepts and applications. Progress in Aerospace Sciences, 114, 100597.CrossRefGoogle Scholar
Hickel, S., Touber, E., Bodart, J., and Larsson, J. 2013. A parametrized non-equilibrium wall-model for large-eddy simulations. In: Eighth International Symposium on Turbulence and Shear Flow Phenomena. Begel House Inc.Google Scholar
Hou, Y., and Angland, D. 2016. A comparison of wall functions for bluff body aeroacoustic simulations. Page 2771 of: 22nd AIAA/CEAS Aeroacoustics Conference.CrossRefGoogle Scholar
IEA. 2021. Key World Energy Statistics 2021. www.iea.org/reports/key-world-energy-statistics-2021.Google Scholar
Jiménez, J., and Moser, R. D. 2000. Large Eddy Simulation: Where are we and what can we expect? AIAA Journal, 38(4), 605–612.CrossRefGoogle Scholar
Jiménez, J. 2004. Turbulent flows over rough walls. Annual Review of Fluid Mechanics, 36, 173–196.CrossRefGoogle Scholar
Jiménez, J. 2012. Cascades in wall-bounded turbulence. Annual Review of Fluid Mechanics, 44, 27–45.CrossRefGoogle Scholar
Jiménez, J. 2018. Coherent structures in wall-bounded turbulence. Journal of Fluid Mechanics, 842, P1.CrossRefGoogle Scholar
Jiménez, J., and Moin, P. 1991. The minimal flow unit in near-wall turbulence. Journal of Fluid Mechanics, 225, 213–240.CrossRefGoogle Scholar
Jiménez, J., and Pinelli, A. 1999. The autonomous cycle of near-wall turbulence. Journal of Fluid Mechanics, 389, 335–359.CrossRefGoogle Scholar
Jiménez, J., Kawahara, G., Simens, M. P, Nagata, M., and Shiba, M. 2005. Characterization of near-wall turbulence in terms of equilibrium and “bursting” solutions. Physics of Fluids, 17(1), 015105.CrossRefGoogle Scholar
Kawai, S., and Larsson, J. 2012. Wall-modeling in large eddy simulation: Length scales, grid resolution, and accuracy. Physics of Fluids, 24(1), 015105.CrossRefGoogle Scholar
Kawai, S., and Larsson, J. 2013. Dynamic non-equilibrium wall-modeling for large eddy simulation at high Reynolds numbers. Physics of Fluids, 25(1), 015105.CrossRefGoogle Scholar
Kline, S. J., Reynolds, W. C., Schraub, F. A., and Runstadler, P. W. 1967. The structure of turbulent boundary layers. Journal of Fluid Mechanics, 30(4), 741–773.CrossRefGoogle Scholar
Kolmogorov, A. N. 1941. The local structure of turbulence in incompressible viscous fluid for very large Reynolds number. Dokl. Akad. Nauk. SSSR, 30, 301–303. Reprinted in Proc. R. Soc. Lond. A 434, (1991), 9–13.Google Scholar
Langford, J. A., and Moser, R. D. 2001. Breakdown of continuity in large-eddy simulation. Physics of Fluids, 13(5), 1524–1527.CrossRefGoogle Scholar
Langford, J. A., and Moser, R. D. 2004. Optimal large-eddy simulation results for isotropic turbulence. Journal of Fluid Mechanics, 521, 273–294.CrossRefGoogle Scholar
Larsson, J., Kawai, S., Bodart, J., and Bermejo-Moreno, I. 2016. Large eddy simulation with modeled wall-stress: recent progress and future directions. Mechanical Engineering Reviews, 3(1), 15–00418.CrossRefGoogle Scholar
Lee, J., Cho, M., and Choi, H. 2013. Large eddy simulations of turbulent channel and boundary layer flows at high Reynolds number with mean wall shear stress boundary condition. Physics of Fluids, 25(11), 110808.CrossRefGoogle Scholar
Lee, M., and Moser, R. D. 2015. Direct numerical simulation of turbulent channel flow up to Reτ ≈ 5200. Journal of Fluid Mechanics, 774, 395–415.CrossRefGoogle Scholar
Lee, M., and Moser, R. D. 2019. Spectral analysis of the budget equation in turbulent channel flows at high Reynolds number. Journal of Fluid Mechanics, 860, 886–938.CrossRefGoogle Scholar
Leveque, E., Touil, H., Malik, S., Ricot, D., and Sengissen, A. 2018. Wall-modeled large-eddy simulation of the flow past a rod-airfoil tandem by the Lattice Boltzmann method. International Journal of Numerical Methods for Heat & Fluid Flow.CrossRefGoogle Scholar
Li, Y., and Meneveau, C. 2004. Analysis of mean momentum flux in subgrid models of turbulence. Physics of Fluids: Brief Communications, 16(9), 3483–3486.CrossRefGoogle Scholar
Lozano-Durán, A., Giometto, M. G., Park, G. I., and Moin, P. 2020. Non-equilibrium three-dimensional boundary layers at moderate Reynolds numbers. Journal of Fluid Mechanics, 883, A20.CrossRefGoogle Scholar
Lucas, J.-M., Cadot, O., Herbert, V., Parpais, S., and Délery, J. 2017. A numerical investigation of the asymmetric wake mode of a squareback Ahmed body-effect of a base cavity. Journal of Fluid Mechanics, 831, 675–697.CrossRefGoogle Scholar
Manhart, M., Peller, N., and Brun, C. 2008. Near-wall scaling for turbulent boundary layers with adverse pressure gradient: A priori tests on DNS of channel flow with periodic hill constrictions and DNS of separating boundary layer. Theoretical and Computational Fluid Dynamics, 22, 243–260.CrossRefGoogle Scholar
Marusic, I, Mathis, R, and Hutchins, N. 2010. Predictive model for wall-bounded turbulent flow. Science, 329(5988), 193–196.CrossRefGoogle ScholarPubMed
Meneveau, C. 1994. Statistics of turbulence subgrid-scale stresses: Necessary conditions and experimental tests. Physics of Fluids, 6(2), 815–833.CrossRefGoogle Scholar
Meneveau, C. 2020. A note on fitting a generalised moody diagram for wall modelled large-eddy simulations. Journal of Turbulence, 21(11), 650–673.CrossRefGoogle Scholar
Mizuno, Y., and Jiménez, J. 2013. Wall turbulence without walls. Journal of Fluid Mechanics, 723, 429–455.CrossRefGoogle Scholar
Mockett, C., Fuchs, M, and Thiele, F. 2012. Progress in DES for wall-modelled LES of complex internal flows. Computers & Fluids, 65, 44–55.CrossRefGoogle Scholar
Moeng, C.-H. 1984. A large-eddy-simulation model for the study of planetary boundary-layer turbulence. Journal of the Atmospheric Sciences, 41(13), 2052–2062.2.0.CO;2>CrossRefGoogle Scholar
Moin, P., and Kim, J. 1982. Numerical investigation of turbulent channel flow. Journal of Fluid Mechanics, 118, 341–377.CrossRefGoogle Scholar
Moser, R. D., Malaya, N. P., Chang, H., Zandonade, P. S., Vedula, P., Bhattacharya, A., and Haselbacher, A. 2009. Theoretically based optimal large-eddy simulation. Physics of Fluids, 21(10), 105104.CrossRefGoogle Scholar
Moser, R. D., Haering, S. W., and Yalla, G. R. 2021. Statistical properties of subgrid-scale turbulence models. Annual Review of Fluid Mechanics, 53, 255–286.CrossRefGoogle Scholar
Nagib, H. M, and Chauhan, K. A. 2008. Variations of von Kármán coefficient in canonical flows. Physics of Fluids, 20(10), 101518.CrossRefGoogle Scholar
Nicoud, F., Baggett, J. S., Moin, P., and Cabot, W. 2001. Large eddy simulation wall-modeling based on suboptimal control theory and linear stochastic estimation. Physics of Fluids, 13(10), 2968–2984.CrossRefGoogle Scholar
Nikitin, N. V., Nicoud, F., Wasistho, B., Squires, K. D., and Spalart, P. R. 2000. An approach to wall modeling in large-eddy simulations. Physics of Fluids, 12(7), 1629–1632.CrossRefGoogle Scholar
Park, G. I., and Moin, P. 2014. An improved dynamic non-equilibrium wall-model for large eddy simulation. Physics of Fluids, 26(1).CrossRefGoogle Scholar
Piomelli, U. 2008. Wall-layer models for large-eddy simulations. Progress in Aerospace Sciences, 44(6), 437–446.CrossRefGoogle Scholar
Piomelli, U, and Balaras, E. 2002. Wall-layer models for large-eddy simulations. Annual Review of Fluid Mechanics, 34, 349–374.CrossRefGoogle Scholar
Porté-Agel, F., Meneveau, C., and Parlange, M. B. 2000. A scale-dependent dynamic model for largeeddy simulation: application to a neutral atmospheric boundary layer. Journal of Fluid Mechanics, 415, 261–284.CrossRefGoogle Scholar
Rogers, M. M., and Moin, P. 1987. The structure of the vorticity field in homogeneous turbulent flows. Journal of Fluid Mechanics, 176, 33–66.CrossRefGoogle Scholar
Rozema, W., Bae, H. J., Moin, P., and Verstappen, R. 2015. Minimum-dissipation models for large-eddy simulation. Physics of Fluids, 27, 085107.CrossRefGoogle Scholar
Schoppa, W, and Hussain, Fazle. 2002. Coherent structure generation in near-wall turbulence. Journal of Fluid Mechanics, 453, 57–108.CrossRefGoogle Scholar
Schumann, U. 1975. Subgrid scale model for finite difference simulations of turbulent flows in plane channels and annuli. Journal of Computational Physics, 18, 376–404.CrossRefGoogle Scholar
Scotti, A., Meneveau, C., and Lilly, D. K. 1993. Generalized Smagorinsky model for anisotropic grids. Physics of Fluids, 5, 2306.Google Scholar
Spalart, P. R. 1997. Comments on the Feasibility of LES for Wings and on the Hybrid RANS/LES Approach. Pages 137–147 in Proceedings of the First AFOSR International Conference on DNS/LES, 1997.Google Scholar
Spalart, P. R. 2009. Detached-eddy simulation. Annual Review of Fluid Mechanics, 41, 181–202.CrossRefGoogle Scholar
Templeton, J. A., Wang, M., and Moin, P. 2006. An efficient wall model for large-eddy simulation based on optimal control theory. Physics of Fluids, 18(2).CrossRefGoogle Scholar
Templeton, J. A., Wang, M., and Moin, P. 2008. A predictive wall model for large-eddy simulation based on optimal control techniques. Physics of Fluids, 20(6).CrossRefGoogle Scholar
Toh, S., and Itano, T. 2005. Interaction between a large-scale structure and near-wall structures in channel flow. Journal of Fluid Mechanics, 524, 249–262.CrossRefGoogle Scholar
Townsend, A. A. R. 1976. The Structure of Turbulent Shear Flow. Cambridge University Press.Google Scholar
Völker, S., Moser, R. D., and Venugopal, P. 2002. Optimal large eddy simulation of turbulent channel flow based on direct numerical simulation statistical data. Physics of Fluids, 14(10), 3675–3691.CrossRefGoogle Scholar
Vreman, A. 2004. An eddy-viscosity subgrid-scale model for turbulent shear flow. Physics of Fluids, 16(10), 3670–3681.CrossRefGoogle Scholar
Wang, M., and Moin, P. 2002. Dynamic wall modeling for large-eddy simulation of complex turbulent flows. Physics of Fluids, 14(7), 2043–2051.CrossRefGoogle Scholar
Werner, H., and Wengle, H. 1993. Large-eddy simulation of turbulent flow over and around a cube in a plate channel. Pages 155–168 in Turbulent Shear Flows 8: Selected Papers from the Eighth International Symposium on Turbulent Shear Flows, Munich, Germany, September 9–11, 1991. Springer.Google Scholar
Wilhelm, S., Jacob, J., and Sagaut, P. 2021. A new explicit algebraic wall model for les of turbulent flows under adverse pressure gradient. Flow, Turbulence and Combustion, 106(1), 1–35.CrossRefGoogle Scholar
Yalla, G. R., Oliver, T. A., Haering, S. W., Engquist, B., and Moser, R. D. 2021a. Effects of resolution inhomogeneity in large-eddy simulation. Physical Review Fluids, 6(7), 074604.CrossRefGoogle Scholar
Yalla, G. R., Oliver, and Moser, R. D. 2021b. Numerical dispersion effects on the energy cascade in large-eddy simulation. Physical Review Fluids, 6(9), L092601.CrossRefGoogle Scholar
Yang, X. I. A., Sadique, J., Mittal, R., and Meneveau, C. 2015. Integral wall model for large eddy simulations of wall-bounded turbulent flows. Physics of Fluids, 27(2), 025112.CrossRefGoogle Scholar
Zandonade, P. S., Langford, J. A., and Moser, R. D. 2004. Finite-volume optimal large-eddy simulation of isotropic turbulence. Physics of Fluids, 16(7), 2255–2271.CrossRefGoogle Scholar