Hostname: page-component-cd9895bd7-lnqnp Total loading time: 0 Render date: 2024-12-18T04:03:41.388Z Has data issue: false hasContentIssue false
  • English
  • Français

A posteriori subgrid-scale model tests based on the conditional means of subgrid-scale stress and its production rate

Published online by Cambridge University Press:  10 May 2009

QINGLIN CHEN ,
MARTIN J. OTTE ,
PETER P. SULLIVAN  and
CHENNING TONG
QINGLIN CHEN
Affiliation:
Department of Mechanical Engineering, Clemson University, Clemson, SC 29634, USA
MARTIN J. OTTE
Affiliation:
Department of Civil and Environmental Engineering, Duke University, Durham, NC 27708, USA
PETER P. SULLIVAN
Affiliation:
National Center for Atmospheric Research, Boulder, CO 80307, USA
CHENNING TONG*
Affiliation:
Department of Mechanical Engineering, Clemson University, Clemson, SC 29634, USA
*
†Email address for correspondence: [email protected]
Get access Rights & Permissions [Opens in a new window]

Abstract

Traditional a posteriori tests of subgrid-scale (SGS) models often compare large eddy simulation (LES) profiles of various statistics with measurements. In this study we propose and employ a new a posteriori test to study SGS model performance. We compare the conditional means of the LES-generated SGS stress and stress production rate conditional on the resolvable-scale velocity with measurements. These statistics must be reproduced by the SGS model for LES to correctly predict the one-point resolvable-scale velocity joint probability density function. Our tests using data obtained in convective atmospheric boundary layers show that the a posteriori results are consistent with our a priori tests based on the same conditional statistics. The strengths and deficiencies of the models observed here were also identified in our a priori tests. The remarkable consistency between the two types of tests suggests that statistical model tests based on the conditional SGS stress and its production rate are a highly capable approach for identifying specific model deficiencies and for evaluating SGS model performance in simulations.

Type
Papers
Information
Journal of Fluid Mechanics , Volume 626 , 10 May 2009 , pp. 149 - 181
Copyright
Copyright © Cambridge University Press 2009

Access options

Get access to the full version of this content by using one of the access options below. (Log in options will check for institutional or personal access. Content may require purchase if you do not have access.)

References

REFERENCES

Bardina, J., Ferziger, J. H. & Reynolds, W. C. 1980 Improved subgrid scale models for large eddy simulation. AIAA Paper 80-1357.CrossRefGoogle Scholar
Businger, J. A., Wynngard, J. C., Izumi, Y. & Bradley, E. F. 1971 Flux-profile relationships in the atmospheric surface layer. J. Atmos. Sci. 28, 181–189.2.0.CO;2>CrossRefGoogle Scholar
Canuto, C., Hussaini, M. Y., Quarteroni, A. & Zang, T. A. 1988 Spectral Methods in Fluid Dynamics. Springer-Verlag.CrossRefGoogle Scholar
Chen, Q. 2006 Investigation of the effects of subgrid-scale turbulence on resolvable-scale statistics. PhD dissertation, Clemson University, Department of Mechanical Engineering.Google Scholar
Chen, Q. & Tong, C. 2006 Investigation of the subgrid-scale stress and its production rate in a convective atmospheric boundary layer using measurement data. J. Fluid Mech. 547, 65–104.CrossRefGoogle Scholar
Chen, Q., Wang, D., Zhang, H. & Tong, C. 2005 Effects of subgrid-scale turbulence on resolvable-scale velocity-scalar statistics. J. Turbul. 6, 36.CrossRefGoogle Scholar
Chen, Q., Zhang, H., Wang, D. & Tong, C. 2003 Subgrid-scale stress and its production rate: conditions for the resolvable-scale velocity probability density function. J. Turbul. 4, 027.Google Scholar
Clark, R. A., Ferziger, J. H. & Reynolds, W. C. 1979 Evaluation of subgrid-models using an accurately simulated turbulent flow. J. Fluid Mech. 91, 1–16.CrossRefGoogle Scholar
Deardorff, J. W. 1980 Stratocumulus-capped mixed layers derived from a three-dimensional model. Bound. Layer Met. 18, 495–527.Google Scholar
Domaradzki, J. A., Liu, W. & Brachet, M. E. 1993 An analysis of subgrid-scale interactions in numerically simulated isotropic turbulence. Phys. Fluids A 5, 1747–1759.CrossRefGoogle Scholar
Edsall, R. M., Thomson, D. W., Wyngaard, J. C. & Peltier, L. J. 1995 A technique for measurement of resolvable-scale flux budgets. In 11th Symposium on Boundary Layers and Turbulence, pp. 15–17. American Meteor Society.Google Scholar
Germano, M., Piomelli, U., Moin, P. & Cabot, W. H. 1991 A dynamic subgrid-scale eddy viscosity model. Phys. Fluids A 3, 1760–1765.Google Scholar
Härtel, C., Kleiser, L., Unger, F. & Friedrich, R. 1994 Subgrid-scale energy-transfer in the near-wall region of turbulent flow. Phys. Fluid 6, 3130–3143.Google Scholar
Hatlee, S. C. & Wynngard, J. C. 2007 Improved subfilter-scale models from the HATS field data. J. Atmos. Sci. 64, 1694–1705.Google Scholar
Higgins, C. W., Meneveau, C. & Parlange, M. B. 2007 The effect of filter dimension on the subgrid-scale stress, heat flux, and tensor alignments in the atmospheric surface layer. J. Atmos. Ocean. Technol. 24, 360–375.Google Scholar
Horst, T. W., Kleissl, J., Lenschow, D. H., Meneveau, C., Moeng, C.-H., Parlange, M. B., Sullivan, P. P. & Weil, J. C. 2004 Hats: field observations to obtain spatially-filtered turbulence fields from transverse arrays of sonic anemometers in the atmospheric surface flux layer. J. Atmos. Sci. 61, 1566–1581.2.0.CO;2>CrossRefGoogle Scholar
Juneja, A. & Brasseur, J. G. 1999 Characteristics of subgrid-resolved-scale dynamics in anisotropic turbulence, with application to rough-wall boundary layers. Phys. Fluid 11, 3054–3068.CrossRefGoogle Scholar
Kaimal, J. C., Wyngaard, J. C., Izumi, Y. & Coté, O. R. 1972 Spectral characteristic of surface-layer turbulence. Q. J. R. Met. Soc. 98, 563–589.Google Scholar
Khanna, S. & Brasseur, J. G. 1997 Analysis of monin-obukhov similarity from large-eddy simulation. J. Fluid Mech. 345, 251–286.CrossRefGoogle Scholar
Klemp, J. B. & Durran, D. R. 1983 An upper boundary-condition permitting internal gravity-wave radiation in numerical mesoscale models. Mon. Wea. Rev. 111, 430–444.2.0.CO;2>CrossRefGoogle Scholar
Kosović, B. 1997 Subgrid-scale modelling for the large-eddy simulation of high-reynolds-number boundary layer. J. Fluid Mech. 336, 151–182.CrossRefGoogle Scholar
Leith, C. E. 1990 Stochastic backscatter in a subgrid-scale model: plane shear mixing layer. Phys. Fluids A 2, 297–299.Google Scholar
Lemone, M. A. 1990 Some observations of vertical velocity skewness in the convective planetary boundary-layer. J. Atmos. Sci. 47, 1163–1169.Google Scholar
Lenschow, D. H. & Stephens, P. L. 1980 The role of thermals in the convective boundary layer. Bound. Layer Meteor. 19, 509–532.Google Scholar
Lilly, D. K. 1967 The representation of small-scale turbulence in numerical simulation experiments. In Proceedings of the IBM Scientific Computing Symposium on Environmental Sciences, p. 195.Google Scholar
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, 83–119.Google Scholar
Lumley, J. L. 1978 Computational modeling of turbulent flows. Adv. Appl. Mech. 18, 123–176.Google Scholar
Lund, T. S. & Novikov, E. A. 1992 Parametrization of subgrid-scale stress by the velocity gradient tensor. Annual Research Briefs, Center for Turbulence Research, pp. 27–43.Google Scholar
Mason, P. J. 1994 Large-eddy simulation: a critical review of the technique. Q. J. R. Meteor. Soc. 120, 1–26.Google Scholar
Mason, P. J. & Thomson, D. J. 1992 Stochastic backscatter in large-eddy simulation of boundary layers. J. Fluid. Mech. 242, 51–78.Google Scholar
McMillan, O. J. & Ferziger, J. H. 1979 Direct testing of subgrid-scale models. Am. Inst. Aeronaut. Astronaut. J. 17, 1340–1346.CrossRefGoogle Scholar
McWilliams, J. C., Moeng, C.-H. & Sullivan, P. P. 1999 Turbulent fluxes and coherent structures in marine boundary layers: Investigations by large-eddy simulation. In Air-Sea Exchange: Physics, Chemistry, Dynamics, and Statistics (ed. Geernaert, G.), pp. 507–538. Kluwer.CrossRefGoogle Scholar
Meneveau, C. 1994 Statistics of turbulence subgrid-scale stress: necessary conditions and experimental tests. Phys. Fluids 6, 815.Google Scholar
Moeng, C.-H. 1984 Large-eddy simulation model for the study of planetary boundary-layer turbulence. J. Atmos. Sci. 41, 2052–2062.2.0.CO;2>CrossRefGoogle Scholar
Moeng, C.-H. & Sullivan, P. P. 2002 Large-eddy simulation. In Encyclopedia of Atmospheric Sciences (ed. Holton, J. R., Pyle, J. & Curry, J. A.), pp. 1140–1150. Academic Press.Google Scholar
Moeng, C. H. & Wyngaard, J. C. 1988 Spectral analysis of large-eddy simulations of the convective boundary layer. J. Atmos. Sci. 45, 3573–3587.2.0.CO;2>CrossRefGoogle Scholar
Nieuwstadt, F. T. M. & de Valk, P. J. P. M. M. 1987 A large eddy simulation of buoyant and non-buoyant plume dispersion in the atmospheric boundary layer. Atmos. Environ. 21, 2573–2587.Google Scholar
Otte, M. J. & Wynngard, J. C. 2001 Stably strasified interfacial-layer turbulence from large-eddy simulation. J. Atmos. Sci. 58, 3424–3442.Google Scholar
Peltier, L. J., Wyngaard, J. C., Khanna, S. & Brasseur, J. 1996 Spectra in the unstable surface layer. J. Atmos. Sci. 53, 49–61.2.0.CO;2>CrossRefGoogle Scholar
Piomelli, U. 1993 High Reynolds-number calculations using the dynamic subgrid-scale stress model. Phys. Fluid A 5, 1484–1490.CrossRefGoogle Scholar
Piomelli, U., Moin, P. & Ferziger, J. H. 1988 Model consistency in large eddy simulation of turbulent channel flows. Phys. Fluid 31, 1884–1891.Google Scholar
Pope, S. B. 2000 Turbulent Flows. Cambridge University press.Google Scholar
Porté-Agel, F., Meneveau, C. & Parlange, M. 2000 a A scale-dependent dynamics model for large-eddy simulation: application to a neutral atmospheric buoyancy layer. J. Fluid Mech. 415, 261–284.Google Scholar
Porté-Agel, F., Parlange, M. B., Meneveau, C. & Eichinger, W. E. 2001 A priori field study of the subgrid-scale heat fluxes and dissipation in the atmospheric surface layer. J. Atmos. Sci. 58, 2673–2698.Google Scholar
Porté-Agel, F., Parlange, M. B., Meneveau, C., Eichinger, W. E. & Pahlow, M. 2000 b Subgrid-scale dissipation in the atmospheric surface layer: effects of stability and filter dimension. J. Atmos. Sci. 57, 75–87.Google Scholar
Sarghini, F., Piomelli, U. & Balaras, E. 1999 Scale-similar models for large-eddy simulations. Phys. Fluids 11, 1596–1607.CrossRefGoogle Scholar
Schumann, U. 1975 Subgrid scale model for finite difference simulations of turbulent flows in plane channels and annuli. J. Comp. Phys. 18, 376–404.Google Scholar
Smagorinsky, J. 1963 General circulation experiments with the primitive equations: I. The basic equations. Mon. Wea. Rev. 91, 99–164.2.3.CO;2>CrossRefGoogle Scholar
Spalart, P. R., Moser, R. D. & Rogers, M. M. 1991 Spectral methods for the Navier–Stokes equations with one infinite and 2 periodic directions. J. Comp. Phys. 96, 297–324.Google Scholar
Sullivan, P. P., Horst, T. W., Lenschow, D. H., Moeng, C.-H. & Weil, J. C. 2003 Structure of subfilter-scale fluxes in the atmospheric surface layer with application to large-eddy simulation modeling. J. Fluid Mech. 482, 101–139.Google Scholar
Sullivan, P. P., McWilliams, J. C. & Moeng, C.-H. 1994 A subgrid-scale model for large-eddy simulation of planetary boundary-layer flows. Bound. Layer Met. 71, 247–276.CrossRefGoogle Scholar
Sullivan, P. P., McWilliams, J. C. & Moeng, C. H. 1996 A grid nesting method for large-eddy simulation of planetary boundary-layer flows. Bound. Layer Met. 80, 167–202.Google Scholar
Tao, B., Katz, J. & Meneveau, C. 2000 Geometry and scale relationships in high Reynolds number turbulence determined from three-dimensional holographic velocimetry. Phys. Fluids 12, 941–944.CrossRefGoogle Scholar
Tong, C., Wyngaard, J. C. & Brasseur, J. G. 1999 Experimental study of subgrid-scale stress in the atmospheric surface layer. J. Atmos. Sci. 56, 2277–2292.2.0.CO;2>CrossRefGoogle Scholar
Tong, C., Wyngaard, J. C., Khanna, S. & Brasseur, J. G. 1997 Resolvable- and subgrid-scale measurement in the atmospheric surface layer. In 12th Symposium on Boundary Layers and Turbulence, pp. 221–222. American Meteor Society.Google Scholar
Tong, C., Wyngaard, J. C., Khanna, S. & Brasseur, J. G. 1998 Resolvable- and subgrid-scale measurement in the atmospheric surface layer: technique and issues. J. Atmos. Sci. 55, 3114–3126.2.0.CO;2>CrossRefGoogle Scholar
Wyngaard, J. C. 1988 Structure of the pbl. In Lectures on Air Pollution Modeling, p. 385. American Meteor Society.Google Scholar