Hostname: page-component-78c5997874-j824f Total loading time: 0 Render date: 2024-11-05T05:01:29.020Z Has data issue: false hasContentIssue false
  • English
  • Français

Investigation of subgrid-scale physics in the convective atmospheric surface layer using the budgets of the conditional mean subgrid-scale stress and temperature flux

Published online by Cambridge University Press:  05 May 2015

Khuong X. Nguyen  and
Chenning Tong
Khuong X. Nguyen
Affiliation:
Department of Mechanical Engineering, Clemson University, Clemson, SC 29634, 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

The subgrid-scale (SGS) physics in the convective atmospheric surface layer is studied using the SGS stress and SGS scalar flux. We derive the budget equations for the conditional mean SGS stress and SGS temperature flux and show that, for transport-equation-based SGS models, the budget terms must be correctly predicted by the SGS model in order for large-eddy simulation (LES) to reproduce the resolvable-scale velocity and temperature probability density functions. Field data from the Advection Horizontal Array Turbulence Study, which notably includes measurements of the fluctuating pressure and the advection of the velocity and temperature fields, are then used to analyse the budget equations. The results reveal the complex behaviour of the dynamics of the convective atmospheric surface layer. The budgets of the conditional mean SGS shear stress and SGS temperature flux are an approximate balance between the conditional mean production and pressure destruction, with the latter causing return to isotropy. The budgets of the normal SGS stress components are more complex. For strongly convective surface layers, energy is redistributed from the (smaller) vertical to the (larger) horizontal stress components during downdrafts, resulting in generation of anisotropy by the conditional mean SGS pressure–strain-rate correlation; wall pressure reflections can also enhance the anisotropy. The conditional mean SGS pressure transport, meanwhile, is a significant source of energy during updrafts as a result of the near-wall pressure minima. The vertical advection also plays a significant role in the transfer of SGS energy. For weakly convective surface layers, pressure transport is small while the SGS pressure–strain-rate correlation reverts to its usual role of causing return to isotropy. The results of the present study, particularly for the conditional mean SGS pressure–strain-rate correlation, provide new insights into the SGS physics first educed in a recent analysis of the mean SGS budgets by Nguyen et al. (J. Fluid Mech., vol. 729, 2013, pp. 388–422) and have important implications for near-wall models utilizing SGS transport equations in the convective atmospheric surface layer.

JFM classification

Geophysical and Geological Flows: Atmospheric flows Turbulent Flows: Turbulence modelling Turbulent Flows: Turbulent boundary layers
Type
Papers
Information
Journal of Fluid Mechanics , Volume 772 , 10 June 2015 , pp. 295 - 329
Check for updates
Copyright
© 2015 Cambridge University Press 

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

Borue, V. & Orszag, S. 1998 Local energy flux and subgrid-scale statistics in three-dimensional turbulence. J. Fluid Mech. 366, 1–31.CrossRefGoogle Scholar
Bou-Zeid, E., Higgins, C., Huwald, H., Meneveau, C. & Parlange, M. B. 2010 Field study of the dynamics and modelling of subgrid-scale turbulence in a stable atmospheric surface layer over a glacier. J. Fluid Mech. 665, 480–515.CrossRefGoogle Scholar
Bradley, E. F., Antonia, R. A. & Chambers, A. J. 1981 Turbulence Reynolds number and the turbulent kinetic energy balance in the atmospheric surface layer. Boundary-Layer Meteorol. 21, 183–197.CrossRefGoogle Scholar
Caughey, S. J. & Wyngaard, J. C. 1979 The turbulence kinetic energy budget in convective conditions. Q. J. R. Meteorol. Soc. 105, 231–239.CrossRefGoogle Scholar
Cerutti, S., Meneveau, C. & Knio, O. M. 2000 Spectral and hyper eddy viscosity in high-Reynolds-number turbulence. J. Fluid Mech. 421, 307–338.CrossRefGoogle Scholar
Chen, Q., Liu, S. & Tong, C. 2010 Investigation of the subgrid-scale fluxes and their production rates in a convective atmospheric surface layer using measurement data. J. Fluid Mech. 660, 282–315.CrossRefGoogle Scholar
Chen, Q., Otte, M., Sullivan, P. P. & Tong, C. 2009 A posteriori subgrid-scale model tests based on the conditional means of subgrid-scale stress and its production rate. J. Fluid Mech. 626, 149–181.CrossRefGoogle 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., 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, 1–19.Google Scholar
Chou, P. Y. 1945 On velocity correlations and the solution of the equations of turbulent fluctuation. Q. Appl. Maths 3, 38–54.CrossRefGoogle Scholar
Deardorff, J. W. 1972 Numerical investigation of neutral and unstable planetary boundary layers. J. Atmos. Sci. 29, 91–115.2.0.CO;2>CrossRefGoogle Scholar
Deardorff, J. W. 1973 The use of subgrid transport equations in a three-dimensional model of atmospheric turbulence. Trans. ASME: J. Fluids Engng 95, 429–438.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
Elliott, J. A. 1972 Microscale pressure fluctuations measured within the lower atmospheric boundary layer. J. Fluid Mech. 53, 351–383.CrossRefGoogle Scholar
Gibson, M. M. & Launder, B. E. 1978 Ground effects on pressure fluctuations in the atmospheric boundary layer. J. Fluid Mech. 86, 491–511.CrossRefGoogle Scholar
Hanjalić, K. & Jakirlić, S. 2002 Second-moment turbulence closure modelling. In Closure Strategies for Turbulent and Transitional Flows (ed. Launder, B. E. & Sandham, N. D.), pp. 47–101. Cambridge University Press.CrossRefGoogle Scholar
Hatlee, S. C. & Wyngaard, J. C. 2007 Improved subfilter-scale models from the HATS field data. J. Atmos. Sci. 64, 1694–1705.CrossRefGoogle Scholar
Higgins, C. W., Parlange, M. B. & Meneveau, C. 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.CrossRefGoogle 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 atmosperic surface flux layer. J. Atmos. Sci. 61, 1566–1581.2.0.CO;2>CrossRefGoogle Scholar
Kaimal, J. C. & Finnigan, J. J. 1994 Atmospheric Boundary Layer Flows. Oxford University Press.CrossRefGoogle Scholar
Kaimal, J. C., Wyngaard, J. C., Haugen, D. A., Coté, O. R., Izumi, Y., Caughey, S. J. & Readings, C. J. 1976 Turbulence structure in the convective boundary layer. J. Atmos. Sci. 33, 2152–2169.2.0.CO;2>CrossRefGoogle Scholar
Kaimal, J. C., Wyngaard, J. C., Izumi, Y. & Coté, O. R. 1972 Spectral characteristic of surface-layer turbulence. Q. J. R. Meteorol. 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
Khanna, S. & Brasseur, J. G. 1998 Three-dimensional buoyancy- and shear-induced local structure of the atmospheric boundary layer. J. Atmos. Sci. 55, 710–743.2.0.CO;2>CrossRefGoogle Scholar
Kleissl, J., Meneveau, C. & Parlange, M. 2003 On the magnitude and variability of subgrid-scale eddy-diffusion coefficients in the atmospheric surface layer. J. Atmos. Sci. 60, 2372–2388.2.0.CO;2>CrossRefGoogle Scholar
Lenschow, D. H., Mann, J. & Kristensen, L.1993 How long is long enough when measuring fluxes and other turbulence statistics? Tech. Rep. NCAR/TN-389+STR.Google Scholar
Lenschow, D. H. & Stephens, P. L. 1980 The role of thermals in the convective boundary layer. Boundary-Layer Meteorol. 19, 509–532.CrossRefGoogle Scholar
Lilly, D. K. 1967 The representation of small-scale turbulence in numerical simulation experiments. In Proceedings IBM Scientific Computing Symp. on Environ. Sci. (ed. Goldstine, H. H.), pp.195–210. IBM Data Processing Division, New York.Google Scholar
Ludwig, F. L., Chow, F. K. & Street, R. L. 2009 Effect of turbulence models and spatial resolution on resolved velocity structure and momentum fluxes in large-eddy simulations of neutral boundary layer flow. J. Appl. Meteorol. Climatol. 48, 1161–1180.CrossRefGoogle Scholar
Lumley, J. L. 1965 Interpretation of time spectra measured in high-intensity shear flows. Phys. Fluids 6, 1056–1062.CrossRefGoogle Scholar
Lumley, J. L. 1978 Computational modeling of turbulent flows. Adv. Appl. Mech. 18, 123–176.CrossRefGoogle Scholar
Mason, P. J. 1994 Large-eddy simulation: a critical review of the technique. Q. J. R. Meteorol. Soc. 120, 1–26.Google Scholar
Mason, P. J. & Thomson, D. J. 1992 Stochastic backscatter in large-eddy simulations of boundary layers. J. Fluid Mech. 242, 51–78.CrossRefGoogle Scholar
McBean, G. A. & Elliott, J. A. 1975 The vertical transports of kinetic energy by turbulence and pressure in the boundary layer. J. Atmos. Sci. 32, 753–766.2.0.CO;2>CrossRefGoogle Scholar
Miller, D. O., Tong, C. & Wyngaard, J. C. 1999 The effects of probe-induced flow distortion on velocity covariances: field observations. Boundary-Layer Meteorol. 91, 483–493.CrossRefGoogle Scholar
Naot, D., Shavit, A. & Wolfshtein, M. 1970 Interactions between components of the turbulent velocity correlation tensor due to pressure fluctuations. Israel J. Tech. 8, 259–269.Google Scholar
Nguyen, K. X., Horst, T. W., Oncley, S. P. & Tong, C. 2013 Measurements of the budgets of the subgrid-scale stress and temperature flux in a convective atmospheric surface layer. J. Fluid Mech. 729, 388–422.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.CrossRefGoogle Scholar
Nishiyama, R. T. & Bedard, A. J. 1991 A quad-disk static pressure probe for measurement in adverse atmospheres – with a comparative review of static pressure probe designs. Rev. Sci. Instrum. 62, 2193–2204.CrossRefGoogle Scholar
Patton, E. G., Horst, T. W., Sullivan, P. P., Lenschow, D. H., Oncley, S. P., Brown, W. O. J., Burns, S. P., Guenther, A. B., Held, A., Karl, T., Mayor, S. D., Rizzo, L. V., Spuler, S. M., Sun, J., Turnipseed, A. A., Allwine, E. J., Edburg, S. L., Lamb, B. K., Avissar, R., Calhoun, R. J., Kleissl, J., Massman, W. J., Paw-U, K. T. & Weil, J. C. 2011 The canopy horizontal array turbulence study. Bull. Am. Meteorol. Soc. 92, 593–611.CrossRefGoogle 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., Yu, Y. & Adrian, R. J. 1996 Subgrid-scale energy transfer and near-wall turbulence structure. Phys. Fluids 8, 215–224.CrossRefGoogle Scholar
Pope, S. B. 2000 Turbulent Flows. Cambridge University Press.CrossRefGoogle Scholar
Pope, S. B. 2010 Self-conditioned fields for large-eddy simulations of turbulent flows. J. Fluid Mech. 652, 139–169.CrossRefGoogle 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, 2673–2698.2.0.CO;2>CrossRefGoogle Scholar
Rajagopalan, A. G. & Tong, C. 2003 Experimental investigation of scalar-scalar-dissipation filtered joint density function and its transport equation. Phys. Fluids 15, 227–244.CrossRefGoogle Scholar
Ramachandran, S.2010 Subgrid modeling using transport equations: large-eddy simulation of the atmospheric boundary layer. PhD Dissertation, The Pennsylvania State University, Department of Meteorology.CrossRefGoogle Scholar
Ramachandran, S. & Wyngaard, J. C. 2011 Subfilter-scale modelling using transport equations: large-eddy simulation of the moderately convective atmospheric boundary layer. Boundary-Layer Meteorol. 139, 1–35.CrossRefGoogle Scholar
Robinson, S. K. 1991 Coherent motions in the turbulent boundary layer. Annu. Rev. Fluid Mech. 23, 601–639.CrossRefGoogle Scholar
Rotta, J. C. 1951 Statistische theorie nichthomogener Turbulenz. Z. Phys. 129, 547–572.CrossRefGoogle Scholar
Sullivan, P. P., Edson, J. B., Horst, T. W., Wyngaard, J. C. & Kelly, M. 2006 Subfilter scale fluxes in the marine surface layer: results from the ocean horizontal array turbulence study (OHATS). In 17th Symposium on Boundary Layers and Turbulence, American Meteorological Society, San Diego, CA, 22–25 May 2006.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.CrossRefGoogle Scholar
Tong, C. 2001 Measurements of conserved scalar filtered density function in a turbulent jet. Phys. Fluids 13, 2923–2937.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 Meteorological Society, Vancouver, BC, Canada, 28 July - 01 August 1997.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
Wand, M. P. & Jones, M. C. 1995 Kernel Smoothing. Chapman & Hall/CRC.CrossRefGoogle Scholar
Wang, D. & Tong, C. 2002 Conditionally filtered scalar dissipation, scalar diffusion, and velocity in a turbulent jet. Phys. Fluids 14, 2170–2185.CrossRefGoogle Scholar
Wang, D., Tong, C. & Pope, S. B. 2004 Experimental study of velocity filtered joint density function and its transport equation. Phys. Fluids 16, 3599–3613.CrossRefGoogle Scholar
Wilczak, J. M. & Bedard, A. J. 2004 A new turbulence microbarometer and its evaluation using the budget of horizontal heat flux. J. Atmos. Ocean. Technol. 21, 1170–1181.2.0.CO;2>CrossRefGoogle Scholar
Wilczak, J. M. & Businger, J. A. 1984 Large-scale eddies in the unstably stratified atmospheric surface layers. Part II: turbulent pressure fluctuations and the budgets of heat flux, stress and turbulent kinetic energy. J. Atmos. Sci. 41, 3551–3567.2.0.CO;2>CrossRefGoogle Scholar
Wilczak, J. M. & Tillman, J. E. 1980 The three-dimensional structure of convection in the atmospheric surface layer. J. Atmos. Sci. 37, 2424–2443.2.0.CO;2>CrossRefGoogle Scholar
Wyngaard, J. C. 1981 The effects of probe-induced flow distortion on atmospheric turbulence measurements. J. Appl. Meteorol. 20, 784–794.2.0.CO;2>CrossRefGoogle Scholar
Wyngaard, J. C. 2004 Toward numerical modeling in the ‘terra incognita’. J. Atmos. Sci. 61, 1816–1826.2.0.CO;2>CrossRefGoogle Scholar
Wyngaard, J. C. & Coté, O. R. 1971 The budgets of turbulent kinetic energy and temperature variance in the atmospheric surface layer. J. Atmos. Sci. 28, 190–201.2.0.CO;2>CrossRefGoogle Scholar
Wyngaard, J. C., Coté, O. R. & Izumi, Y. 1971 Local free convection, similarity, and the budgets of shear stress and heat flux. J. Atmos. Sci. 28, 1171–1182.2.0.CO;2>CrossRefGoogle Scholar
Wyngaard, J. C., Siegel, A. & Wilczak, J. M. 1994 On the response of a turbulent-pressure probe and the measurement of pressure transport. Boundary-Layer Meteorol. 69, 379–396.CrossRefGoogle Scholar