Abstract
We perform large-eddy simulation (LES) of a moderately convective atmospheric boundary layer (ABL) using a prognostic subfilter-scale (SFS) model obtained by truncating the full conservation equations for the SFS stresses and fluxes. The truncated conservation equations contain production mechanisms that are absent in eddy-diffusivity closures and, thus, have the potential to better parametrize the SFS stresses and fluxes. To study the performance of the conservation-equation-based SFS closure, we compare LES results from the surface layer with observations from the Horizontal Array Turbulence Study (HATS) experiment. For comparison, we also show LES results obtained using an eddy-diffusivity closure. Following past studies, we plot various statistics versus the non-dimensional parameter, Λ w /Δ, where Λ w is the wavelength corresponding to the peak in the vertical velocity spectrum and Δ is the filter width. The LES runs are designed using different domain sizes, filter widths and surface fluxes, in order to replicate partly the conditions in the HATS experiment. Our results show that statistics from the different LES runs collapse reasonably and exhibit clear trends when plotted against Λ w /Δ. The trends exhibited by the production terms in the modelled SFS conservation equations are qualitatively similar to those seen in the HATS data with the exception of SFS buoyant production, which is underpredicted. The dominant production terms in the modelled SFS stress and flux budgets obtained from LES are found to approach asymptotically constant values at low Λ w /Δ. For the SFS stress budgets, we show that several of these asymptotes are in good agreement with their corresponding theoretical values in the limit Λ w /Δ → 0. The modelled SFS conservation equations yield trends in the mean values and fluctuations of the SFS stresses and fluxes that agree better with the HATS data than do those obtained using an eddy-diffusivity closure. They, however, underpredict considerably the level of SFS anisotropy near the wall when compared to observations, which could be a consequence of the shortcomings in the model used for the pressure destruction terms. Finally, we address the computational cost incurred due to the use of additional prognostic equations.
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References
Andren A, Brown AR, Graf J, Mason PJ, Moeng CH, Nieuwstadt FTM, Schumann U (1994) Large-eddy simulation of a neutrally stratified boundary layer. Q J Roy Meteorol Soc 120: 1457–1484
Brasseur JG, Wei T (2010) Designing large-eddy simulation of the turbulent boundary layer to capture law-of-the-wall scaling. Phys Fluids 22: 1–21
Businger JA, Wyngaard JC, Izumi Y, Bradley EF (1971) Flux–profile relationships in the atmospheric surface layer. J Atmos Sci 28: 181–189
Chamecki M, Meneveau C, Parlange MB (2007) The local structure of atmospheric turbulence and its effect on the Smagorinsky model for large eddy simulation. J Atmos Sci 64: 1941–1958
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
Chen Q, Wang D, Zhang H, Tong C (2005) Effects of subgrid-scale turbulence on resolvable-scale velocity-scalar statistics. J Turb 6: 1–31
Chen Q, Otte M, Sullivan P, Tong C (2009) A posteriori subgrid-scale models tests based on the conditional means of subgrid-scale stress and its production rate. J Fluid Mech 626: 149–181
Deardorff JW (1973) The use of subgrid transport equations in a three-dimensional model of atmospheric turbulence. J Fluids Eng 95: 429–438
Deardorff JW (1980) Stratocumulus-capped mixed layers derived from a three-dimensional model. Boundary-Layer Meteorol 18: 495–527
Hatlee SC, Wyngaard JC (2007) Improved subfilter-scale models from the HATS field data. J Atmos Sci 64: 1694–1705
Higgins CW, Meneveau C, Parlange MB (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
Horst TW, Kleissl J, Lenschow DH, Meneveau C, Moeng CH, Parlange MB, Sullivan PP, Weil JC (2003) Hats: field observations to obtain spatially filtered turbulence fields from crosswind arrays of sonic anemometers in the atmospheric surface layer. J Atmos Sci 61: 1566–1581
Khanna S, Brasseur JG (1997) Analysis of Monin-Obukhov similarity from large-eddy simulation. J Fluid Mech 345: 251–286
Khanna S, Brasseur JG (1998) Three-dimensional buoyancy- and shear-induced local structure of the atmospheric boundary layer. J Atmos Sci 55: 710–743
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
Klemp J, Durran D (1983) An upper boundary condition permitting internal gravity wave radiation in numerical mesoscale models. Mon Weather Rev 11: 430–444
Lilly DK (1967) The representation of small-scale turbulence in numerical experiments. In: Proceedings of IBM scientific computing symposium on environmental sciences, Thomas J. Watson Research Center, IBM, Yorktown Heights, NY, pp 195–210
Moeng CH (1984) A large-eddy simulation model for the study of planetary boundary-layer turbulence. J Atmos Sci 41: 2052–2062
Moeng CH, Wyngaard JC (1986) An analysis of closures for pressure-scalar covariances in the convective boundary layer. J Atmos Sci 43: 2499–2513
Moeng CH, Wyngaard JC (1988) Spectral analysis of large eddy simulations of the convective boundary layer. J Atmos Sci 45: 3573–3587
Mydlarski L (2003) Mixed velocity-passive scalar statistics in high-Reynolds-number turbulence. J Fluid Mech 475: 173–203
Otte MJ, Wyngaard JC (2001) Stably stratified interfacial-layer turbulence from large-eddy simulation. J Atmos Sci 58: 3424–3442
Paulson CA (1970) The mathematical representation of wind speed and temperature profiles in the unstable atmospheric surface layer. J Appl Meteorol 9: 857–861
Peltier LJ, Wyngaard JC, Khanna S, Brasseur JG (1996) Spectra in the unstable surface layer. J Atmos Sci 53: 49–61
Porté-Agel F, Parlange MB, Meneveau C, Eichinger WE (2001) A priori field study of the subgrid-scale heat fluxes and dissipation in the atmospheric surface layer. J Atmos Sci 58: 2673–2698
Rotta JC (1951) Statistiche theorie nichthomogener turbulenz. Z Phys 129: 547–572
Schumann U (1975) Subgrid scales model for finite difference simulation of turbulent flows in plane channels and annuli. J Comput Phys 18: 376–404
Schumann U (1991) Subgrid length-scales for large-eddy simulation of stratified turbulence. Theor Comput Fluid Dyn 2: 279–290
Smagorinsky J (1963) General circulation experiments with the primitive equations I. The basic experiment. Mon Weather Rev 91: 99–164
Sreenivasan KR (1995) On the universality of the Kolmogorov constant. Phys Fluids 7: 2778–2784
Sreenivasan KR (1996) The passive scalar spectrum and the Obukhov-Corrsin constant. Phys Fluids 8: 189–196
Sullivan PP (2008) Using HATS databases to evaluate subfilter-scale rate equations for LES. In: Geophysical turbulent phenomena workshop, National Center for Atmospheric Research, Boulder, CO
Sullivan PP, Moeng C (1994) A comparison of shear- and buoyancy-driven planetary boundary layer flows. J Atmos Sci 51: 999–1022
Sullivan PP, McWilliams JC, Moeng C (1994) A subgrid-scale model for large-eddy simulation of planetary boundary-layer flows. Boundary-Layer Meteorol 71: 247–276
Sullivan PP, McWilliams JC, Moeng C (1996) A grid nesing method for large-eddy simulation of planetary boundary layer flows. Boundary-Layer Meteorol 80: 167–202
Sullivan PP, Horst TW, Lenschow DH, Moeng C, Weil JC (2003) Structure of subfilter-scale fluxes in the atmospheric surface layer with application to large-eddy simulation modelling. J Fluid Mech 482: 101–139
Tennekes H, Lumley JL (1972) A first course in turbulence. The MIT Press, Cambridge MA 300pp
Tong C, Wyngaard J, Khanna S, Brasseur JG (1998) Resolvable- and subgrid-scale measurement in the atmospheric surface layer: technique and issues. J Atmos Sci 55: 3114–3126
Vreman B, Geurts B, Kuerten H (1994) Realizability conditions for the turbulent stress tensor in large-eddy simulation. J Fluid Mech 278: 351–362
Wyngaard JC (2004) Towards numerical modeling in the “terra incognita”. J Atmos Sci 61: 1816–1826
Wyngaard JC (2010) Turbulence in the atmosphere, 1st edn. Cambridge University Press, UK, p 408
Wyngaard JC, Coté OR, Izumi Y (1971) Local free convection, similarity, and the budgets of shear stress and heat flux. J Atmos Sci 28: 1171–1182
Zhou Y, Brasseur JG, Juneja A (2001) A resolvable subfilter-scale model specific to large-eddy simulation of under-resolved turbulence. Phys Fluids 13: 2602–2610
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Ramachandran, S., Wyngaard, J.C. Subfilter-Scale Modelling Using Transport Equations: Large-Eddy Simulation of the Moderately Convective Atmospheric Boundary Layer. Boundary-Layer Meteorol 139, 1–35 (2011). https://doi.org/10.1007/s10546-010-9571-3
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DOI: https://doi.org/10.1007/s10546-010-9571-3