Addressing the Grid-Size Sensitivity Issue in Large-Eddy Simulations of Stable Boundary Layers
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Addressing the Grid-Size Sensitivity Issue in Large-Eddy Simulations of Stable Boundary Layers Yi Dai1 · Sukanta Basu1
· Björn Maronga2,3 · Stephan R. de Roode1
Received: 1 February 2020 / Accepted: 29 July 2020 © The Author(s) 2020
Abstract We have identified certain fundamental limitations of a mixing-length parametrization used in a popular turbulent kinetic energy-based subgrid-scale model. Replacing this parametrization with a more physically realistic one significantly improves the overall quality of the largeeddy simulation (LES) of stable boundary layers. For the range of grid sizes considered here (specifically, 1 m–12.5 m), the revision dramatically reduces the grid-size sensitivity of the simulations. Most importantly, the revised scheme allows us to reliably estimate the firstand second-order statistics of a well-known LES intercomparison case, even with a coarse grid size of O(10 m). Keywords Buoyancy length scale · Prandtl number · Stable boundary layer · Subgrid-scale model
1 Introduction The first large-eddy simulation (LES) intercomparison study (Beare et al. 2006), organized under the auspices of the Global Energy and Water Exchanges (GEWEX) Atmospheric Boundary Layer Study (GABLS), has had a lasting impact on research on the stable boundary layer (SBL). In the past decade and a half, the key findings from this study (henceforth referred to as GABLS1–LES) were cited by numerous papers; a few examples are:
“Adequate WSBL [weakly stable boundary layer] resolution is attained with 2-m grids (Beare et al. 2006), but higher resolution is required for moderate and very stable stratification (e.g., SBL depths of less than 50 m or so).” (Fernando and Weil 2010)
B
Sukanta Basu [email protected]
1
Faculty of Civil Engineering and Geosciences, Delft University of Technology, Delft, The Netherlands
2
Geophysical Institute, University of Bergen, Bergen, Norway
3
Institute of Meteorology and Climatology, Leibniz University Hannover, Hannover, Germany
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Y. Dai et al.
“Even for weak to moderately stable conditions, LES of the NBL [nocturnal boundary layer] requires a grid spacing of O(1 m) (Beare et al. 2006), which greatly increases the computational burden.” (van Stratum and Stevens 2015) “In particular, it is often observed that grid convergence for simulations of the stable boundary layer is lacking, see Beare et al. (2006) and Sullivan et al. (2016). The latter used fine grid spacings down to [0.39] m (pseudo-spectral code) and still reported a sensitivity of their results to the grid spacing. Until now, a convincing explanation for this behaviour has been lacking, creating a limitation for the application of LES models for simulating the stable boundary layer.” (Maronga et al. 2019) Similar statements on the grid-size sensitivity can be found in other peer-reviewed publications and are often heard in any contemporary workshop or conference session on SBL. Such an overwhelming consensus among the SBL–LES community at large is somewhat disconcerting given the fact that a handful of papers e
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