Large-eddy simulation of the stable boundary layer: Revisiting GABLS with a linear algebraic subgrid-scale turbulence model

The stable boundary layer (SBL) has a more delicate dynamical balance than the neutral or convective boundary layers. Thus, understanding and parameterizing its development has been much slower, and experimental and numerical studies of the SBL are challenging. The thin, cooled surface layer of the SBL is governed by the geostrophic wind and surface cooling. The turbulence is regulated by shear, dissipation, and buoyancy destruction. Two characteristics of the SBL that make numerical studies difficult are: (1) the energetic eddies in the SBL can be smaller than 1 m, so using a domain that is both large enough and resolved enough can be computationally expensive, and (2) the turbulence is anisotropic because stratification inhibits vertical motions. The second factor has led to the development of subgrid-scale (SGS) turbulence models that can provide anisotropy.

In this paper, we investigate the manner in which our Linear Algebraic Subgrid-Scale model (LASS - see Enriquez, 2013) can simulate a cooling SBL. As a prologue, we show how LASS behaves under different cooling fluxes and how it provides appropriate anisotropy. Then, we examine how LASS performs in a moderately stable case, the Global Energy and Water Cycle Experiment Atmospheric Boundary Layer Study (GABLS). This case is based on Arctic observations, simulated first by Kosović and Curry (2000) and later with a variety of LES turbulence models by Beare et al. (2006).

SGS Turbulence Anisotropy

Since the vertical motions are damped by the stable stratification, the turbulence should be anisotropic. Few SGS turbulence models can provide this one property. We characterize the SGS stress anisotropy with a Lumley diagram (Fig. 1). The colored shapes on the Lumley triangle are at the six vertical points nearest the surface, with red being nearest the surface and violet being furthest. After cooling the surface with a surface flux of -0.01 K m s^-1, the anisotropy characteristics are similar to those found in a neutral boundary layer (Enriquez, 2013). The anisotropy decreases with distance from the wall and is on the left side of the triangle, indicating disc-shaped eddies.

GABLS Comparisons

In general, our profiles exhibit a noticeable super-geostrophic jet near the top of the boundary layer and a positive curvature in the potential temperature. These common characteristics are also portrayed in Beare et al. (2006) and Huang and Bou-Zeid (2013). For resolutions of 12.5 m and 6.25 m, the LASS simulations fall within the spread of the equivalent Beare et al. (2006) data. The LASS model runs tend to predict slightly higher potential temperatures right above the surface than the other LES runs.

As the resolution increases, we see (1) that the jet becomes more evident and that the peak shifts towards the ground and (2) the potential temperature decreases slightly by the surface and increases towards the top of the domain. The main difference between the two runs is seen in the wind speed profiles. In particular, the profile at the top of the boundary layer is the most changed. For a LES that used a turbulence model that provided backscatter, Beare et al. (2006) also showed that as resolution increased there was a general decrease in the height of the jet, along with an increase in the jet strength. Backscatter was used to explain the boundary layer depth enhancement for the coarser resolutions. This trend in LASS may also be due to backscatter since the inclusion of buoyancy in our model allows backscatter for the stable boundary layer because of the interaction between the buoyancy, production, and dissipation terms.

We also compare our 12.5 m and 6.25 m resolution profiles with the 2 m data of Beare et al. (2006), which can be seen in Fig. 2. They concluded that a resolution of 3.125 m or less is ideal for simulating a moderately SBL, while reasonable behavior can still be obtained with a resolution of 6.25 m. Our results here, confirm their findings. While, the 12.5 m resolution run does not capture the low-level jet as well as the 2 m resolution runs, the 6.25 m run appears to do quite well. It predicts the stronger and lower jet. The potential temperature profile provided by the 6.25 m run fits the 2m data much better than the 12.5 m run, confirming our previous experience (Enriquez, 2013) with LASS that it is able to resolve structures that are about the same size as those resolved with a Dynamic Wong-Lilly simulation at twice the resolution.

Figure 1. Lumley triangle of the LASS SGS stress anisotropy tensors from LES of the SBL with 8 m and 16 m horizontal resolution. These simulations had a surface cooling -0.01 K m s^-1. Colors symbolize the SGS anisotropy at the six points nearest to the surface. The red shapes are closest while the violet shapes are furthest from the surface.

 

 

Figure 2. Comparison of LES wind speed (left) and potential temperature (right) profiles at 12.5 m and 6.25 m resolutions with Beare et al. (2006) 2 m data.

 

Acknowledgments

We appreciate our helpful discussions with Professor Tina Chow and Dr. Bowen Zhou of UC Berkeley and Dr. Peter Sullivan of NCAR. We are grateful to NCAR's CISL for the computing-time allocation used in this research. This material is based upon work supported by the National Science Foundation under Grant No. AGS-1001262.