Simulation of an Evolving Convective Boundary Layer Using a Scale-Dependent Dynamic Smagorinsky Model at Near-Gray-Zone Resolutions

Abstract

A scale-dependent Lagrangian-averaged dynamic Smagorinsky subgrid scheme with stratification effects is used to simulate the evolving convective boundary layer of the Wangara (Australia) case study in the gray-zone regime (specifically, for grid lengths from 25 to 400 m). The dynamic Smagorinsky and standard Smagorinsky approaches are assessed for first- and second-order quantities in comparison with results derived from coarse-grained large-eddy simulation (LES) fields. In the LES regime, the subgrid schemes produce very similar results, albeit with some modest differences near the surface. At coarser resolutions, the use of the standard Smagorinsky approach significantly delays the onset of resolved turbulence, with the delay increasing with coarsening resolution. In contrast, the dynamic Smagorinsky scheme much improves the spinup and so is also able to maintain consistency with the LES temperature profiles at the coarser resolutions. Moreover, the resolved part of the turbulence reproduces well the turbulence profiles obtained from the coarse-grained fields, especially in the near gray zone. The dynamic scheme does become somewhat overenergetic with further coarsening of the resolution, especially near the surface. The dynamic scheme reaches its limit in the current configuration when the test filter starts to sample at the unresolved scales, returning very small Smagorinsky coefficients. Sensitivity tests reveal that the dynamic model can adapt to changes in the imposed numerical or subgrid diffusion by adjusting the Smagorinsky constant to the changing flow field and minimizing the dissipation effects on the resolved turbulence structures.

A dynamic extension of the pragmatic blending scheme for scale‐dependent sub‐grid mixing

“…(), similar to Efstathiou et al. , (; ). 3D dry LEM simulations are presented for two different horizontal resolutions of Δ x = 400 and 800 m which are considered representative of the grey zone (also Efstathiou and Beare, ; Efstathiou et al.…”

“…() as implemented for the LEM by Efstathiou et al. (). The dynamic blending uses Equations as above, but Equation is replaced by while the dynamic model mixing length ( l LASD ) is given by …”

“…Efstathiou et al. () modified and implemented the LASD scheme in the LEM and used it to simulate an evolving CBL at near‐grey‐zone resolutions at and beyond the LES regime. The dynamic model was shown to significantly improve the initial BL development due to the faster spin‐up of appropriate resolved motions.…”

“…Nonetheless, the LASD model exhibited a usability limit when applied at coarser grid spacings further into the grey zone (Efstathiou et al. ).…”

“…LASD is blended with a non‐local 1D BL scheme in the LEM and tested for an evolving CBL similarly to Efstathiou et al. , (; ). In particular, the ability of the new blending scheme to provide a smooth transition of the first‐ and second‐order quantities across the grey zone is examined in comparison with the standard blending scheme and with coarse‐grained LES results.…”