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

Abstract

A recent pragmatic blending approach treats sub-grid turbulent mixing using a weighted average of a 1D mesoscale model and a 3D Smagorinsky formulation. Here the approach is modified and extended to incorporate a scale-dependent dynamic Smagorinsky scheme instead of a static Smagorinsky scheme. Results from simulating an evolving convective boundary layer show that the new scheme is able to improve the representation of turbulence statistics and potential temperature profiles at grey-zone resolutions during the transition from the shallow morning to the deep afternoon boundary layer. This is achieved mainly because the new scheme enables and controls an improved spin-up of resolved turbulence. The dynamic blending scheme is shown to be more adaptive to the evolving flow and somewhat less sensitive to the blending parameters. The new approach appears to offer a more robust and more flexible formulation of blending and the results strongly encourage further assessment and development. KEYWORDSboundary-layer scheme, dynamic turbulence model, grey zone, sub-grid parametrization 1 the resolved scales. This approach is common in performing large-eddy simulations (LESs), and such simulations have proved valuable for our understanding of boundary-layer (BL) turbulence and for developing BL parametrizations suitable for NWP. However, if the dominant turbulence length-scales are similar to the grid scale, then models will partially resolve the dominant modes of BL turbulence. These resolutions comprise the terra incognita or the grey zone of BL turbu-This is an open access article under the terms of the Creative Commons Attribution License, which permits use, distribution and reproduction in any medium, provided the original work is properly cited.

The Atmospheric Boundary Layer and the “Gray Zone” of Turbulence: A Critical Review

“…However, the diffusive nature of the Smagorinsky scheme can result in the delayed spin‐up of nonlocal motions especially during the handover from the nonlocal mesoscale to the Smagorinsky scheme in deepening CBLs, as shown in Efstathiou et al (2016). Efstathiou and Plant (2019) extended the blending approach by incorporating a scale‐dependent dynamic Smagorinsky scheme instead of the standard static Smagorinsky scheme. They found some promising results in idealized simulations of an evolving CBL, particularly in relation to the spin‐up of resolved turbulence (cf.…”

“…Some promising results have emerged from both major categories. Some simple blending/hybrid schemes using nonlocal turbulence (Boutle et al, 2014; Efstathiou & Plant, 2019; Shin & Hong, 2015), TKE (Ito et al, 2015; Zhang et al, 2018), or mass‐flux approaches (Honnert et al, 2016) may significantly improve the representation of first‐order quantities and turbulence statistics in the CBL gray zone.…”

Gray Zone Partitioning Functions and Parameterization of Turbulence Fluxes in the Convective Atmospheric Boundary Layer

“…Deriving partitioning functions of turbulence fluxes in gray zone is of particular significance to represent the scale dependency of SGS transport. This is because such functions can aid in blending local/nonlocal heat fluxes (Shin & Hong, 2015;Zhang et al, 2018), mixing or dissipation length scales (Boutle et al, 2014;Efstathiou & Beare, 2015;Zhang et al, 2018), or eddy diffusivity coefficients (Efstathiou et al, 2016;Efstathiou & Plant, 2019) between mesoscale and microscale, required for the development of gray zone parameterizations. However, these attempts have been limited to solely address the scale dependency of TKE and vertical heat flux since the earliest study of Honnert et al (2011) and later in Sin and Hong (2013Hong ( , 2015, Boutle et al (2014), and Kurowski and Teixeira (2018).…”

“…Efstathiou et al (2016) followed this approach but applying to the CBL in terms of different convective forcings. Efstathiou and Plant (2019) further modified this model in blending the YSU PBL scheme with the dynamic Smagorinsky SGS model (Bou‐Zeid et al, 2005). They found that the use of dynamic Smagorinsky model outperforms that of standard Smagorinsky model (Smagorinsky, 1963) for the blending in gray zone grid spacings.…”

“…Considering that , all the turbulence is subgrid and modeled by the so‐called one‐dimensional (1‐D) planetary boundary layer (PBL) schemes (Cohen et al, 2015), which only treat the vertical mixing under the assumption of horizontal homogeneity (Honnert et al, 2011). At higher spatial grid spacings, typically subkilometer (Doubrawa & Muñoz‐Esparza, 2020; Efstathiou & Plant, 2019; Zhang et al, 2018), horizontal components of turbulent fluxes become important, while reaching to the microscale range (Wyngaard, 2004), and one‐dimensional treatment of turbulence becomes problematic (Zhang et al, 2018). Using a sufficiently fine grid spacing (Δ micro ), spanning from (100 m) down to a few meters (Muñoz‐Esparza et al, 2014), the energy‐containing large eddies can be explicitly resolved (large‐eddy simulation) and the contribution of small subgrid scale (SGS) eddies can be parameterized using SGS models.…”