A Variable Mesh Spacing for Large-Eddy Simulation Models in the Convective Boundary Layer

Abstract

A variable vertical mesh spacing for large-eddy simulation (LES) models in a convective boundary layer (CBL) is proposed. The argument is based on the fact that in the vertical direction the turbulence near the surface in a CBL is inhomogeneous and therefore the subfilter-scale effects depend on the relative location between the spectral peak of the vertical velocity and the filter cut-off wavelength. From the physical point of view, this lack of homogeneity makes the vertical mesh spacing the principal length scale and, as a consequence, the LES filter cut-off wavenumber is expressed in terms of this characteristic length scale. Assuming that the inertial subrange initial frequency is equal to the LES filter cut-off frequency and employing fitting expressions that describe the observed convective turbulent energy one-dimensional spectra, it is feasible to derive a relation to calculate the variable vertical mesh spacing. The incorporation of this variable vertical grid within a LES model shows that both the mean quantities (and their gradients) and the turbulent statistics quantities are well described near to the ground level, where the LES predictions are known to be a challenging task.

A New Planetary Boundary Layer Scheme Based on LES: Application to the XPIA Campaign

“…Unlike the stable conditions, a weak velocity gradient appears for the unstable conditions thanks to the strong buoyancy and weaker winds. This leads to slightly varying wind speed in the surface layer and nearly constant wind speed until the entrainment zone consistently with the previous studies, for example Moeng and Sullivan () and Degrazia et al (). As can be expected, in comparison to stable cases, wind speed gradients are lower for the neutral case, revealing the well‐reported change of wind gradient from very stable conditions through weakly stable condition (Huang & Bou‐Zeid, ).…”

“…The dimensions and grid resolutions of the computational domain are determined depending on the atmospheric stability and in accordance with the earlier studies. So the domain size and the grid resolution are 5 × 5 × 2 km 3 and 40 × 40 × 16 m 3 for the unstable PBL (Brooks & Fowler, 2012;Cancelli et al, 2014;Degrazia et al, 2009), 3 × 3 × 1 km 3 and 24 × 24 × 10 m 3 for the neutral PBL (Khani & Porté-Agel, 2017), and 0.4 × 0.4 × 0.4 km 3 and 6.25 × 6.25 × 6.25 m 3 for the stable PBL (Basu & Porté-Agel, 2006), respectively. The details of the domain size, L, grid resolution, Δ, and the number of grid points, N, are given in Table 2.…”

The nocturnal boundary layer transition from weakly to very stable. Part II: Numerical simulation with a second‐order model

“…A and B are arbitrary constants (Degrazia et al, 2009;Schmengler et al, 2015), assumed as 3.5 and 20.6, respectively, in this simulation. As in previous studies (Costa et al, 2011;Maroneze et al, 2019), the second-order equations are solved at intermediate levels, located in between the main levels.…”

Stable Boundary Layer Regimes in Single-Column Models

“…The vertical discretization of Eqs. (1)- (3) and (11), for the E-l model, is done in a linearly varying mesh spacing proposed by Degrazia et al (2009). To increase the resolution on the upper domain the grid increment was modified and written as (Schmengler et al 2015)…”