In a recent study (Želi et al. in Bound Layer Meteorol 176:229–249, 2020), we have shown that the explicit algebraic Reynolds-stress (EARS) model, implemented in a single-column context, is able to capture the main features of a stable atmospheric boundary layer (ABL) for a range of stratification levels. We here extend the previous study and show that the same formulation and calibration of the EARS model also can be applied to a dry convective ABL. Five different simulations with moderate convective intensities are studied by prescribing surface heat flux and geostrophic forcing. The results of the EARS model are compared to large-eddy simulations of Salesky and Anderson (J Fluid Mech 856:135–168, 2018). It is shown that the EARS model performs well and is able to capture the counter-gradient heat flux in the upper part of the ABL due to the presence of the non-gradient term in the relation for vertical turbulent heat flux. The model predicts the full Reynolds-stress tensor and heat-flux vector and allows us to compare other important aspects of a convective ABL such as the profiles of vertical momentum variance. Together with the previous studies, we show that the EARS model is able to predict the essential features of the ABL. It also shows that the EARS model with the same model formulation and coefficients is applicable over a wide range of stable and moderately unstable stratifications.

中文翻译：

---

包含反梯度通量的对流大气边界层的显式代数雷诺应力建模

在最近的一项研究中（Želi 等人，在 Bound Layer Meteorol 176:229–249, 2020）中，我们已经表明，在单列上下文中实施的显式代数雷诺应力 (EARS) 模型能够捕获一系列分层水平的稳定大气边界层 (ABL) 的主要特征。我们在这里扩展了之前的研究，并表明 EARS 模型的相同公式和校准也可以应用于干对流 ABL。通过规定地表热通量和地转强迫，研究了五种具有中等对流强度的不同模拟。将 EARS 模型的结果与 Salesky 和 ​​Anderson (J Fluid Mech 856:135–168, 2018) 的大涡模拟进行比较。结果表明，由于垂直湍流热通量关系中存在非梯度项，EARS 模型性能良好，并且能够捕获 ABL 上部的反梯度热通量。该模型预测完整的雷诺应力张量和热通量矢量，并允许我们比较对流 ABL 的其他重要方面，例如垂直动量方差的轮廓。与之前的研究一起，我们表明 EARS 模型能够预测 ABL 的基本特征。它还表明，具有相同模型公式和系数的 EARS 模型适用于广泛的稳定和中度不稳定分层。该模型预测完整的雷诺应力张量和热通量矢量，并允许我们比较对流 ABL 的其他重要方面，例如垂直动量方差的轮廓。与之前的研究一起，我们表明 EARS 模型能够预测 ABL 的基本特征。它还表明，具有相同模型公式和系数的 EARS 模型适用于广泛的稳定和中度不稳定分层。该模型预测完整的雷诺应力张量和热通量矢量，并允许我们比较对流 ABL 的其他重要方面，例如垂直动量方差的轮廓。与之前的研究一起，我们表明 EARS 模型能够预测 ABL 的基本特征。它还表明，具有相同模型公式和系数的 EARS 模型适用于广泛的稳定和中度不稳定分层。