The aim of this work is to present a theoretical scheme of dry thermal convection and convective rolls in atmospheric boundary layer with a linear eddy viscosity for a steady-state stationary case. For this theoretical study, a few approximations valid for atmospheric boundary layer were used, such as the Boussinesq approximation, and also, the second-order spatial derivative of velocity has been neglected. Analytical models for dry air thermal updraft velocity are presented and wavelength between convective rolls and aspect ratio of rolls have been derived. Using these results, it is shown how the transition between cellular-type convection and roll-type convection depends on thermal stratification of boundary layer, the temperature excess of convective cell at ground level and other meteorological parameters. The analytical results are in agreement with both observational and numerical studies for horizontal convective rolls existent in scientific literature. In addition, it is shown how this presented model can be applied for layers with non-linear eddy viscosity and how it can be used in future studies, and what its limitations are.

这项工作的目的是提出一种在稳态边界条件下干式热对流和大气边界层中具有线性涡流粘度的对流辊的理论方案。在本理论研究中，使用了一些对大气边界层有效的近似值，例如Boussinesq近似值，并且忽略了速度的二阶空间导数。给出了干燥空气热上升速度的分析模型，并得出了对流辊之间的波长和辊的纵横比。利用这些结果，表明蜂窝型对流和滚动型对流之间的过渡如何取决于边界层的热分层，对流单元在地平面上的温度过高和其他气象参数。分析结果与科学文献中存在的水平对流辊的观测和数值研究都一致。此外，还显示了该提出的模型如何应用于具有非线性涡流粘度的层，以及如何在未来的研究中使用它，以及它的局限性。