A simple analytical model is developed for the flow downwind of a step change of the aerodynamic roughness length in the atmospheric boundary layer. The region downwind of the roughness transition is assumed to be composed of two equilibrium layers, corresponding to the downwind and upwind conditions, and separated by a third, transition, layer. The key assumption in deriving the model is that the eddy viscosity in the transition region is composed of a linearly varying component and an augmentation, which is parabolic in the vertical coordinate. The model is fully predictive up to two parameters that need to be specified. The first parameter is the ratio between the equilibrium boundary-layer height and the internal boundary-layer height. The second parameter controls the degree of nonlinearity of the eddy viscosity augmentation. An empirical relation is developed for the first parameter, while a range of values (between 0.1 and 0.3) is recommended for the second. The model is tested with results from field observations, wind-tunnel experiments, and numerical simulations of the flow behind a sudden jump in surface roughness. These tests show that the flow field and surface stresses are predicted accurately for smooth-to-rough as well as rough-to-smooth transitions.

中文翻译：

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表面粗糙度跳跃背后的表面剪切应力和速度分布的预测分析模型

为大气边界层中气动粗糙度长度阶跃变化的顺风流开发了一个简单的分析模型。假设粗糙度过渡的顺风区域由两个平衡层组成，对应于顺风和逆风条件，并由第三个过渡层隔开。推导模型的关键假设是过渡区域的涡粘性由线性变化的分量和在垂直坐标中呈抛物线的增广组成。该模型最多可完全预测需要指定的两个参数。第一个参数是平衡边界层高度与内部边界层高度之间的比率。第二个参数控制涡流粘度增加的非线性程度。为第一个参数开发了经验关系，而为第二个参数推荐了一个值范围（0.1 到 0.3 之间）。该模型通过现场观测、风洞实验和表面粗糙度突然跳跃背后流动的数值模拟的结果进行了测试。这些测试表明，流场和表面应力可以准确地预测为平滑到粗糙以及从粗糙到平滑的过渡。