A model for the roughness length and its correlation with the roughness shear stress on organized rough walls of varying geometry are presented and verified. The roughness length is nondimensionalized by the characteristic roughness length and is expressed as a function of roughness density with a wake-interference parameter. The dimensionless roughness length is independent of Reynolds number. When the model is applied to the whole range of roughness densities, the rough walls can be smooth, transitionally rough, and fully rough. A large number of data from classical experiments and recent simulations are analyzed to evaluate the proposed correlations, which are found to be consistent with the analyzed datasets. The proposed expression for the dimensionless roughness length and the expression for the dimensionless roughness shear stress, proposed previously by the author (Boundary-Layer Meteorology, 2020, Vol. 174, 393–410), are found to be identical in form. Numerous extant measurements of the two roughness parameters can be reproduced when the wake-interference parameters in the two models are treated as identical. The parameters of the roughness-length model are closely related to the geometry of the roughness elements. Different types of roughness elements can be distinguished by the values of the parameters. These results provide the foundation for constructing the unified roughness model for organized rough walls of varying geometry.

提出并验证了粗糙度长度模型及其与不同几何形状的有组织的粗糙壁上的粗糙度剪切应力的相关性。粗糙度长度由特征粗糙度长度无量纲化，并用尾流干涉参数表示为粗糙度密度的函数。无量纲粗糙度长度与雷诺数无关。当模型应用于整个粗糙度密度范围时，粗糙壁可以是光滑的、过渡粗糙的和完全粗糙的。分析了来自经典实验和最近模拟的大量数据以评估所提出的相关性，发现这些数据与分析的数据集一致。提出的无量纲粗糙度长度的表达式和无量纲粗糙度剪切应力的表达式，作者先前提出的 (Boundary-Layer Meteorology, 2020, Vol. 174, 393–410) 在形式上是相同的。当两个模型中的尾流干扰参数被视为相同时，可以重现对两个粗糙度参数的大量现有测量。粗糙度-长度模型的参数与粗糙度元素的几何形状密切相关。不同类型的粗糙度元素可以通过参数的值来区分。这些结果为构建不同几何形状的有组织的粗糙墙的统一粗糙度模型提供了基础。当两个模型中的尾流干扰参数被视为相同时，可以重现对两个粗糙度参数的大量现有测量。粗糙度-长度模型的参数与粗糙度元素的几何形状密切相关。不同类型的粗糙度元素可以通过参数的值来区分。这些结果为构建不同几何形状的有组织的粗糙墙的统一粗糙度模型提供了基础。当两个模型中的尾流干扰参数被视为相同时，可以重现对两个粗糙度参数的大量现有测量。粗糙度-长度模型的参数与粗糙度元素的几何形状密切相关。不同类型的粗糙度元素可以通过参数的值来区分。这些结果为构建不同几何形状的有组织的粗糙墙的统一粗糙度模型提供了基础。