We propose a single generalized function for dimensionless wind and temperature gradients in stable and unstable conditions based on Monin–Obukhov similarity theory. The proposed function may be matched with the currently accepted universal functions for the dimensionless wind-speed and temperature gradients using the empirical coefficients a and b to yield differences within ± 14% for both wind and temperature gradients in the interval of $$-2$$ - 2 < z / L < 0.5 ( z is height and L is the Obukhov length). In neutral conditions, wind and temperature profiles are the same as the standard log-law profile. Under unstable conditions, the differences are smaller than 1.5%; conversely, under stable conditions, the differences reach up to $$-~5.2$$ - 5.2 %. The coefficients a and b are analyzed here to evaluate the limits of this proposed semi-empirical function and possible physical characteristics are discussed. Although we use the same theoretical assumptions and limitations of Monin–Obukhov similarity theory in the surface layer, the proposed function has the flexibility of adjusting the wind and temperature gradients for specific sites using the empirical coefficients a and b within the range 0–1, with stable and unstable conditions able to be described by a single general function.

中文翻译：

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表层广义无量纲风温梯度

我们基于 Monin-Obukhov 相似理论提出了稳定和不稳定条件下无量纲风和温度梯度的单一广义函数。所提出的函数可以与目前公认的无量纲风速和温度梯度通用函数相匹配，使用经验系数 a 和 b，在 $$-2$ 区间内产生±14% 的风和温度梯度差异$ - 2 < z / L < 0.5（z 是高度，L 是奥布霍夫长度）。在中性条件下，风和温度曲线与标准对数定律曲线相同。在不稳定条件下，差异小于1.5%；相反，在稳定条件下，差异可达 $$-~5.2$$ - 5.2 %。这里分析了系数 a 和 b，以评估该提议的半经验函数的限制，并讨论了可能的物理特性。尽管我们在表层使用了与 Monin-Obukhov 相似理论相同的理论假设和局限性，但所提出的函数具有使用经验系数 a 和 b 在 0-1 范围内调整特定地点的风和温度梯度的灵活性，稳定和不稳定的条件可以用一个单一的一般函数来描述。