论文标题
雨滴大小分布的随机理论
Stochastic Theory of the Size Distribution of Raindrops
论文作者
论文摘要
一个多世纪以来，雨滴大小分布一直是广泛的科学研究的主题，通常由包括Marshall-Palmer指数方程，伽玛，Weibull，Log-Normal和其他数学功能在内的模型描述。在这项工作中，我们提出了一种理论，该理论将热力学和流体动力学的确定性原理与随机元素相结合，以预测预期的雨滴直径并描述地面水平的跌落尺寸分布。重要的是，我们的方法避免假设特定的滴度分散过程或依靠多变量的经验数据拟合。我们得出了关键雨滴参数（例如中位直径，预期最小直径和最大直径）的分析方程，并作为降雨强度的功能。我们的理论预测与广泛的已发表的实验数据息息相关，涵盖了各种全球位置的降雨强度从0.4至40 mm/h。此外，与对超大雨滴的观察一致，我们的理论表明，最大的地面雨滴直径约为10 mm。我们为气象学参数（例如Marshall-Palmer常数和总雨滴浓度）建立了分析表达式，并根据经验数据进行了验证。这里提出的理论方法可以在气候建模，喷雾和气雾剂动力学，气泡和颗粒，外星降雨和古气候学中找到广泛的应用。
For over a century, raindrop size distributions have been a subject of extensive scientific study, typically described by models including the Marshall-Palmer exponential equation, gamma, Weibull, lognormal, and other mathematical functions. In this work, we present a theory that integrates deterministic principles from thermodynamics and fluid dynamics with stochastic elements to predict expected raindrop diameters and describe ground-level drop-size distributions. Importantly, our approach avoids assuming specific drop-size dispersion processes or relying on multi-variable empirical data fitting. We derive analytical equations for key raindrop parameters (e.g., median diameter, expected minimum and maximum diameters) and drop-size distributions as functions of rainfall intensity. Our theoretical predictions align well with extensive published experimental data, covering rainfall intensities from 0.4 to 40 mm/h across diverse global locations. Additionally, consistent with observations of super-large raindrops, our theory suggests a maximum ground-level raindrop diameter limit of around 10 mm. We establish analytical expressions for meteorological parameters like the Marshall-Palmer constant and total raindrop concentration, validated against empirical data. The theoretical approach presented here can find broad applications in climate modeling, sprays and aerosol dynamics, bubbles and particles, extraterrestrial rainfall, and paleoclimatology.
