Investigation of the Rain Process Using Mathematical Models and Observational Data

题目：用数学模型和观测数据研究降雨过程这个项目将提高我们对雨滴生长和相互作用的方式的理解，从而产生范围广泛的雨滴大小。一些液滴之间的碰撞导致简单的合并并形成更大的液滴；另一些可能导致碰撞的液滴破裂，产生更小的卫星液滴。这个问题的数学公式需要了解不同大小的液滴的下落速度和碰撞截面、破裂的概率以及卫星液滴的大小分布。该项目的第一阶段将提供关于液滴破碎的稀疏现有实验室数据的分析近似。这对于推广描述碰撞-合并过程中液滴大小分布演变的方程以包括液滴破碎的影响是必不可少的。第二阶段将比较模式预测与多普勒雷达在自然云中测量到的雨滴大小分布。如果预测结果与观测结果一致，将支持在不同环境条件下对降雨发展的理论计算中使用该模式。

AbstractATM-9812085Brown, Philip S.Trinity CollegeTitle: Investigation of the Rain Process Using Mathematical Models and Observational DataThis project will improve our understanding of the way raindrops grow and interact with each other to produce a broad range of drop sizes. Some collisions between drops lead to simple coalescence and the formation of a larger drop; others may cause breakup of the colliding drops and the production of smaller, satellite droplets. A mathematical formulation of this problem requires knowledge of the fall speeds and collision cross sections of drops of different sizes, the probability of breakup, and the size distribution of the satellite droplets. The first phase of the project will provide analytical approximations to the sparse existing laboratory data on drop breakup. This is essential for generalizing the equations that describe the evolution of the drop-size distribution by the collision-coalescence process to include the effects of drop breakup. The second phase will compare model predictions with the drop-size distributions measured by Doppler radar in natural clouds. If the predictions agree with observations it will support the use of the model in theoretical calculations of rain development under different environmental conditions.