相关碰撞和间歇性对幸运水滴增长的影响
Effects of correlated collisions and intermittency on the growth of lucky droplets
AI总结：
研究通过湍流模拟探讨相关碰撞和间歇性对幸运水滴增长的影响，发现相关碰撞加速初期增长，间歇性可缩短跨越大小间隙的时间。
摘要：
为了触发降水，暖云中的水滴需要达到足够的大小。仅基于凝结和重力碰撞的理论估计无法解释观测到的降水起始时间尺度，对于多种水滴大小范围而言。这表明需要由湍流介导的碰撞增长来解决所谓的'大小间隙问题'。对于降水起始而言，统计异常值，称为'幸运水滴'，只需跨越大小间隙即可。在本研究中，我们探讨了湍流对水滴增长的影响，重点是相关碰撞和间歇性。利用湍流流动中水滴的直接数值模拟，我们建立了一个非马尔可夫随机框架，以评估由连续碰撞之间的相关性引起的水滴大小分布中的记忆效应。使用我们的框架，我们发现相关碰撞加速了幸运水滴的初始增长，但对后期阶段有次要影响。因此，我们忽略了碰撞中的相关性，并建模了一个云团集合，代表体积平均耗散率的波动。在此，每个云团中的水滴大小分布由一个具有时间依赖碰撞率的线性主方程描述，该碰撞率根据体积平均耗散率确定。我们对这个玩具模型的分析显示，间歇性可以显著减少幸运水滴跨越大小间隙所需的时间。
英文摘要：
To trigger precipitation, water droplets in warm clouds need to attain a sufficient size. Theoretical estimates based on condensation and gravitational collisions alone fail to explain the observed timescales for the onset of precipitation for a range of droplet sizes. This suggests the involvement of collisional growth mediated by turbulence to resolve the so-called ``size-gap problem''. For the onset of rain, it is sufficient that statistical outliers, coined ``lucky droplets'', cross the size gap. In this study, we explore the influence of turbulence on droplet growth, focusing on correlated collisions and intermittency. Using direct numerical simulations of droplets in turbulent flow, we constrain a non-Markovian stochastic framework that allows us to assess memory effects on the droplet-size distribution arising from correlations between consecutive collisions. Using our framework, we find that correlated collisions accelerate the initial growth of lucky droplets but have sub-leading effect at later stages. Consequently, we neglect correlations from collisions and model an ensemble of cloud parcels representing fluctuations in the volume-averaged dissipation rate. Here, the distribution of droplet sizes in each parcel is described by a linear master equation with a time-dependent collision rate according to the volume-averaged dissipation rate. Our analyses of this toy model show that intermittency can significantly reduce the time required by lucky droplets to cross the size gap.
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