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The equations of motion for moist atmospheric air

机译:潮湿大气的运动方程

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摘要

How phase transitions affect the motion of moist atmospheric air remains controversial. In the early 2000s two distinct differential equations of motion were proposed. Besides their contrasting formulations for the acceleration of condensate, the equations differ concerning the presence/absence of a term equal to the rate of phase transitions multiplied by the difference in velocity between condensate and air. This term was interpreted in the literature as the "reactive motion" associated with condensation. The reasoning behind this reactive motion was that when water vapor condenses and droplets begin to fall the remaining gas must move upward to conserve momentum. Here we show that the two contrasting formulations imply distinct assumptions about how gaseous air and condensate particles interact. We show that these assumptions cannot be simultaneously applicable to condensation and evaporation. Reactive motion leading to an upward acceleration of air during condensation does not exist. The reactive motion term can be justified for evaporation only; it describes the downward acceleration of air. We emphasize the difference between the equations of motion (i.e., equations constraining velocity) and those constraining momentum (i.e., equations of motion and continuity combined). We show that owing to the imprecise nature of the continuity equations, consideration of total momentum can be misleading and that this led to the reactive motion controversy. Finally, we provide a revised and generally applicable equation for the motion of moist air.
机译:相变如何影响潮湿大气的运动仍然存在争议。在 2000 年代初期,提出了两种不同的微分运动方程。除了冷凝水加速度的对比公式外,这些方程在项的存在/不存在方面有所不同,项等于相变速率乘以冷凝水和空气之间的速度差。该术语在文献中被解释为与冷凝相关的“反应性运动”。这种反应运动背后的原因是,当水蒸气凝结并且液滴开始下降时,剩余的气体必须向上移动以保持动量。在这里,我们表明,这两个对比鲜明的公式暗示了关于气态空气和冷凝水颗粒如何相互作用的不同假设。我们表明,这些假设不能同时适用于冷凝和蒸发。在冷凝过程中导致空气向上加速的反作用运动不存在。反作用运动项只能用于蒸发;它描述了空气的向下加速度。我们强调运动方程(即约束速度的方程)和约束动量方程(即运动和连续性方程的组合)之间的区别。我们表明,由于连续性方程的不精确性,对总动量的考虑可能会产生误导,这导致了反应运动的争议。最后,我们提供了一个修正的、普遍适用的湿空气运动方程。

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