Abstract

A set of nonlinear differential equations describing the parameters during the rise of a thermal (its velocity, radius, and excess temperature) as a function of height and time is numerically solved. It is found that the rise velocity varies nonmonotonically: it increases rapidly at first and its increase rate decreases with the increasing drag of the incoming air; for a long time (tens to thousands of seconds), this velocity remains close to the maximum (approximately 10…180 m/s), and then it decreases relatively slowly (for hundreds to thousands of seconds) to zero. It is shown that the more the thermal is heated and the larger its size, the faster it rises and reaches higher altitudes for a longer time. During the rise, the radius of the thermal increases by a factor of 6…25 depending on its initial size and initial temperature due to the entrained cold air. The greater the current radius value, the higher the increase rate of the thermal radius. The size of a small thermal increases by more times than that of a big thermal. The thermal radius increases until it is completely stopped. Less heated thermals rise more slowly, entrain smaller amounts of cold air, and increase less in size. It is shown that the cooling rate is proportional to the thermal rise velocity and is maximum when the maximum value of this velocity is reached. The warmer thermal cools more rapidly than the less heated one. The thermal cooling rate depends relatively weakly on its initial size. The limitations of the used model (the uniformity and isothermality of the atmosphere and neglect of the effect of thermal radiation, wind, and turbulence on the thermal cooling) are discussed. Despite the limitations, in general, the model is confirmed by the results of observations of the rise of the thermal generated during the explosion of the Chelyabinsk meteoroid.

中文翻译：

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地球大气中类星体热的上升

摘要

数值求解了一组非线性的微分方程，这些方程描述了随着温度和高度的变化而在热量上升过程中的参数（其速度，半径和过高温度）。发现上升速度是非单调变化的：它起初迅速增加，其增加率随着进入空气阻力的增加而减小；在很长一段时间（几万到几千秒）中，该速度保持接近最大值（大约10…180 m / s），然后相对缓慢地降低（几百到几千秒）至零。结果表明，热量被加热得越多，热量就越大，上升越快，到达更高海拔的时间就越长。在上升期间 由于夹带的冷空气，热的半径根据其初始大小和初始温度增加了6…25倍。当前半径值越大，热半径的增加率越高。小热量的大小比大热量的大小增加了更多倍。热半径增加，直到完全停止。较少的加热热量上升较慢，夹带较少的冷空气，并且尺寸增加较小。结果表明，冷却速度与热上升速度成正比，并且在达到该速度的最大值时达到最大。较热的热量比不热的热量更快地冷却。热冷却速率相对较弱地取决于其初始尺寸。讨论了所用模型的局限性（大气的均匀性和等温性，以及忽略了热辐射，风和湍流对热冷却的影响）。尽管有局限性，但总体而言，该模型已通过车里雅宾斯克流星体爆炸过程中产生的热量上升的观测结果得到证实。