A rich variety of scaling laws for the evolution of convective buoyant thermals generated by an explosive release of energy has been established. Such events may correspond to a blast, spark, or volcano eruption. It was found that an occurrence of a particular scaling law depends on the interplay of many factors, viz., (1) amount of energy released in the environment, (2) time since the release, and (3) spatial scale of the release domain. The analytical treatment involves solutions of coupled equations for mass, momentum and buoyancy (heat) conservation in the Boussinesq and non-Boussinesq approximation. A model for the entrainment flow that accounts for a strong thermal flux has been proposed. For the limiting case of a weak thermal and the Boussinesq approximation (low density contrast between the buoyant thermal and the ambient environment) the celebrated Batchelor, Morton, and Turner scalings are recovered. Results have been favorably compared with limited data available in the literature.

中文翻译：

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缩放定律可实现极强的散热

已经建立了多种因爆炸性释放能量而产生的对流浮力热演化的定标律。此类事件可能对应于爆炸，火花或火山喷发。已经发现，特定比例定律的发生取决于许多因素的相互作用，即。，（1）在环境中释放的能量，（2）释放以来的时间和（3）释放域的空间尺度。分析处理涉及在Boussinesq和非Bousinesq近似中的质量，动量和浮力（热）守恒耦合方程的解。已经提出了考虑强热通量的夹带流模型。对于弱热和Boussinesq近似（浮力热与周围环境之间的低密度对比）的极限情况，恢复了著名的Batchelor，Morton和Turner缩放比例。将结果与文献中有限的数据进行了有利的比较。