论文标题
超音速湍流中密度的有限冲击模型
Finite shock model of density in supersonic turbulence
论文作者
论文摘要
等温，超音速，湍流气体中密度的概率分布大约是对数正常的。这种行为可以追溯到穿过介质的冲击波，该冲击波通过局部声音马赫数平方的随机系数随机调节密度。只要由于中心极限定理，一定的气体经历了大量的冲击，其密度分布是对数正态的。我们探索了一个模型，其中包裹在放松到环境密度之前会经历有限数量的冲击，从而导致密度分布与对数正态的偏离。我们使用各种R.M.马赫数范围从低至0.1到25时超音速。我们发现，有限公式的拟合比对数正态的数量级好。该模型自然延伸到不存在冲击的亚音速流。
The probability distribution of density in isothermal, supersonic, turbulent gas is approximately lognormal. This behaviour can be traced back to the shock waves travelling through the medium, which randomly adjust the density by a random factor of the local sonic Mach number squared. Provided a certain parcel of gas experiences a large number of shocks, due to the central limit theorem, the resulting distribution for density is lognormal. We explore a model in which parcels of gas undergo finite number of shocks before relaxing to the ambient density, causing the distribution for density to deviate from a lognormal. We confront this model with numerical simulations with various r.m.s. Mach numbers ranging from subsonic as low as 0.1 to supersonic at 25. We find that the fits to the finite formula are an order of magnitude better than a lognormal. The model naturally extends even to subsonic flows, where no shocks exist.
