Reply by the Authors to H. S. Ribner
Reply by the Authors to H. S. Ribner
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作者对 H.S. Ribner 的回复
作者：
S. Barre;D. Alem;J. Bonnet
Ribner对Barre等人关于紊流功率谱密度和激波波数的无量纲化的论文所作的评论，对我们来说是很有启发性的。这就是为什么我们将提出，在本答复中，与Ribner提出的数据简化方法所获得的结果。从Ribner的评论看来，也许紊流频率可以是很好的简化参数，因为速度乘以波数的乘积在激波固定的坐标系中保持了频率的不变性。假设这一点，我们就可以比较这两个谱与上游波数的关系。这在图1中完成。这个新的图可以取代原文的图15。我们可以看到现在的版本和以前的版本有很大的不同。然后，通过将绘制的波数除以穿过激波的平均流速比，使激波后谱左移。在新的版本中，震后谱的面积是震前谱面积的1.5倍。这个比值对应于穿过激波的纵向湍流能量放大。这与原始论文中的情况不同，其中两个光谱用相同的面积表示。考虑到放大率，这种表示也是Ribner的建议，它使我们能够立即可视化整个冲击的能量再分配的演变。图2（可以代替原始论文中的图16）表示了采用新的数据简化方法的图1中所示的两个光谱的比值。很明显，放大率低于初始版本。数据简化方法中的所有这些修改都不会改变本工作的结论。人们总是发现，小尺度比大尺度放大得更多。然后，我们得到的波数在1300 rRT的范围内的最大放大比为3.5。该波数值对应于震前纵向积分尺度波数的约4.5倍。正如Ribner在他的评论中所建议的那样，目前的实验结果与他的理论结果非常一致。10
T HE comments expressed by Ribner on the paper by Barre et al. * concerning the nondimensionalization of the turbulence power spectral densities and wave numbers across the shock were, for us, quite instructive. That is why we will present, in this Reply, the results obtained with the data reduction method proposed by Ribner. From Ribner's Comment it appears that perhaps the turbulence frequency can be the good reduction parameter because the product velocity times the wave number preserves the invariance of frequency in a shock-fixed frame. Assuming that, we can then compare the two spectra expressed vs the upstream wave number. This is done in Fig. 1. This new figure may replace Fig. 15 of the original paper. We can see a strong difference between the present and the previous version. The postshock spectra are then shifted left by dividing the plotted wave number by the mean flow velocity ratio across the shock. In the new version, the postshock spectra are represented with an area that is 1.5 times the preshock spectra area. This ratio corresponds to the longitudinal turbulent energy amplification across the shock. This was not the case in the original paper, where the two spectra were represented with the same area. This presentation, taking into account the amplification ratio, is also Ribner's suggestion, which allows us to immediately visualize the evolution of the energetic repartition across the shock. Figure 2 (which may replace Fig. 16 in the original paper) represents the ratio of the two spectra as they are presented in Fig. 1 with the new data reduction method. It is clear that the amplification rates are lower then in the initial version. All of these modifications in the data reduction method do not change the conclusions of this work. It is always found that the small scales are more amplified than the large one. We then obtain a maximum amplification ratio of 3.5 for wave numbers in the range of 1300 rrT. This wave number value corresponds to about 4.5 times the preshock longitudinal integral scale wave number. As Ribner suggested in his Comment, the present experimental results are now in quite good agreement with his theoretical results. 10