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首页> 外文期刊>Physica Scripta: An International Journal for Experimental and Theoretical Physics >Kinetic energy of the rotational flow behind an isolated rippled shock wave
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Kinetic energy of the rotational flow behind an isolated rippled shock wave

机译：孤立的波纹冲击波后面的旋转流动的动能

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摘要

The kinetic energy of the perturbation velocity field generated by a corrugated isolated shock is analyzed as a function of the shock Mach number (M-s) and the fluid compressibility (characterized here with the ideal gas ratio of specific heats.) within the framework of a linear theory. The shock front dynamics is analyzed, evaluating the zeros and critical points of the temporal evolution of the pressure perturbations behind the shock front. These characteristic times are essential in determining the spatial distribution of the velocity fluctuations in the inhomogeneously compressed fluid. The velocity perturbations are followed in time and space behind the corrugated shock front until an asymptotic stage emerges. Graf's addition theorem of the Bessel functions is seen to be an adequate mathematical tool with which to evaluate the detailed temporal evolution. The kinetic energy density is analyzed in time and space well into the asymptotic stage. Exact criteria are given, based on the properties of the asymptotic velocity field, in order to determine the critical points of the kinetic energy density. The space integral of the kinetic energy density is studied, and an explicit analytical formula can be written in finite form and in terms of known functions. The integrated kinetic energy (KE) is analyzed at the limits of very weak and very strong shocks. For very weak shocks the kinetic energy scales as KE similar to u(i)(2), where u(i) is the asymptotic normal velocity perturbation at the surface x = 0. For very strong fronts, the scaling changes to KE similar to u(i)(2) lnM(s). The logarithmic factor is due to contribution of the bulk vorticity profile, which becomes important at high compressions.
机译：被波纹化隔离冲击产生的扰动速度场的动能被分析为冲击马赫数（MS）和流体压缩性（这里以特定热的理想气体比表征为特定的热量。）。在线性的框架内理论。分析了冲击前动态，评估了震动前后压力扰动的时间演变的零和关键点。这些特征时间对于确定不均匀压缩流体中的速度波动的空间分布至关重要。速度扰动跟随时间和瓦楞击震颤后面的空间，直到渐近阶段出现。 GRAF的Bessel功能的附加定理被认为是一种足够的数学工具，可以评估详细的时间演进。在时间和空间分析动能密度进入渐近阶段。基于渐近速度场的性质，给出了确切的标准，以确定动能密度的关键点。研究了动能密度的空间积分，并且可以以有限形式和已知功能编写明确的分析公式。在非常弱和非常强烈的冲击的极限下分析了集成的动能（KE）。对于非常弱的冲击，动能尺度与u（i）（2）相似，其中U（i）是表面x = 0的渐近正常速度扰动。对于非常强的前沿，将缩放变为ke类似于U（i）（2）LNM。对数因子是由于散装涡度曲线的贡献，这在高压缩中变得重要。

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