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Chaotic Phenomena of Strong Shock Waves in a Bubbly Liquid

气泡液体中强冲击波的混沌现象

基本信息

批准号：
07650207
负责人：
YOSHINAGA Takao
金额：
$ 1.02万
依托单位：
Osaka University
依托单位国家：
日本
项目类别：
Grant-in-Aid for Scientific Research (C)
财政年份：
1995
资助国家：
日本
起止时间：
1995 至 1996
项目状态：
已结题

项目摘要

It is known that shock waves in a bubbly liquid are followed by oscillatory wave trains behind the shock front. This study shows that irregular wave behavior of such wave trains is chaotic phenomena when the shock wave is strong.The following two kinds of analyzes are made to the irregular wave profiles which have been observed through the experiments using the vertical shock tube filled with a bubbly liquid :(a) In a 3-dimensional phase space which consists of the pressure and its first and second order time derivatives, the separation distance is examined between two nearby trajectories which are measured in the different two positions on the shock tube.(b) Using the Fourier and Wavelet Transformations, spectral distributions of the pressure wave profiles is examined.From the first analysis, it is found that the distance between initially nearby trajectories increases exponentially for strong shock waves, where the effect of inhomogeneous distribution of bubbles on the irregular behavior is considered to be sufficiently small. On the other hand, in the second analysis, the Fourier transformation shows that, when the shock waves become strong, waves consist of frequency components with an incomensurate ratio to the main frequency as well as higher harmonics. In addition to this, through the Wavelet transformation, characteristic properties of the self-similarity are found in the temporal-frequency distribution in the transform coefficients.Resulting from this, it is highly expected for the strong shock waves that the irregular wave behavior is chaotic phenomena on which the nonlinearity plays an important role.

众所周知，气泡液体中的冲击波在冲击波阵面之后跟随有振荡波列。研究表明，当冲击波较强时，这种波列的不规则波行为是混沌现象。对用充满气泡液体的垂直激波管实验观察到的不规则波剖面作了以下两种分析：（a）在由压力及其一阶和二阶时间导数组成的三维相空间中，检查在激波管上不同两个位置测量的两个附近轨迹之间的间隔距离。(b)利用傅立叶变换和小波变换，分析了压力波的谱分布，发现对于强激波，初始附近的轨迹之间的距离呈指数增长，气泡的不均匀分布对不规则行为的影响被认为是足够小的。另一方面，在第二次分析中，傅立叶变换表明，当冲击波变强时，波由与主频率以及高次谐波具有不相称比率的频率分量组成。此外，通过小波变换，发现了变换系数的时频分布具有自相似性的特征，由此，强激波的不规则波行为是混沌现象，非线性在其中起着重要作用。