Chaotic Phenomena of Strong Shock Waves in a Bubbly Liquid

Research Project

Project/Area Number	07650207
Research Category	Grant-in-Aid for Scientific Research (C)
Allocation Type	Single-year Grants
Section	一般
Research Field	Fluid engineering
Research Institution	Osaka University
Principal Investigator	YOSHINAGA Takao Osaka University, Faculty of Engineering Science, Associate Professor, 基礎工学部, 助教授 (40158481)
Project Period (FY)	1995 – 1996
Project Status	Completed (Fiscal Year 1996)
Budget Amount *help	¥1,600,000 (Direct Cost: ¥1,600,000) Fiscal Year 1996: ¥1,000,000 (Direct Cost: ¥1,000,000) Fiscal Year 1995: ¥600,000 (Direct Cost: ¥600,000)
Keywords	shock wave / bubbly liquid / dispersive wave / chaos / nonlinear / フーリエ変換 / ウェーブレット変換 / フラクタル
Research Abstract	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.