Application of Chaos Theory to Ocean Wave Analysis

• Main Authors: Suen, Dar-Sheng, 孫達生
• Other Authors: Kao Chiao-Chuen, Laurence S.H. Chung
• Format: Others
• Language: zh-TW
• Published: 1998
• Online Access: http://ndltd.ncl.edu.tw/handle/03731110862971228511

碩士 === 國立成功大學 === 水利及海洋工程學系 === 86 === Chaos theory is increasingly used both to classify a system and as an aid tomodeling. Also, on applying chaos theory to random process analysis has becomea tool for better understanding of signals. This study is trying to combine the time-delay embedding method (TDEM) with the correlation dimension method (CDM) to investigate the chaotic behavior of simulated wave signals and fieldobserved wave data. The comparison of chaotic properties between collected field data and simulated data shows the deficiency in the assumption that ran-dom wave profiles are the result of linear superposition of infinite number ofinfinitesimal wavelets with various frequencies. Some simple signals, which is composed of linearly regular waves,were chosento examine the criteria of computation and to realize its physical meanings onapplying the tools of TDEMand CDM. To investigate whether the time series is chaotic, a set of m-dimensional vectors should be reconstructed from the orig-inal time series and then its trajectory is examined using the correlation integral method. As expected, it is impossible to define a straight line of slope in the correlation integral plot. That is, there is no possibility thatthe time series generated by linearly regular waves are chaotic. The questionis raised now. Since the random waves are often represented by some spectral forms, do these representation still inherit chaotic characteristics? Unfortu-nately, no matter how many wave components are considered, which consist of 2,3 or up to 128 components of the JONSWAP form, the simulated wave series are always not chaotic. A second question may be asked that does the noise affectthe chaotic properties in the wave data? Many sets of random noises were thengenerated and to be added to the simulated wave in order to investigate its chaoticity. It was shown that the noise itself is not chaotic, in addition, the simulated waves contaminated with noises are not chaotic, either. The second aim of the work is to justify observed wave signal as chaotic andto characterize its dynamics through the analysis of the correlation dimension.The results showed a highly chaotic behavior in both wave elevation and sign-ificant wave heights. Also, the strong dependence of correlation dimension D2on significant wave height may give us a rough information on calculating D2. If the relationship could be more justified, then the tedious estimation of correlation dimensions will be much simplified.