Fractals and Nonlinearity of Ocean Waves

Authors

  • Harman Ajiwibowo Faculty at Ocean Engineering Program, Department of Civil Engineering, Bandung Institute of Technology (ITB).

DOI:

https://doi.org/10.5614/jts.2003.10.3.2

Keywords:

Fractals, nonlinear, Waves, Rescaled range analysis, Benoit, Fractal dimension, Nonlinearity Parameter, Skewness.

Abstract

Abstract. From observations using secondary field data and dimension calculations, ocean waves exhibit fractals. Fractals are also hypothesized to have a direct relation with the degree of the waves nonlinearity. We took
secondary data of 40 time series of wave record taken from Grays Harbor Wave Refraction Experiment, Washington in 1999. The data are divided into two groups, one group being data taken from the water depth of 25 meters and second group being data taken from water depth of 12 meters. The selection of data is in such a way that the second group is the waves traveling from the first group. We use rescaled range analysis to calculate the fractal dimension of the waves and Goda nonlinearity parameter as a measure of the waves nonlinearity. From the results, we confirm that fractals are a function of waves nonlinearity.

Abstrak. Dari data sekunder dan perhitungan dimensi, gelombang laut mempunyai karakteristik fraktal. Bentuk fractal dari gelombang laut diasumsikan mempunyai hubungan langsung dengan ketidaklinearan dari gelombang laut. Untuk pembuktian asumsi ini diambil data pengamatan 40 data seri waktu yang diambil dari eksperimen refraksi di Grays Harbor, Washington tahun 1999. Data ini dibagi menjadi 2 grup, grup pertama adalah data yang diambil di perairan dengan kedalaman 25 meter dan grup kedua diambil dari data yang diambil di perairan dengan kedalaman 12 meter. Pengambilan data di grup kedua adalah sedemikan rupa sehingga data ini adalah berasal dari gelombang yang berjalan dari data grup pertama. Setelah dilakukan perhitungan dimensi kurva dengan menggunakan Analisa Rescaled Range dan mengambil parameter Goda sebagai ukuran ketidaklinearan gelombang laut, didapati bahwa bentuk fraktal gelombang laut berhubungan langsung dengan ketidaklinearan gelombang.

References

Benoit Fractal Analysis System, 2000, Trusoft International Inc., St. Petersburg, FL.

Gelfenbaum, et.al., 1999, "Grays Harbor Wave Refraction Experiment: Data Report" , U.S. Geological Survey and U.S. Department of Interior, WA.

Goda, Y., 1985, "Random Seas and Design of Maritime Structures" , University of Tokyo Press, Tokyo, Japan.

Hurst, H.E , 1965, "Long Term Storage: An Experimental Study" . Constable, London.

Mandelbrot, B.B., 1983, "The Fractal Geometry of Nature" . W.H. Freeman and Company, New York, 468 p.

Munzenmayer, Katja, 1993, "The Fractal Structure of Surface Water Waves Near Breaking" , Master Thesis, Department of Mathematics,

Oregon State University, Corvallis, OR.

Vanouplines, P., 1995, "Rescaled Range Analysis and The Fractal Dimension of Pi" , University Library, Free University Brussels, Belgium..

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Published

2010-09-01

How to Cite

Ajiwibowo, H. (2010). Fractals and Nonlinearity of Ocean Waves. Jurnal Teknik Sipil, 10(3), 93-98. https://doi.org/10.5614/jts.2003.10.3.2

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Articles