The fractal structure of surface water waves near breaking Public Deposited

http://ir.library.oregonstate.edu/concern/graduate_thesis_or_dissertations/9c67wq994

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  • The goal of this research project is to determine the fractal nature, if any, which certain surface water waves exhibit when viewed on a microscopic scale. We make use of the mathematical formulation of non-viscous fluids describing their physical properties. Using these expressions and including boundary conditions for free surfaces as well as taking the surface tension into consideration, we obtain a partial differential equation describing the dynamics of surface water waves. A brief introduction to the study of fractal geometry with several examples of well-known fractals is included. An important property of fractals is their non-integral dimension. Several methods of determining the dimension of a curve are described in this paper. Our wave equation is examined under different assumptions representing the conditions of a surface water wave near its breaking point. Solutions are developed using analytical and numerical methods. We determine the dimension of 'rough' solutions using one of the methods introduced and conclude that under certain conditions, surface water waves near their breaking point exhibit a fractal structure on a microscopic scale.
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  • File scanned at 300 ppi (Monochrome, 24-bit Color) using Capture Perfect 3.0.82 on a Canon DR-9080C in PDF format. CVista PdfCompressor 4.0 was used for pdf compression and textual OCR.
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  • description.provenance : Submitted by Kevin Martin (martikev@onid.orst.edu) on 2012-12-13T21:59:14Z No. of bitstreams: 1 MünzenmayerKatja1994.pdf: 4581983 bytes, checksum: 00183460c7c8c2dc97a5081aab1ca8a9 (MD5)
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  • description.provenance : Approved for entry into archive by Patricia Black(patricia.black@oregonstate.edu) on 2012-12-13T22:05:18Z (GMT) No. of bitstreams: 1 MünzenmayerKatja1994.pdf: 4581983 bytes, checksum: 00183460c7c8c2dc97a5081aab1ca8a9 (MD5)
  • description.provenance : Approved for entry into archive by Patricia Black(patricia.black@oregonstate.edu) on 2012-12-13T22:42:37Z (GMT) No. of bitstreams: 1 MünzenmayerKatja1994.pdf: 4581983 bytes, checksum: 00183460c7c8c2dc97a5081aab1ca8a9 (MD5)

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