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. / Graduation date: 1994
| Identifer | oai:union.ndltd.org:ORGSU/oai:ir.library.oregonstate.edu:1957/35779 |
| Date | 27 July 1993 |
| Creators | M��nzenmayer, Katja |
| Contributors | Guenther, Ronald B. |
| Source Sets | Oregon State University |
| Language | en_US |
| Detected Language | English |
| Type | Thesis/Dissertation |
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