The fractal dimension of measured ocean wave profiles is found to be in the
range of 1.5-1.8. This non-integer dimension indicates the fractal nature of the
waves. Standard formulations to analyze waves are based on a differential
approach. Since fractals are non-differentiable, this formulation fails for waves with
fractal characteristics. Integral solutions for long waves that are valid for a non-differentiable
fractal surfaces are developed. Field observations show a positive
correlation between the fractal dimension and the degree of nonlinearity of the
waves, wave steepness, and breaking waves. Solutions are developed for a variety
of linear cases. As waves propagate shoreward and become more nonlinear, the
fractal dimension increases. The linear solutions are unable to reproduce the change
in fractal dimension evident in the ocean data. However, the linear solutions do
demonstrate a finite speed of propagation.
The correlation of the fractal dimension with the nonlinearity of the waves
suggests using a nonlinear wave equation. We first confirm the nonlinear behavior
of the waves using the finite difference method with continuous function as the
initial condition. Next, we solve the system using a Runge-Kutta method to
integrate the characteristics of the nonlinear wave equation. For small times, the
finite difference and Runge-Kutta solutions are similar. At longer times, however,
the Runge-Kutta solution shows the leading edge of the wave extending beyond the
base of the wave corresponding to over-steepening and breaking.
A simple long wave solution on multi-step bottom is developed in order to
calculate the reflection coefficient for a sloping beach. Multiple reflections and
transmissions are allowed at each step, and the resulting reflection coefficient is
calculated. The reflection coefficient is also calculated for model with thousands of
small steps where the waves are reflected and transmitted once over each step. The
effect of depth-limited breaking waves is also considered. / Graduation date: 2003
| Identifer | oai:union.ndltd.org:ORGSU/oai:ir.library.oregonstate.edu:1957/30149 |
| Date | 13 September 2002 |
| Creators | Ajiwibowo, Harman |
| Contributors | McDougal, William G. |
| Source Sets | Oregon State University |
| Language | en_US |
| Detected Language | English |
| Type | Thesis/Dissertation |
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