Models for Steep Ocean Irregular Waves and Their Applications
Chapter 1 INTRODUCTION
Ocean waves are often irregular and multi-directional. They are usually described by a superposition of many monochromatic wave components of different frequencies, amplitudes and directions. In the case of uni-directional wave, the wave components can be derived by applying Fast Fourier Transform (FFT) to measured wave records. When ocean waves are multi-directional and three or more wave records are available, directions of waves can be resolved approximately based on wave components of these wave records. Because of nonlinear nature of surface gravity waves, wave components derived from the FFT in general consist of twokinds of wave components: free-wave and bound-wave components
The basic wave components are known as free-wave (or linear) components, whose wavelength and period obey the dispersion relation. They are dominant in entire frequency domain when ocean waves are not very steep. When ocean waves are very steep, they are still dominant near the (spectral) peak wave frequency.
Owing to the nonlinear free-surface boundary conditions, free waves interact among them. The interactions can be classified into ``strong'' and ``weak'' wave-wave interactions. Strong interactions are observable soon after free waves start to interact, while weak interactions become substantial only after hundreds of wave periods (Su & Green 1981, Phillips 1979). Weak interactions, also known as resonance wave interactions, may occur when the frequencies and wavelengths of wave components satisfy the resonance conditions. The resonance interactions result in energy transfer among free waves of different frequencies (Phillips 1960, Hasselmann 1962). Nonlinear energy transform among free waves are crucial to the wave energy growth and distribution over the frequency domain in the air-sea interactions (Komen et al. 1994). Owing to their importance to the long-term evolution of wave spectra, so far the overwhelming majority of studies on nonlinear wave dynamics have focused on the resonance wave interactions.
The bound-wave (also known as force-wave) components result from the strong interactions among free waves. Hence, the former is a ‘parasite’ relying on the latter. The fundamental difference between the two is that the wavelength and period of a bound wave do not obey the dispersion relation while those of a free wave do. When ocean waves are not very steep, bound waves usually are insignificant in comparison with free waves. However, when ocean waves are steep, in the frequency ranges either far below or well above the spectral peak frequency, bound waves are comparable to or even greater than the corresponding free waves.
Although the bound waves are observable immediately after the interactions among free waves start, they disappear after the interacting free waves no longer overlap (Yuen & Lake 1982). In other words, the strong interactions do not result in long-lasting effects, as do the weak interactions in energy transfer among free waves. This probably is the reason why the former has not received enough attention as the latter. Nevertheless, the effects of strong interactions on resultant wave properties are crucial to many ocean engineering and scientific practices, such as wave measurements and structure-wave interactions, especially when waves are steep.
Current engineering practices use linear wave theory (LWT), in particular linear spectral methods to estimate irregular wave properties. In using a linear spectral method, nonlinear wave interactions are ignored in the decomposition of a measured wave field as well as in the calculation of wave properties. In short, bound waves are treated as free waves of the same frequency. When ocean waves are not steep, the free waves are dominant in almost the entire frequency range and a linear spectral method may be a simple and fairly good approximation. When ocean waves are steep, the free waves near the spectral peak frequency still remain dominant but the bound waves may become dominant or comparable to the free waves in the frequency ranges either much lower or higher than the peak frequency (Zhang et al. 1996). It is known that the relationship between the elevation and potential amplitudes of a free wave is quite different from that of a bound wave of the same frequency. The ignorance of bound waves in linear spectral methods may result in large discrepancies. For example, the predicted wave kinematics based on measured wave elevation and predicted wave elevation based on measured dynamic pressure using a linear spectral method, were found to be inaccurate (Tørum & Gudmestad 1989, Spell et al. 1996, Meza et al. 1999).
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