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 two kinds 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.
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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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