Directional Waves in the Nearshore Coastal Region of Perth ...

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Directional waves in the nearshore coastal region of Perth, Western AustraliaHuey Jean Tanη – elevation of the water surface, " = cos( kx # ! t)h – water depthH2Figure 2.2: The wave parameters of a two-dimensional simple progressive wave propagating in thepositive x-direction (after USACE 2002)2.2.2 Irregular WavesThe ocean surface is often a combination of several wave components that were individuallygenerated by wind in different regions and have travelled to the observation point. Hence realwave systems would be irregular and random, and successive waves may have differingperiods and heights (Figure 2.3). Therefore, statistical and probabilistic methods have to beutilised to describe the natural time-dependent three-dimensional characteristics of real wavesystems (USACE 2002). There are two methods for treating irregular waves: wave-by-waveanalysis (time domain) and spectral analysis (frequency domain)Literature Review 7
Directional waves in the nearshore coastal region of Perth, Western AustraliaHuey Jean TanFigure 2.3: Wave parameters for an irregular and random sea state (USACE 2002)Wave-by-wave AnalysisThe wave-by-wave (or wave train) analysis determines wave properties by obtaining theaverage statistical quantities of heights and periods of individual wave components (USACE2002). The undulations of the water surface from the mean water level are manually identifiedas individual wave using the zero-downcrossing method to obtain representative waveparameters, and using this information, statistical characteristics of the wave record can beestimated and statistics of the record are compiled (USACE 2002). Wave height is the verticaldistance between the highest and lowest points between two successive zero-downcrossing(i.e. crossing the zero line on a negative gradient) points; wave period is horizontal distance(see Figure 2.3). All the local maxima and minima not crossing the zero-line is discarded.This time-domain method requires direct measurements of sea surface, and the wave recordsmust be sufficiently large to obtain reliable statistics. The primary disadvantage to the waveby-waveanalysis is that it does not give an indication about the direction of the waves;therefore a single wave at a point may actually be the local superposition of two smallerintersecting waves from different directions (USACE 2002).Spectral AnalysisSpectral analysis utilises Fourier theory to transform the irregular ocean surface into asummation of simple sine waves, and wave characteristics are defined in terms of itsspectrum. The wave spectrum denotes which frequencies have significant energy content. Thesurface elevation time series in both Figure 2.4 and Figure 2.5compares the spectra of regularand irregular waves. In contrast to the wave-by-wave analysis which attempts to defineindividual waves, the spectral method attempts to describe the distribution of the surfacevariation from the mean level with respect to the frequency of the signal (USACE 2002).8 Literature Review
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Directional Waves in the Nearshore Coastal Region of Perth ...

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