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 Tan3.2 DATA ANALYSISMajority of the data analysis in this study was carried out using MATLAB ® , a high level,vector-orientated, mathematical programming language developed by The MathWorks Inc.(Appendix B).A sequence of observations made through time may be described as a time series. The datacollected by the S4DW current meter in this study are therefore time series of currentvelocities measured at a fixed location. These time series are stochastic, discrete, uniformlysampled and of finite length. In this study, the time series data were processed using spectralanalysis. Spectral analysis can be used to decompose a time series into its constituentfrequency components, and different frequency bands can be isolated. In particular, thismethod allows the separation of the sea and swell components of the wave field. In this study,sea waves are defined as waves with periods between 2 s and 6.65 s (i.e. 0.15 < f < 0.5) andswell waves are defined as waves with periods between 6.65 s and 20 s (i.e. 0.05 < f < 0.15).The wave spectrum in Figure 3.2 demonstrates the frequency cut-offs for swell and seawaves; this particular wave spectrum shows that the wave field is dominated by sea waveenergy.In this study, the data records were transformed from the time domain to the frequencydomain via the Fast Fourier Transform (FFT). The application of the FFT requires that thenumber of data points in the series should be a power of 2. In addition to this, it is desirable touse a considerable length of data as this increases the accuracy of the conversion performedby the FFT. As mentioned in Section 3.1.2, there were 2160 data points recorded for every 18minute burst at City Beach and 2400 data recorded for every 20 minute burst at Cables ASR.The number of data analysed in the present study is 2048, which is the maximum power of 2value within the data record (N = 2048 = 2 11 ). This ensures optimum spectral resolution andminimum occurrence of error for the given data record. A set of wave parameters useful tothis study was extracted from each data burst (Table 3.2).Approach 27
Directional waves in the nearshore coastal region of Perth, Western AustraliaHuey Jean TanFigure 3.2: A wave spectral energy plot indicating the frequency cut-offs for the swell and seacomponents of the wave field.Table 3.2: Wave parameters extracted from the data in the frequency domainSymbol Description Method of Calculation Unitsm 0 Total variance (zeroth moment of spectral( f )dfdensity)! " mS20m 0,sea Variance of sea componentmS( f )df2m 0,swellH sH s,seaVariance of swell componentSignificant wave height estimateSignificant wave height of sea component! 0.50. 15! 0.15 S0. 05( f )dfm 24 m0m4 m 0,seamH s,swell Significant wave height of swell 4 m m0,swellcomponentT p Peak period. Wave period corresponding 1/f p sto the maximum spectral energy.T p,sea Peak period of the sea component 1/f p,sea sT p,swell Peak period of the swell component 1/f p,swell sNote: f p is the spectral peak frequency, the frequency at which the maximum spectral density occurs28 Approach
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Directional Waves in the Nearshore Coastal Region of Perth ...

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