APPENDIX A: LINEAR ARRAYS - THEORY AND APPLICATION 

 Introduction 



1. This section is intended to provide the reader and/or potential user 

 of the Field Research Facility (FRF) linear array y?ith a fundamental under- 

 standing of linear array theory and its application to wind wave directional 

 estimation. The appendix will discuss: (a) bottom-mounted pressure sensors 

 and their limitations, (b) directional information contained in arrays of 

 pressure sensors, and (c) problems in directional resolution and aliasing. 



Wave Information from Bottom-Mounted Pressure Sensors 



2. Bottom-mounted pressure sensors measure fluctuations about hydro- 

 static pressure caused by passing surface waves. These fluctuations can be 

 translated to surface elevation using linear wave theory, which indicates how 

 wave -induced pressure fluctuations are attenuated with depth. When a sensor 

 is at a depth of half the wavelength of a surface wave, pressure fluctuations 

 from that wave are so small as to be imperceptible to many pressure sensors. 

 Therefore, the shorter the wavelength (the higher the wind wave frequency), 

 the greater is the pressure attenuation with depth. Since a pressure sensor 

 detects each wave frequency in a composite sea differently, there is no simple 

 equivalence between time series of elevation and pressure. Pressure fluctua- 

 tions caused by each frequency component of a wind wave field will require a 

 specific surface correction to extract the surface elevation amplitude. 



3. Two important points are to be learned from this: (a) if the 

 sensors are placed too deep, high-frequency, small -wavelength wind waves will 

 be filtered out (fluctuations will be too small to be detected at the bottom) ; 

 and (b) if the interest is not in the bottom pressure field but in surface 

 elevations, a pressure time series must be decomposed into its Fourier 

 coefficients and the coefficients surface corrected to obtain the elevation 

 amplitude for each frequency of wind wave. 



4. For this discussion, surface elevation information will be con- 

 sidered in terms of its complex Fourier coefficients (one pair of coefficients 

 for each frequency) . The frequency variance spectrum (proportional to and 



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