Preliminary Results of Some 

 Stereophotographic Sorties Flown Over 

 the Sea Surface 



L. H. HOLTHUIJSEN 



Delft University of Technology 



The Netherlands 



SYNOPSIS 



Preliminary results are presented of a study which 

 is concerned with the directional characteristics 

 of wind generated waves. The basic approach adopted 

 was to measure the actual sea surface elevation as a 

 function of horizontal coordinates by means of stereo- 

 photogrammetric techniques. The surface representa- 

 tions thus obtained were Fourier transformed to 

 estimate two-dimensional wave number spectra. 



Basic considerations concerning the photogram- 

 metrical process, the transformation rules and the 

 statistical significance of the results are described. 

 The required stereo photographs were obtained during 

 photographic missions carried out in 1973 and 1976 

 off the island of Sylt (Germany) and off the coast 

 of Holland. So far three two-dimensional spectra, 

 each from a different flight, have been calculated. 

 The sea and weather conditions during these flights 

 are briefly stated. The wind direction in these 

 flights was off-shore. 



Frequency spectra computed from the observed wave 

 number spectra are compared with an assumed frequency 

 spectrum and an observed frequency spectrum. The 

 agreement is reasonable but some discrepancy needs 

 to be resolved. For two of the three observations 

 the directional distribution of the wave energy is 

 strongly asymmetrical around the wind direction. 

 This asymmetry seems to correspond to asymmetry in 

 the up-wind coast line. 



From the observed spectra a directional spreading 

 parameter has been computed as a function of wave 

 number. The results in normalized form agree well 

 with published data. The absolute values of the 

 spreading parameter for two spectra are within 30% 

 of the anticipated values. For the third spectrum 

 the values were almost five times too large but a 

 comparison in this case may not be proper. In one 

 of the spectra some indications of bi-modality around 

 the wind direction have been observed in the direc- 

 tional distribution function near the peak of the 

 spectrum. 



1 . INTRODUCTION 



Observations of the two-dimensional spectrum of wind 

 generated waves are relatively few and are mostly 

 based on methods with rather poor directional resolu- 

 tion. The techniques which are used for the observa- 

 tions may be based on such systems as a sparse wave 

 gauge array [e.g., Panicker and Borgman (1970)] or a 

 buoy capable of detecting directional characteristics 

 of the sea surface [e.g., Longuet-Higgins et al . 

 (1963) ] . The few detailed observations which have 

 been published were based on other techniques such 

 as high-frequency radio-wave backscatter [e.g., 

 Tyler et al . (1974)], analysis of the sea surface 

 brightness [e.g., Stilwell (1969), Sugimori (1975)] 

 or stereophotography [e.g.. Cote et al. (I960)]. 

 These provided information with a high directional 

 resolution but the analysis of the results in terms 

 of wave characteristics has not been very extensive. 



The Delft University of Technology and the Min- 

 istry of Piiblic Works in the Netherlands have devel- 

 oped a system based on stereophotography which 

 monitors the instantaneous sea surface elevation as 

 a function of horizontal coordinates. It has been 

 used in this and other studies and it is anticipated 

 that it will also be used in future studies of wave 

 phenomena such as wave transformation in the surf 

 zone or wave patterns around marine structures. The 

 present study, which is a joint effort of the Uni- 

 versity and the Ministry, is aimed at observing and 

 interpreting two-dimensional spectra of wind gener- 

 ated waves in a variety of atmospheric conditions. 

 The study is primarily directed towards the evalu- 

 ation of the shape characteristics of the directional 

 energy distribution of the waves. 



For this study a few hundred stereo pictures have 

 been taken since 1973 and the analysis has just be- 

 gun. The results reported here are preliminary in 

 that the number of analyzed pictures is only a frac- 

 tion of the total and in that the interpretation of 

 these pictures has not as yet been completed. The 

 spectra which are presented here were calculated 



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