KNOWN AND UNKNOWN PROPERTIES OF 



THE TWO-DIMENSIONAL WAVE 



SPECTRUM AND ATTEMPTS TO 



FORECAST THE TWO-DIMENSIONAL 



WAVE SPECTRUM FOR THE *NORTH 



ATLANTIC OCEAN 



Willard J. Pierson, Jr. 



New York University 

 New York, New York 



ABSTRACT 



The two-dimensional wave spectrum has been estimated once by stereo 

 photogrammetric techniques, and a number of times by buoys developed 

 by the National Institute of Oceanography, The results obtained do not 

 contradict each other. Some questions have recently been resolved and 

 one remains unresolved. There do not appear to be spectral compo- 

 nents in a pure wind sea traveling in a direction opposed to the wind. 

 The theory relating wave number to frequency from linear considera- 

 tions can be applied. Whether or not the spectrum is bi-modal as a 

 function of direction for certain frequencies is not yet decided. A form 

 for the directional spectrum of a fully developed wind sea is proposed. 



Under certain assumptions about the generation of wind seas attempts 

 to forecast the two-dimensional spectrum at 519 points on the North 

 Atlantic have been made. Verification of the forecasts against ob- 

 served two-dimensional spectra are not possible. However, they verify 

 fairly well in terms of significant height and against the observed fre- 

 quency spectra and in terms of swell and wave decay. It appears that 

 the forecasting procedure is fairly close to being correct. 



INTRODUCTION 



Nearly all of the papers at this symposium are concerned with the deter- 

 ministic mathematics applicable to the analysis of the classical hydrodynamic 

 problems that are concerns of the naval hydrodynamicist. However, one of the 

 inputs to the problem of understanding the motions of marine craft at sea is 

 essentially probabilistic in nature. The actual sequence of waves that will be 

 met on a given cruise can never be predicted before the fact. To predict certain 



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