Models of Frequency Spectra 



9. The potential number of frequency spectrum shapes is infinite even 

 within the confines of the simple linear wave theory used to describe a wave 

 field. Fortunately, nature behaves in such a way that the most common shapes 

 of interest can be represented by a rather small class of mathematical func- 

 tions. These functions are called models of ocean wave frequency spectra. 

 Several models have evolved following physical arguments and observations by 

 various investigators. 



10. One of the most consistent models for high-frequency wind waves was 

 derived by Phillips (1958). An extension of this model by Pierson and 

 Moscowitz (1964) led to a model for fully developed wind seas in deep water. 

 Observations during the Joint North Sea Wave Project (JONSWAP) (Hasselmann at 

 al . 1973) enabled a further extension of the model for application to develop- 

 ing wind seas in deep water. Transformation of this model to shallow water by 

 Bouws , Gunther, and Vincent (1985) has led to what is known as the TMA (TEXEL, 

 MARSEN and ARSLOE) frequency spectrum. Both the JONSWAP and TMA spectral 

 models are being used by CERC for coastal engineering design studies (in the 

 form of physical models). In further developments along this line, the TMA 

 model has recently been modified by Miller and Vincent (1990) to account for 

 nonlinear wave -wave interactions in the middle frequencies as derived by 

 Kitaigorodskii (1983) . These models require only a few parameters (usually 

 six or fewer) to describe the whole frequency distribution of wind wave 

 energy. 



Importance of Directionally Distributed Wave Energy 



Heuristic approach 



11. Wave energy can be distributed in direction in the same sense that 

 it can be distributed in frequency. That is, at a given frequency, wave 

 energy can be coming from more than one direction. A simple way to visualize 

 this concept is to imagine looking seaward from a beach at two approaching 

 wave trains. The two wave trains have the same period, i.e. , the same fre- 

 quency. However, they are readily distinguishable because they approach the 

 observer from different angles so that the pattern of wave crests for each 

 wave train can be seen. If one train is coming from 45 deg to the observer's 



