Generation, Growth and Propagation of Waves 97 



cording to Schott, c = 0-76(7, that is, the wave velocity is less than the wind 

 velocity. According to the newer theory, it is perfectly possible that c > U. 

 Observations from the trade wind region, where the wind blows over large 

 areas with great uniformity and moderate velocity, show clearly that wave 

 velocities may exceed wind velocities in the generating area. Table 12 by 

 Sverdrup and Munk is a compilation of wave characteristics in tradewind 

 regions and is highly instructive. 



6. Growing of Spectral Components of the Wind-Generated Sea 



The introduction of the wave spectrum in studying the characteristics 

 of the wind-generated sea led to the problem of the growth of the individual 

 components of sea motion. Neumann (1952, 1953, 1954) and, in another 

 way also Darbyshire (1952), have tried to solve this problem. Since the 

 ocean waves will only grow as long as the energy supplied by the wind 

 exceeds the loss in energy, the complete energy equations permit to compute 

 this growing theoretically. The computations by Neumann are physically 

 more founded than those by Sverdrup and Munk, as Neumann took into 

 account the internal friction and turbulence in the water as well as the 

 periodical changes of wind stress along the profile. Again, the results are 

 represented in diagrams with dimensionless wave quantities and become 

 especially clear when the co-cumulative energy spectra (CCS-curves) are 

 used. An example is given in Fig. 43a for wind speeds of 10 to 36 knots. 

 The energy spectrum in this figure is the same as in Fig. 33, but Fig. 43a 

 contains also duration or fetch lines. 



The intersection points of the CCS-curves with the duration or fetch lines, 

 respectively, show the limit of the development of the composite wave motion 

 at the given duration or fetch. Physically, it means that the state of development 

 is limited by a certain maximum amount of total energy which the wave 

 motion can absorb from the wind with the given conditions. The E value 

 of the ordinate of each intersection point is a practical measure of the total 

 energy accumulated in the wave motion of the non-fully arisen state, limited 

 either by the fetch or duration. From the E = l(gg)E* value, the wave height 

 characteristics can be computed, as in the case of a fully arisen sea. 



The upper limit of significant periods in not fully arisen sea is approx- 

 imately determined by the "frequency of intersection",/, that is, the frequency 

 of the intersection point between the CCS-curve of a given wind speed and 

 the given fetch or duration line, respectively. By this, theoretically, the wave 

 spectrum is cut off abruptly at a given maximum period, T t (or minimum 

 frequency, fy without considering possible wave components with periods 

 a little longer than T t = l/f t , which are just in the beginning stage of de- 

 velopment. These wave components probably have a small amplitude, and 

 contribute so small amounts of energy to the total wave energy that they 

 may be neglected in most practical cases of wave forecasting. 



