TM No. 377 



Since the high frequency region of the auto- spectrum was of primary 

 interest, the values of $m (listed in the appendix B) were averaged over 

 50-mcps increments from 250 to 1000 mcps. Weighted values of the spectral 

 energy were then plotted (figure V-36) as a function of frequency (following 

 the method of Burling, 1959) • The weighting is in terms of various powers of 

 the frequency ( f n ). The curves indicate that the slope of ^ u for 250 ~ f 

 1000 mcps appears to vary as f~5, since: 



< 



[$J1 £ 5 sT CONSTANT. (V-29) 



Another group of BBELS-11 observations were examined for the f n slope 

 relationship - the average spectra for serial 0U8, 052, 05U, 057A, 057B, and O58. 

 These observations were at 0.5 meter depth between 2009 hours on 29 March and 

 1137 hours on 30 March 1965 • The winds varied over this period from 7-3 m sec"! 

 ENE to Ik m sec - l WNW. Examination of the spectral plots in appendix B shows a 

 similarity in the values of $\jj between 300 mcps and 1500 mcps and in the up- 

 frequency slope of the function. Figure V-37 shows the average auto- spectra 

 (weighted by f n ) as a function of frequency. The curve for ^ w f5 (triangles) 

 appears to be quite independent of frequency over the range from U00 mcps to 1300 

 mcps. A slight rise in the curve beyond 1300 mcps indicates, perhaps, a transi- 

 tion. 



The wave particle motion spectra display a clear functional relationship to 

 frequency which is similar to that of the free surface spectra ^"» . The 

 concept of the equilibrium range of spectra can now be further examined in the 

 light of these findings. 



Consider the visible phenomena of wave generation. When the wind blows over 

 calm water, the first response in the sea surface is the production of high fre- 

 quency capillary waves having wave lengths of a few millimeters. In a rather 

 continuous manner, progressively larger waves are formed, which become less and 

 less governed by surface tension forces, but tend to propagate in response to 

 gravity. At any given instant during this wave generation process, an auto- 

 spectrum may be associated with the wave motions. The spectrum is continuously 

 changing with time, since the process, at this stage, is not stationary. With 

 time, the maximum energy peak gradually moves down- frequency. For a given wind 

 speed and other associated parameters, a stabilization now occurs within a 

 certain frequency range. Within this certain band no more energy can be perma- 

 nently added; i.e., it has become saturated. 



Figure V-38 shows an idealized auto- spectrum of the free surface variable 

 C§>» or the wave velocity component ^^ w . The two peaks associated with swell 

 and wind waves are shown at f ms and f mW3 respectively. The equilibrium range is 

 divided into the inertial subrange and the dissipation range. The dissipation 

 range is associated with the high frequency turbulence visualized as small scale 

 eddies and white caps. All wave energy is eventually dissipated in this range, 

 either by breaking waves in the open sea or by the formation of breakers on the 



133 



