TM No. 377 



higher frequencies with depth. Auto-spectra of wave motions proved to have 

 similar spectral peaks to the auto-spectra of free surface elevation data 

 observed with an electronic wave staff. 



6. Slopes of the auto-spectra of the particle velocity motions at the 

 frequencies above the spectral peaks indicate that the spectral energy decreased 

 as the minus-fifth power of the frequency. This law, predicted by Phillips (l953)j 

 has been observed for free surface auto-spectra (Burling, 1959) > and. is supposed 

 to indicate the presence of an equilibrium range of frequencies where there 

 exists a saturation of energy. 



7. Continuous observations of wave motions under time-varying wind 

 conditions show spectral changes associated with wave buildup, including the 

 down-frequency shifting of the spectral density peak. A 2l+-hour study of the 

 vertical motion auto-spectra, made during extreme condition of wind variations, 

 delineated unique spectra associated with different parameters such as wind speed, 

 fetch, and duration. 



8. LIMDUM I data indicated a linear decrease in the spatial correlation 

 coefficient of similar velocity components with depth. 



9. The covariance function u'w" indicated predominantly negative an d, i n 

 many cases, relatively large values. The inferred Reynolds stresses (-puLW ) 

 were thus generally positive, with a large range of values averaging about 15-20 

 dyne cm" . This indicated a downward transport of wind- imparted horizontal 

 momentum. The stresses tended to attenuate with depth in a manner similar to 

 the variances of the motions. 



10. Qua-speetra were much larger than co-spectra for the OMDUM III measure- 

 ments. Contributions to both qua-spectra and co-spectra were predominantly from 

 the ambient wave frequencies, as indicated by the auto-spectral and coherence 

 function peaks. 



11. Estimates of mean shear of horizontal^ motion allowed approximate 

 evaluation of the dissipation function -p^u/f^ . The positive values 

 obtained indicate predominant kinetic energy flow from mean motion to the 

 wave motions. 



12. For completeness, some hypothetical two-dimensional wave models were 

 constructed which contained perturbations realizable from physical interaction 



of wind stress at the wave surface. These models displayed variances, covariances, 

 auto-spectra and cross-spectra similar to those obtained from the real data. These 

 models also served to demonstrate how physical properties can be ascertained from 

 the rather esoteric statistics of cross-spectra and coherence. 



Small mean phase shifts (possibly caused by surface wind forces) can produce 

 covariances of the order of magnitude observed within the wave motions; however, 

 artificial phase shifts in the instrumentation can also contribute to the 

 covariance . 



165 



