TM No. 377 



A typical value for 6 may be 5°; -4. (for OMDUM III) is 11 cm; and, assuming 

 short waves having L = 12 m, the resulting A<$ = 0.29°. Assuming velocity 

 amplitudes for u' and w' of 20 cm sec~l, the estimated stress 7" S 1 dyne cm -2 

 (see equation (V-^6)). Therefore, a non-zero average value of 6 could contribute 

 to the covariance and associated stress. 



Substituting equation (V-56) into (V-U6) yields (for small £$): 



0*3 =. • (V-57) 



Cm 



For small waves, L and A are small; but for large waves, A 2 dominates in eq uation 

 (V-57) over L" 1 . Thus, for a given angle 0, an induced contribution to u'w' is 

 more important for the smaller waves. Also, the amplitude A exponentially decreases 

 with depth, whereas L is independent of depth. Statistically, L virtually in- 

 creases with depth, since the higher frequency waves (i.e., those of shorter wave 

 length) are rapidly filtered out with depth. 



For serial 120-123, where the angle 6 varied from 0°, 20°, 50° and 80°; 

 the covariances were -7.6, -10.3, -11.2 and -15.1 cm 2 sec -2 , respectively. The 

 wind was increasing in speed and varying in direction, and swell direction was 

 variable but roughly normal to the wind waves; but, aside from these factors, it 

 appears that the directionality may have provided a phase shift effect. 



It is evident fr om t his cursory perusal of the instrument-biasing effects, 

 that the covariances u'w* obtained with the wave meters must be open to some 

 question. Further work is required to verify or disprove their validity. 



Dissipation of Kinetic Energy 



It is instructive to consider the energy dissipation associated with the 

 wave motions. By recalling term C of equation (V-35) and using actual data, 

 one can estimate some values of the term: 



oft 



This dissipation term is derived in appendix A. 



During BBELS-15, using LIMDUM I, eight observations of the u wind wave 

 component were made simultaneously at two depths 2.5 meters apart. The mean 

 values u. and the mean vertical gradients of u (i.e., ^^/h\ ) are given in 

 table V-5. The last three columns list the values of equation (V-58) in 



156 



