TM No. 377 



contributing to the variances is determined largely "by the physical dimensions 

 of the turbulence meter. The meters used were 15 - 18 cm in diameter. Eddy 

 structure of this dimension or smaller, although perturbing the highly responsive 

 impellers, would probably present a highly biased effect or a smearing of the 

 high frequency motions because of the complex interaction of the meter geometry 

 with the water flow through and around it. 



The residual variance at deeper levels may therefore be caused by the inter- 

 action of the mean horizontal tide flow with the meter, artificially generating 

 turbulence about the meter which is then registered. The calibration tests, 

 however, did not support this interpretation for steady or slowly varying flow up 

 to at least 115 cm sec"l. As discussed in chapter II, there was no vertical 

 impeller response for a series of horizontal flow calibrations. 



A further examination of the observed vertical distributions of the variances, 

 as they pertain to the distribution of wave energy, seems called for. For better 

 interpretation, the variances QJ* and (J[u *" can be indicated by their equiva- 

 lents u 71 and w** ; where u' and w r are the deviations from the mean u an d w 

 (see equation (111-12)). Appendix A shows that the terms /0#'* and f Uj? 1 

 represent dynamic pressures (or normal stresses), expressed in dynes cm" 2 , acting 

 in the direction of the respective velocity fluctuations u' or w 1 . If a dynamic 

 pressure (force per unit area) is integrated over a depth D, normal to this area, 

 this integral represents the turbulent kinetic energy contained in a volume of 

 unit cross section and depth D. A similar integration can be done using the mean 

 values u and w, giving the volume integral of the kinetic energy associated with 

 the mean motion. For example, the total kinetic energy of a volume of water bounded 

 by the free surface y and the depth D (and of unit cross section) may be given by: 



•Mr- 2. 



r-D 



J*r 



(ffVfi?*)4sf£p 



r 



rD 



(p*+(o A )te 



(V-17) 



T 



B 



where E kt is in units of erg cm" 2 . Integral A is the kinetic energy associated 

 with mean motion; integral B is the kinetic energy associated with the turbulent 

 or wave-induced oscillatory motions. 



In the problem of two dimensional wave motion, w = and u is the mean 



121 



