TM No, 377 



The vertical spacing of the cylinders is S^ - S meters „ With this system 

 one can measure instantaneous vertical shear of horizontal velocities given 



as 



acc ^ U (*■»*) -IaC*** *) . (111=57) 



2* Varianc e . The variances of the orthogonal pairs - using equation 

 (III-15)* can be represented as; 



0Z L = jIcY*^*)]^"* CC* [W'ft^t)] * . (IH-58) 

 Using equation (III-38): 



nt{t-*i*) - ^{z») -h u'fe*)*) • (in- 59) 



The iZtfru) is the mean value of 'U {?-*,?) averaged over the sampling period T. 



The variances of the spatially separated data pairs ; from equation (111-55)* 

 are therefore s 



j^Y^^/j 1 *"o Lv^/Op > (II3>60) 



and similarly for the vertical velocity components „ 



The variances of the velocity components are proportional to dyanmic 

 pressures (see appendix A) and also to the turbulent kinetic energy associ- 

 ated with motion in a particular component direction*, Hence ; the variances 

 allow estimation of the spatial distribution of kinetic energy,. Application 

 of this concept is discussed in chapter V<, 



3„ Linear Correlation Coefficient , The linear correlation coefficient , 

 defined by equation ( 1X1=29 }^ is given for the orthogonal components 'Tx(t'» ) t-) 

 and tufa*,,*) as; 



*Ui*J = ■ ., ' (III-61) 



{\*L'fa,*)f \U>'(^>*)] 1 Y L 



The term in the numerator is the covariance function at zero lag given by 

 equation (111=28). This parameter denotes the amount of correlation between 

 the orthogonal velocity components „ 



63 



