TM NOo 377 



The following parameters of the wave particle motions are pertinent and 

 should be measured s variability, ccvariability, auto-spectra, cross-spectra, 

 and velocity shear e (Complete definition and discussion of the statistical 

 parameters are contained in chapter III ) 



-^ Variability,, It is only natural to examine the variability or the 



variance of the -velocity observations „ Since the fluctuations of the wave 

 motions must be due in large part to the gross movements of the dominant 

 waves, the variance should serve as a scale by which to estimate the magni- 

 tude or energy of the waves « The change in variance of a velocity component 

 can be evaluated as a function of depth (from the mean free surface), am- 

 bient wind speed,, and the observable wave parameters such as estimated wave 

 length, height and period,, 



2„ Covariability o Interrelations of the velocity components can be 

 obtained by estimating the covarian.ee 'between two, simultaneously measured, 

 orthogonal, velocity components, or between two, similar, velocity compo- 

 nents that are specially separated,, 



3° Auto- and Cross°Spectra 8 The auto-spectra obtained from the auto- 

 covariance functions can be used to examine the contributions of the motions 

 to the variance as a function of frequency,, Examination of the auto-spectra 

 associated with various depth and wind conditions can indicates (l) the 

 relative energy distribution with frequency as affected hj the driving 

 forces of the wind, and (2) the attenuation with depth 



The eross-speetra obtained from the covariance functions can indicate 

 the degree to which the waves behave in a classical sense, and hence the 

 degree of turbulence or qu&sl-randomness inherent in the motions. The 

 cross-spectral functions can provide information regarding the magnitude 

 of positive (or negative) correlation of two velocity components as a 

 function of frequency,, 



**•<> Velocity Shear e The vertical shear of the horizontal velocity 

 which is determined from measurements of the mean current at two depths 

 simultaneously, is a measure of the meaa vortlcity and can be related to 

 depth, variance, covariance, wind speed, and other parameters «, 



By identifiying and estimating the magnitude of the vertical distri- 

 bution of those quantities associated with stress and dissipation, one may 

 be able to offer a conceptual description of the mode of wind momentum 

 transfer t«^ «nfl within the water column*, and perhaps make some inferences 

 as to the disposition of the wind-imparfced kiiaetle energy „ Of particular 

 interest is the transfer of kinetic energy from the turbulent eddy motion 

 to the mean motion,, This is expressed by -p<*nJ(aa/aa), where the baa- 

 indicates a time average of the horizontal velocity u„ ' This quantity is 

 described by Webster (1961) in a study of the kinetic energy balance of 

 the Gulf Streamo 



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