TM No. 377 



current. The upper limit of integral B in equation (V-17) is the mean free 

 surface <£" , which is located at 2 = 0. Thus, the turbulent kinetic energy asso- 

 ciated with two-dimensional wave motion is: 



W = 2-P ) (w % + ufi)d*i (v-18) 



From the wave measurements, distributions of u'* and w'* are available as 

 a function of depth (see table IV- 3); hence, the numerical integration of equation 

 (V-l8) can obtain estimates of E^ w . 



Six sets of BBELS wave observations were used to calculate the integral Efc w . 

 The results are given in table V-2, which lists the wind velocity V (cm sec-1), the 

 depth of numerical integration D (m), and E^w (erg cm -2 ). The other parameters are 

 discussed later. 



Note that for BBELS-5 and 7, the OMDUM II system obtained both u and w at 

 various depths; hence, equation (V-l8) was used to estimate Ekw F°^ BBELS-11 and 

 Ik, however, the LUVDUM I system obtained only values of w. The following integral 

 was used for these calculations: 



-D 



(V-19) 



£*" ~ f UJ' L d* 



It is assumed that in equation (V-l8): 



-U' 1 = u>"- (v " 20) 



This assumption is certainly not unreasonable in dealing with surface waves, 

 for which, classically, equation (V-20) holds. In fact, it may turn out that 

 equation (V-20) is a better assumption than using the experimentally obtained u, 

 which intuitively seemed too small. If equation (V-19) is used in all calcula- 

 tions of E^ w (i.e., discarding u completely), the E^w integrals will be roughly 

 10-20 percent larger than values obtained using equation (V-l8). These numeri- 

 cally integrated estimates of E^ w are approximations and should be considered as 

 merely indicative of the order of magnitude of the wave turbulent kinetic energy. 

 The E kw values thus obtained are similar in magnitude to wave energies tabulated 

 by Stewart (1961) for similar wind conditions. 



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