2an Qr 



2ar 



Fig. 13 - Comparison ofdirect- 

 interaction and computer -experiment 

 results for spectrum as a function of 

 horizontal wave number for the case 

 shown in Fig. IZ. The dots are the 

 numerical experiment; the crosses in 

 circles, the direct-interaction ap- 

 proximation. The horizontal wave 

 number plotted horizontally is the 

 spectrum level vertically. 



small size in a random fashion, but do not distort the small eddies appreciably. 

 In the Fourier representation, this means that the excitation at wave numbers in 

 the energy -containing range does not affect the dynamics of energy transfer at 

 high wave numbers. 



The direct-interaction approximation for energy transfer, as given by Eqs. 

 (12) and (16), expresses the transfer as an integral over the past history of the 

 fluid. The function u(k; t', s) in Eq. (15) is an Eulerian time -cor relation for 

 wave number k . If the equations are Fourier-transformed back to physical 

 space, the time integrals may be interpreted as tracing the velocity correlations 

 back in time at fixed points in space. However, the Eulerian time correlations 

 at high wave numbers (small spatial separations) are strongly affected by the 

 distortionless random convection of small eddies by large eddies. u(k; t, s) does 

 not convey sufficient information to tell whether or not the decorrelation at high 

 wave numbers is due to convection without energy transfer, or to the internal 



804 



