Kraichnan 



8 - 



kL(0) 



Fig. 4 - Evolution of the dissipation 

 spectrum for the run shown in Fig. 3 



S(t) = - 



2_ 

 35 



Buj (x,t) 



3x, 



'\ 



3ui (x,t) 



3x, 



3/2 



-^ f k^ T(k,t) dk , 



u(t)J J 



(21) 



obtained from a variety of initial spectra, ranging in form from a very concen- 

 trated spectrum (all initial excitation confined to a single 1/4 octave k-band, 

 Run 11) to the nearly self -preserving spectrum of Eq. (20), Run 10. The initial 

 values of R^ range from 16 to 47. Note that, after a transient behavior which is 

 strongly dependent on initial conditions s(t) settles down to a value ^0.4 which is 

 insensitive to initial conditions. This value agrees well with laboratory measure- 

 ments of s(t) in the same range of R;^ [lO], subject to some uncertainty because 

 only crude estimates of wire-length corrections to the measurements can be 

 made. The insensitivity of s(t) to initial conditions makes this a comparatively 

 well-posed comparison with experiment. Equation (21) shows that s(t) is 



796 



