There's several concepts I don't have a clear understanding of:
Plots of the turbulent energy cascade have a wave frequency as the axis - yet I see definitions of this "frequency" as the inverse of the eddy size. How does one get Hertz from this if the dimensional unit is one of length. And what does this frequency or wave number really mean? Looking at the ordinate (energy spectrum), is a point on the chart the total combined energy of all eddies of the particular size (frequency) corresponding to the abscissa value?
I'm not sure I really understand what is meant by the time scale of eddies. Sometimes the term "turnover" time is used. Particularly for large eddies, is it the time for the eddy to reach the Kolmogorov scale and then quickly dissipate after that? Also, can't smaller eddies recombine to former larger eddies? Physically, I don't understand what the timescale means.
Are there any formulas available for determining the time it takes turbulence to "die out" if the energy supply for the turbulence is suddenly cut off. I've read that it is typically several "turnover" times of the integral eddies. Can someone point me to a more rigorous method for determining this time?
One other question regarding stopping the energy supply producing turbulence. If stopped, does that mean that smaller eddies can no longer combine to produce larger eddies?
Thanks.
