Exploring Orbital Velocity vs RMS of Eddy Velocities

[rdemyan]

Is there a difference between the orbital velocity of an eddy and the root mean square of the velocity fluctuations? I'm particularly interested in understanding the eddy turnover time of the largest eddies in a turbulent flow, which is given by the characteristic eddy size and the characteristic eddy velocity. As I understand it, this characteristic eddy velocity is the orbital velocity. The turnover time is the time needed for the spinning eddy to complete one revolution; so the orbital velocity should be used. Frankly I'm not convinced that the orbital velocity is the same as the root mean square of the velocity fluctuations. It seems that many books derive equations based on this assumption, but the authors are usually careful to state that the velocities are "of the order of" which then allows for the derivation of relatively simple equations. I would greatly appreciate thoughts on this.

 

[boneh3ad]

I've never heard it called orbital velocity before. I'll preface this by saying I'm not super well-versed in turbulence theory.

If you look at a turbulent power spectrum, it is highly biased toward low frequencies representing the largest eddies. This implies that the rms of the fluctuations technically contains all scales but is overwhelmingly dominated by the large scales. If an author makes the assumption you discuss, it's basically equivalent to making the assumption that the power contained in the large scales is much larger than small scales so the rms of the fluctuations are a good stand-in for the large scales.