A Is Orbital Velocity the Same as RMS of Eddy Velocities in Turbulent Flow?

AI Thread Summary
The discussion centers on the distinction between orbital velocity and the root mean square (rms) of velocity fluctuations in turbulent flow. The eddy turnover time, which relates to the size and velocity of the largest eddies, is suggested to be characterized by orbital velocity. There is skepticism about whether orbital velocity equates to rms velocity fluctuations, as many texts use this assumption cautiously. The turbulent power spectrum indicates that low frequencies dominate, suggesting that rms fluctuations are primarily influenced by larger scales. This raises questions about the validity of using rms as a reliable measure for large-scale turbulence characteristics.
rdemyan
Messages
67
Reaction score
4
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.
 
Physics news on Phys.org
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.
 
Thread 'Gauss' law seems to imply instantaneous electric field'
Imagine a charged sphere at the origin connected through an open switch to a vertical grounded wire. We wish to find an expression for the horizontal component of the electric field at a distance ##\mathbf{r}## from the sphere as it discharges. By using the Lorenz gauge condition: $$\nabla \cdot \mathbf{A} + \frac{1}{c^2}\frac{\partial \phi}{\partial t}=0\tag{1}$$ we find the following retarded solutions to the Maxwell equations If we assume that...
Maxwell’s equations imply the following wave equation for the electric field $$\nabla^2\mathbf{E}-\frac{1}{c^2}\frac{\partial^2\mathbf{E}}{\partial t^2} = \frac{1}{\varepsilon_0}\nabla\rho+\mu_0\frac{\partial\mathbf J}{\partial t}.\tag{1}$$ I wonder if eqn.##(1)## can be split into the following transverse part $$\nabla^2\mathbf{E}_T-\frac{1}{c^2}\frac{\partial^2\mathbf{E}_T}{\partial t^2} = \mu_0\frac{\partial\mathbf{J}_T}{\partial t}\tag{2}$$ and longitudinal part...
Back
Top