What are the length and time scales in turbulence? I haven't been able to understand what are does someone mean by length and time scales, while talking about turbulence. Can someone explain it?
 A: Basically, the scale of a certain parameter is the order of magnitude of that parameter. Being able to determine the scales of a parameters in a complex system (like turbulence problems) is very useful. 
For turbulence, the size of the largest eddies is given by the characteristic length scale you are working with, $L$, and the smallest eddy size is given by the so called, Kolmogorov length scale, $\eta$.
This scale goes like, $\eta = \left(\frac{\nu^3}{\epsilon}\right)^{1/4}$, where $\nu$  is the viscosity and $\epsilon$ is the dissipation rate per unit mass. 
It is interesting to note that $L/\eta= \text{Re}^{3/4}$.
Another commonly encountered length scale is known as Taylor micro-scale and provides a good estimate for the fluctuating strain rate field.
The times scale for the so called "large eddy turnover" is simply the time scale of the flow, $L/U$
The time scales for the small eddies can also be derived using the viscosity and dissipation, $t_\eta = \left(\frac{\nu}{\epsilon}\right)^{1/2}.$
Similarly, $t_L/t_\eta= \text{Re}^{1/2}.$
Good books I can suggest are the book S. B. Pope (Turbulent Flows) and T.H. Lumely (A first course in Turbulence).
