9
$\begingroup$

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?

$\endgroup$
9
$\begingroup$

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).

$\endgroup$

Your Answer

By clicking “Post Your Answer”, you agree to our terms of service, privacy policy and cookie policy

Not the answer you're looking for? Browse other questions tagged or ask your own question.