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Energy density at a given scale in terms of the Energy Spectrum

Background: Let us have a turbulent fluid with a random velocity field $\mathbf{u}(\mathbf{x})$. The volume averaged kinetic energy density $\mathscr{E}_K$ can be expressed as $$\mathscr{E}_K=\frac{1}{...
Sayan Mandal's user avatar
  • 1,006
1 vote
1 answer
109 views

Calculating an anisotropic or component Taylor microscale

The Taylor microscale in isotropic turbulence is given by: $$\lambda = \sqrt{ 15 \frac{\nu \ v'^2}{\epsilon} }$$ where v' is the root mean square of the velocity fluctuations. In general, for ...
rdemyan's user avatar
  • 71
2 votes
1 answer
419 views

About the formula of the Taylor microscale

I am running simulations of a non-isotropic turbulent flow and I need to compute the Taylor microscale. The formula one can find in the book Turbulent flows (Stephen B. Pope) is : $\lambda = \sqrt{10} ...
StrangeGorov's user avatar
0 votes
1 answer
110 views

How does the eddy velocity scale with its time scale?

According to Kolmogorov's energy casacade model, if we have a flow with inertial velocity scale $\mathcal{V}$, inertial length scale $\mathcal{L}$ then we can calculate the eddy velocity of an eddy ...
Thomas Wagenaar's user avatar
11 votes
2 answers
46k views

What does the Reynolds Number of a flow represent physically?

What does the Reynolds Number of a flow represent physically? I am having trouble understanding the meaning and the utility of the Reynolds number for a certain flow, could someone please tell me how ...
user27182's user avatar
  • 1,657