Hello all

Does any one know how to esitmate Kolmogorov micro scale?

I know Kolmogorov scale can be obtained from viscosity and dissipation rate per unit mass. Should I obtain dissipation rate from DNS or experiment results ? Can I estimate Kolmogorov scale without DNS or experiments?

If you know the kinetic energy q/2 and the integral length scale L , you may used the following relationship for the dissipation rate eps :

eps ~ ((q/2)^3/2)/L

Moreover, if you define a tridimensionnal spectrum E(K) by :

E(K) = AK^s for (K<Kmax)

E(K) = c_k eps^2/3 K^(-5/3) (K>=Kmax)

E(K) = 0 (K>Kkol)

where s is the slope of the spectrum for large scale (s=2 to 4).

Then you can find A by continuity in Kmax and eps, L and q/2 from the following relationship :

q/2 = int (E(K)dK)

eps = 2 nu int (K^2E(K)dK)

q/2 L = int(E(K)/KdK) (may be 2*pi somewhere)

this could give you a good idea of the different equalities between all this quantities for turbulence near equilibrium.

It should have been :

Moreover, if you define a tridimensionnal spectrum E(K) by :

E(K) = AK^s (K<=Kmax)

E(K) = c_k eps^2/3 K^(-5/3) (Kkol>=K>=Kmax)

E(K) = 0 (K>=Kkol)

PS : for K>=Kmax, one can also used the Pao formulation.