# Kolmogorov scale

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 December 11, 2001, 08:06 Kolmogorov scale #1 T.Misawa Guest   Posts: n/a 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?

 December 11, 2001, 12:09 Re: Kolmogorov scale #2 sylvain Guest   Posts: n/a 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) = 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.

 December 12, 2001, 05:02 Re: Kolmogorov scale #3 sylvain Guest   Posts: n/a 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.

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