I have been trying to estimate the Kolmogorov length scale in turbulent mixing layer. I was using the energy spectrum for estimating length scale, but it gives just one value for a specified time. Since the mixing layer is not isotropic, i believe the length scale varies spatially and i was wondering if anyone can help explain how to estimate these values for each point at a specified time. Any help is appreciated!!
Assume that at the Kolmogorov lenght scale the local Reynolds number is O(1).
The Kolmogorov scale uses the assumption that the turbulence becomes isotropic at very small scales and loses even its directional identity, even if at large scales the turbulence is anisotropic.
The Kolmogorov scale further limits the size of eddy where it does not transfer energy to any other eddy, but the kinetic energy gets dissipated through viscous action.
The Kolmogorov scale remains the same irrespective of whether it is a mixing layer or any other kind of flow, depending only upon the kinematic viscosity and rate of dissipation of turbulent kinetic energy.
In the end, it is a hypothesis, and till date no one has experimentally measured these scales. So you can make a good informed guess only using a suitable relationship.
I feel using energy spectrum and rate of dissipation of turbulent kinetic energy can give a good guess.
Please note and argue that at and near Kolmogorov scales the viscous effects become strong enough to force isotropy in turbulence. All directional info is lost along with anisotropy.
You need to first get a good estimate of the local dissipation rate which is supposed to change spatially in your case.
You could use the Anaflame toolbox for matlab. Specifically, you need to have a uniform grid of velocity and use the spectrum2d routine to get the energy associated to each wave number. In that spectrum you will observe which scales present your problem.
https://www.lss.ovgu.de/Info/Downloads/Anaflame/Overview+2D/vel+and+turb+tools/spectrum2d.html
Jiarong Hong I understand. Can you explain how can i estimate the local dissipation rate in a mixing layer? Is there any well-defined equation i can use?
There are standard formulas for the dissipation rate derived from TKE equation, (~products of velocity gradients). you can also estimate the dissipation rate using the local TKE production rate (assuming the TKE production rate is balanced by dissipation rate ~U'^3/l, this is a very crude approximation); you can also estimate dissipation rate using structural function and Kolmogorov 4/5 law. Pope's turbulence book has all these formulas. Which method to use depending on what information you have available.
Please refer the book, A first course in turbulence by Tennekis and Lambley.
Hello,
In our 2007 Journ. Fluid. Mech. paper with Olivier Kimmoun, we have measured spatially the Kolmogorov length scales. It was in the water, under water waves propagating and breaking to the shore. ( from P.I.V measurments) . See figure 31 of the paper. The turbulence under breaking waves is probably as complex as the turbulence in a mixing layer :-) .. So, it is possible to have a map of the Kolmogorov length scale. Ref: Kimmoun O. and Branger H., “A Particle Image Velocimetry investigation on laboratory surf-zone breaking waves over a sloping beach”, Journ. of Fluid Mech., Vol 588, pp 353-397, 2007, http://hal.archives-ouvertes.fr/hal-00192468/fr/, doi:10.1017/S0022112007007641
Best Regards
Hubert
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