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I would like to calculate the time it takes for the largest eddies to be reduced to a specific size eddy (for example, the Kolmogorov length scale, but I would like a general equation if possible). I'm confused by the term turnover time and how it relates to the time it takes an eddy of size "l" to be reduced to a smaller size eddy.

rdemyan
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  • Related https://physics.stackexchange.com/q/540879/226902 https://physics.stackexchange.com/q/481660/226902 https://physics.stackexchange.com/q/298533/226902 – Quillo Sep 29 '22 at 07:31

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The answer to that question may not be as straightforward as one would think. How fast does a perturbation of the large scale propagates to the smaller scales? It could be instantaneous, but if this was the case then the cascade wouldn't be local. The answer to your question probably is related to how fast the energy is transferred through the scales, this has been studied by Cardesa et al. in their paper 'The temporal evolution of the energy flux across scales in homogeneous turbulence'. They estimate the delay between the energy injection and the energy dissipation, but in the figure 2c) of this paper you can see a colormap that shows the delay in energy transfer at different scales.

AdBahamonde
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