On turbulent length scales...

The figures to the right show the number of observations distributed over different values of the mixing coefficient (K_ρ). The top figure shows Day 2 and the bottom figure shows Day 3. Let us speculate a little about the similarities and the differences between these two spectra...

Now, K_ρ is the product of the turbulent velocity (square root of the turbulent energy) and the turbulent length scale. On scales longer than (~30 times!) the Kolmogorov scale dissipation is little. The turbulent energy at a given time will a later time appear at a shorter length scale, i.e. at a smaller K_ρ value. So, what I am saying is that the figures to the right can be seen as spectra of TKE for length scales. So why do I not plot that instead?!