where ⁠ 1 / 2 ⁠ ⟨ u i u i ⟩ is the mean turbulent kinetic energy of the flow. The wavenumber k corresponding to length scale r is k = ⁠ 2π / r ⁠. Therefore, by dimensional analysis, the only possible form for the energy spectrum function according with the third Kolmogorov's hypothesis is