Kolmogorov's second similarity hypothesis (1941) predicts that in the inertial subrange, the 1D energy spectrum is E(k) = CK ε2/3 k-5/3, where ε is the energy dissipation rate and CK ≈ 1.5 is the Kolmogorov constant. This famous -5/3 power law has been verified experimentally across many orders of magnitude and is one of the most robust results in turbulence theory. Below, a synthetic turbulent signal is generated and its power spectrum displayed in real time.
Turbulent velocity signal u(t)
Power spectrum E(k) — log-log