Superfast amplification and superfast nonlinear saturation of perturbations as the mechanism of turbulence

Ruelle predicted that the maximal amplification of perturbations in homogeneous isotropic turbulence is exponential exp(σ√Ret) (where σ√Re is the maximal Lyapunov exponent). In our earlier works, we predicted that the maximal amplification of perturbations in fully developed turbulence is faster than exponential and is given by exp(σ√Re√t+σ1t) where σ√Re√t√ is much larger than σ√Ret for small t . That is, we predicted superfast initial amplification of perturbations. Built upon our earlier numerical verification of our prediction, here, we conduct a large numerical verification with resolution up to 20483 and Reynolds number up to 6210 . Our direct numerical simulation here confirms our analytical prediction. Our numerical simulation also demonstrates that such superfast amplification of perturbations leads to superfast nonlinear saturation. We conclude that such superfast amplification and superfast nonlinear saturation of ever existing perturbations suggest a mechanism for the generation, development and persistence of fully developed turbulence.