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Ruelle predicted that the maximal amplification of perturbations inhomogeneous isotropic turbulence is exponential $e^{\sigma \sqrt{Re} t}$ (where$\sigma \sqrt{Re}$ is the maximal Liapunov exponent). In our earlier works, wepredicted that the maximal amplification of perturbations in fully developedturbulence is faster than exponential $e^{\sigma \sqrt{Re} \sqrt{t} +\sigma_1t}$. That is, we predicted superfast initial amplification of perturbations.Built upon our earlier numerical verification of our prediction, here weconduct a large numerical verification with resolution up to $2048^3$ andReynolds number up to $6210$. Our direct numerical simulation here confirms ouranalytical prediction. Our numerical simulation also demonstrates that suchsuperfast amplification of perturbations leads to superfast nonlinearsaturation. We conclude that such superfast amplification and superfastnonlinear saturation of ever existing perturbations serve as the mechanism forthe generation, development and persistence of fully developed turbulence.

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