Superfast amplification and superfast nonlinear saturation of perturbations as a mechanism of turbulence. (10th December 2020)

• Record Type: Journal Article
• Authors: Li, Y. Charles; Ho, Richard D. J. G.; Berera, Arjun; Feng, Z. C.
• Is Part Of: Journal of fluid mechanics. Volume 904(2020)
• Publication Date: 2020-12-10
• Subjects: homogeneous turbulence, -- transition to turbulence; Fluid mechanics -- Periodicals; 532.005
• DOI: 10.1017/jfm.2020.715
• Languages: English
• ISSNs: 0022-1120

Abstract

Abstract: Abstract : Ruelle predicted that the maximal amplification of perturbations in homogeneous isotropic turbulence is exponential $\exp ({\sigma \sqrt {Re} \, t})$ (where $\sigma \sqrt {Re}$ 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 $\exp ({\sigma \sqrt {Re} \sqrt {t} +\sigma _1 t})$ where $\sigma \sqrt {Re} \sqrt {t}$ is much larger than $\sigma \sqrt {Re} \, t$ 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 $2048^3$ 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.