Reynolds number of transition and large-scale properties of strong turbulence

Abstract

A turbulent flow is characterized by velocity fluctuations excited in an extremely broad interval of wave numbers $k>{\Lambda }_f$ where ${\Lambda }_f$ is a relatively small set of the wave-vectors where energy is pumped into fluid by external forces. Iterative averaging over small-scale velocity fluctuations from the interval ${\Lambda }_f<k\le {\Lambda }_0$, where $\eta =2\pi /{\Lambda }_0$ is the dissipation scale, leads to an infinite number of "relevant" scale-dependent coupling constants ( Reynolds numbers ) $R{e}_n(k)=O(1)$. It is shown that in the i.r. limit $k\to {\Lambda }_f$, the Reynolds numbers $Re(k)\to R{e}_{tr}$ where $R{e}_{tr}$ is the recently numerically and experimentally discovered universal Reynolds number of "smooth" transition from Gaussian to anomalous statistics of spatial velocity derivatives. The calculated relation $Re({\Lambda }_f)=R{e}_{tr}$ "selects" the lowest - order non-linearity as the only relevant one. This means that in the infra-red limit $k\to {\Lambda }_f$ all high-order nonlinearities generated by the scale-elimination sum up to zero.

arXiv admin note: substantial text overlap with arXiv:1308.4205

Cited by in corpus (3)

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