Abstract
Renormalization or coarse-graining applied to basic equations governing multi -scale phenomena, leading to effective equations for large-scale properties is often called model-building. Unlike fluids in thermodynamic equilibrium, in case of high-Reynolds number turbulent flows the procedure leads to generation of an infinite number relevant high-order nonlinearities which are hard to deal with. In this paper, based on the recently discovered universality of transition to strongly non-Gaussian (anomalous) statistics of velocity derivatives, we show that in the infrared limit \(k\rightarrow 2\pi /L\), where \(L\) is the integral scale corresponding to the top of inertial range, the lowest-order contributions to the renormalized perturbation expansion give asymptotically exact equations for the large-scale features of the flow. The quality of the derived models is demonstrated on a few examples of complex flows. At the small scales \(\varDelta < L\), an infinite number of \(O(1)\) non-linear terms, generated by the procedure invalidate low-order models widely used for Large-Eddy-Simulations (LES) of turbulent flows.
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Yakhot, V., Bartlett, C., Chen, H., Shock, R., Staroselsky, I., Wanderer, J. (2015). Universal Reynolds Number of Transition and Derivation of Turbulent Models. In: Girimaji, S., Haase, W., Peng, SH., Schwamborn, D. (eds) Progress in Hybrid RANS-LES Modelling. Notes on Numerical Fluid Mechanics and Multidisciplinary Design, vol 130. Springer, Cham. https://doi.org/10.1007/978-3-319-15141-0_3
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