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Multi-scale model of gradient evolution in turbulent flows

Luca Biferale·Laurent Chevillard·Charles Meneveau·Federico Toschi
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Abstract

A multi-scale model for the evolution of the velocity gradient tensor in fully developed turbulence is proposed. The model is based on a coupling between a ``Restricted Euler'' dynamics [{\it P. Vieillefosse, Physica A, {\bf 14}, 150 (1984)}] which describes gradient self-stretching, and a deterministic cascade model which allows for energy exchange between different scales. We show that inclusion of the cascade process is sufficient to regularize the well-known finite time singularity of the Restricted Euler dynamics. At the same time, the model retains topological and geometrical features of real turbulent flows: these include the alignment between vorticity and the intermediate eigenvector of the strain-rate tensor and the typical teardrop shape of the joint probability density between the two invariants, $R-Q$, of the gradient tensor. The model also possesses skewed, non-Gaussian longitudinal gradient fluctuations and the correct scaling of energy dissipation as a function of Reynolds number. Derivative flatness coefficients are in good agreement with experimental data.

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Luca Biferale, Laurent Chevillard, Charles Meneveau, Federico Toschi. 2006-12-06. Multi-scale model of gradient evolution in turbulent flows. https://doi.org/10.1103/physrevlett.98.214501

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