Multi-scale model of gradient evolution in turbulent flows

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dc.creatorBiferale, Luca
dc.creatorChevillard, Laurent
dc.creatorMeneveau, Charles
dc.creatorToschi, Federico
dc.date2006-12-06
dc.date.accessioned2026-07-07T08:08:58Z
dc.date.available2026-07-07T08:08:58Z
dc.descriptionA 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.
dc.description4 pages, 4 figures
dc.identifierhttps://arxiv.org/abs/nlin/0612014
dc.identifierhttp://arxiv.org/abs/nlin/0612014
dc.identifierPhys. Rev. Lett. 98, 214501 (2007)
dc.identifierdoi:10.1103/PhysRevLett.98.214501
dc.identifier.urihttp://salesiana.dossiersoluciones.com/handle/123456789/131441
dc.subjectChaotic Dynamics
dc.titleMulti-scale model of gradient evolution in turbulent flows
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