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A dissipative random velocity field for fully developed fluid turbulence

Published online by Cambridge University Press:  04 April 2016

Rodrigo M. Pereira Open the ORCID record for Rodrigo M. Pereira [Opens in a new window] ,
Christophe Garban  and
Laurent Chevillard
Rodrigo M. Pereira*
Affiliation:
Univ Lyon, Ens de Lyon, Univ Claude Bernard, CNRS, Laboratoire de Physique, 46 allée d’Italie F-69342 Lyon, France CAPES Foundation, Ministry of Education of Brazil, Brasília/DF 70040-020, Brazil
Christophe Garban
Affiliation:
Université de Lyon, Institut Camille Jordan, 43 blvd. du 11 novembre 1918, F-69622 Villeurbanne CEDEX, France
Laurent Chevillard
Affiliation:
Univ Lyon, Ens de Lyon, Univ Claude Bernard, CNRS, Laboratoire de Physique, 46 allée d’Italie F-69342 Lyon, France
*
†Email address for correspondence: [email protected]
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Abstract

We investigate the statistical properties, based on numerical simulations and analytical calculations, of a recently proposed stochastic model for the velocity field (Chevillard et al., Europhys. Lett., vol. 89, 2010, 54002) of an incompressible, homogeneous, isotropic and fully developed turbulent flow. A key step in the construction of this model is the introduction of some aspects of the vorticity stretching mechanism that governs the dynamics of fluid particles along their trajectories. An additional further phenomenological step aimed at including the long range correlated nature of turbulence makes this model dependent on a single free parameter, ${\it\gamma}$, that can be estimated from experimental measurements. We confirm the realism of the model regarding the geometry of the velocity gradient tensor, the power-law behaviour of the moments of velocity increments (i.e. the structure functions) including the intermittent corrections and the existence of energy transfer across scales. We quantify the dependence of these basic properties of turbulent flows on the free parameter ${\it\gamma}$ and derive analytically the spectrum of exponents of the structure functions in a simplified non-dissipative case. A perturbative expansion in power of ${\it\gamma}$ shows that energy transfer, at leading order, indeed take place, justifying the dissipative nature of this random field.

JFM classification

Turbulent Flows: Intermittency Turbulent Flows: Isotropic turbulence Turbulent Flows: Turbulence modelling
Type
Papers
Information
Journal of Fluid Mechanics , Volume 794 , 10 May 2016 , pp. 369 - 408
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Copyright
© 2016 Cambridge University Press 

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