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Optimal fluxes and Reynolds stresses

Published online by Cambridge University Press:  15 November 2016

Javier Jiménez
Javier Jiménez*
Affiliation:
School of Aeronautics, Universidad Politécnica de Madrid, 28040 Madrid, Spain
*
†Email address for correspondence: jimenez@torroja.dmt.upm.es
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Abstract

It is remarked that fluxes in conservation laws, such as the Reynolds stresses in the momentum equation of turbulent shear flows, or the spectral energy flux in anisotropic turbulence, are only defined up to an arbitrary solenoidal field. While this is not usually significant for long-time averages, it becomes important when fluxes are modelled locally in large-eddy simulations, or in the analysis of intermittency and cascades. As an example, a numerical procedure is introduced to compute fluxes in scalar conservation equations in such a way that their total integrated magnitude is minimised. The result is an irrotational vector field that derives from a potential, thus minimising sterile flux ‘circuits’. The algorithm is generalised to tensor fluxes and applied to the transfer of momentum in a turbulent channel. The resulting instantaneous Reynolds stresses are compared with their traditional expressions, and found to be substantially different. This suggests that some of the alleged shortcomings of simple subgrid models may be representational artefacts, and that the same may be true of the intermittency properties of the turbulent stresses.

JFM classification

Mathematical Foundations: Mathematical Foundations Turbulent Flows: Turbulence theory Turbulent Flows: Turbulent boundary layers
Type
Papers
Information
Journal of Fluid Mechanics , Volume 809 , 25 December 2016 , pp. 585 - 600
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Copyright
© 2016 Cambridge University Press 

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