Restricted scaling range models for turbulent velocity and scalar energy transfers in decaying turbulence

Abstract

The effect of finite Reynolds numbers and/or internal intermittency on the total kinetic energy and scalar energy transfers is examined in detail. For this purpose, two distinct models for velocity and scalar energy transfer are proposed in the specific context of freely decaying isotropic turbulence. The first one extends the already existing dynamical models (hereafter DYM, i.e. based on transport equations originated in Navier–Stokes and advection-diffusion transport equations). The second one relies on the characteristic time of the strain at a specific scale (hereafter SBM). Both models account for the Reynolds number dependence of the scaling exponent of the second-order structure functions, over a range of scales where such exponents may be defined, i.e. a restricted scaling range (RSR). Therefore, the models developed aim at reproducing the energy transfer over the RSR. The predicted energy transfer is very sensible to variations of the scaling exponent, especially at low Reynolds numbers. The approach towards the asymptotic 4/3 law is closely reproduced by the two models. The dynamical model reproduces the experimental results accurately especially in the vicinity of the Taylor microscale, while the SBM agrees almost perfectly with measurements at nearly all scales.

Keywords:

• energy transfer
• finite Reynolds number
• decaying isotropic turbulence

Acknowledgements

The financial support of the ‘Agence Nationale de la Recherche’ (ANR), under the project ‘ANISO’, is gratefully acknowledged. RAA acknowledges the support of the Australian Research Council.