Length scales and eddy viscosities in turbulent free shear flows

Abstract : In the present paper, we address the important point of the proportionality between the longitudinal integral lengthscale ($L$) and the characteristic mean flow width ($\delta$) using experimental data of an axisymmetric wake and a turbulent planar jet. This is a fundamental hypothesis when deriving the self-similar scaling laws in free shear flows, irrespective of turbulence dissipation scaling. We show that $L/\delta$ is indeed constant, at least in a range of streamwise distances between 15 and 50 times the characteristic inlet dimension ($L_{ref}$, nozzle width or wake generator size). Furthermore, we revisit turbulence closure models such as the Prandtl mixing length \cite{prandtl1925} and the constant eddy viscosity in the light of the non-equilibrium dissipation scalings. We show that the mixing length model, with $l_m\sim \delta$, does not comply with the scalings stemming from the non-equilibrium version of the theory; we instead obtain $l_m\sim \delta \sqrt{Re_G/Re_{0\delta}}$, where $Re_G$ and $Re_{0\delta}$ are a global and local Reynolds number, respectively. Similarly, the eddy viscosity model holds in the case of the non-equilibrium version of the theory provided that the eddy viscosity is constant everywhere, not only across sections orthogonal to the streamwise direction as in the equilibrium case. We conclude comparing the results of the different models with each other and with experimental data and with an improved model (following Townsend) that accounts for the intermittency of the flow and corrects for the eddy viscosity variation across the flow boundaries.
Document type :
Preprints, Working Papers, ...

http://hal.univ-grenoble-alpes.fr/hal-02061929
Submitted on : Friday, March 8, 2019 - 2:12:20 PM
Last modification on : Sunday, March 10, 2019 - 1:04:50 AM

Identifiers

• HAL Id : hal-02061929, version 1
• ARXIV : 1811.02444

Citation

Gioacchino Cafiero, Martin Obligado, John Christos Vassilicos. Length scales and eddy viscosities in turbulent free shear flows. 2019. ⟨hal-02061929⟩

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