Length scales in turbulent free shear flows

ABSTRACT

We address the important point of the proportionality between the longitudinal integral lengthscale (L) and the characteristic mean flow width (δ) 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 flow. We show that L/δ is indeed constant, at least in a range of streamwise distances between 15 and 50 times the characteristic inlet dimension. We revisit turbulence closure models such as the Prandtl mixing length and the eddy viscosity in the light of the non-equilibrium dissipation scaling. We show that the mixing length model does not comply with the scalings stemming from the non-equilibrium version of the theory even if it does comply with the theory’s equilibrium version. 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. We conclude by comparing the results of the different models with each other and with experimental data and with an improved model (following Townsend) that corrects for the eddy viscosity by considering the intermittency of the flow.

KEYWORDS:

• Jets
• wakes
• non equilibrium turbulence
• turbulence modeling

Disclosure statement

No potential conflict of interest was reported by the author(s).

ORCID

G. Cafiero  http://orcid.org/0000-0003-1251-4802

M. Obligado  http://orcid.org/0000-0003-3834-3941

Additional information

Funding

GC and JCV were supported by ERC Advanced Grant 320560 awarded to JCV.