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Asymptotic scaling laws for the irrotational motions bordering a turbulent region

Xavier, R. P., Teixeira, M. A. C. and da Silva, C. B. (2021) Asymptotic scaling laws for the irrotational motions bordering a turbulent region. Journal Of Fluid Mechanics, 918. ISSN 0022-1120

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To link to this item DOI: 10.1017/jfm.2021.296

Abstract/Summary

Turbulent flows are often bounded by regions of irrotational or non-turbulent flow, where the magnitude of the potential velocity fluctuations can be surprisingly high. This includes virtually all turbulent free-shear flows and also turbulent boundary layers, and is particularly true near the so-called turbulent/non-turbulent interface (TNTI) layer, which separates the regions of turbulent and non-turbulent fluid motion. In the present work, we show that in the non-turbulent region and for distances x_2 sufficiently far from the TNTI layer, the asymptotic variation laws for the variance of the velocity fluctuations ⟨u_i^2⟩ (i=1,2,3), Taylor micro-scale λ and viscous dissipation rate ε depend on the shape of the kinetic energy spectrum in the infrared region E(k) ∼ k^n. Specifically, by using rapid distortion theory (RDT), we show that for Saffman turbulence (E(k) ∼ k^2), we obtain the asymptotic laws ⟨u_i^2⟩ ∼ x_2^(−3) (i=1,2,3), λ ∼ x_2 and ε ∼ x_2^(−5). Additionally, we confirm the classical results obtained by Phillips (Proc. Camb. Phil. Soc., vol. 51, 1955, p. 220) for Batchelor turbulence (E(k) ∼ k^4), with ⟨u_i^2⟩ ∼ x_2^(−4) (i=1,2,3), λ ∼ x_2 and ε ∼ x_2^(−6). The new theoretical results are confirmed by direct numerical simulations (DNS) of shear-free turbulence and are shown to be independent of the Reynolds number. Therefore, these results are expected to be valid in other flow configurations, such as in turbulent planar jets or wakes, provided the kinetic energy spectra in the turbulence region can be described by a Batchelor or a Saffman spectrum.

Item Type:Article
Refereed:Yes
Divisions:Science > School of Mathematical, Physical and Computational Sciences > Department of Meteorology
ID Code:97856
Uncontrolled Keywords:Turbulence theory, Shear layer turbulence, Homogeneous turbulence
Publisher:Cambridge University Press

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