Asymptotic scaling laws for the irrotational motions bordering a turbulent region

Lists

Download

Preview

main_PRODUCTION (1).pdf - Accepted Version (5MB) | Preview

Tools

Xavier, R. P., Teixeira, M. A. C. ORCID: https://orcid.org/0000-0003-1205-3233 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 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.

Altmetric Badge

Item Type	Article
URI	https://reading-clone.eprints-hosting.org/id/eprint/97856
Item Type	Article
Refereed	Yes
Divisions	Science > School of Mathematical, Physical and Computational Sciences > Department of Meteorology
Uncontrolled Keywords	Turbulence theory, Shear layer turbulence, Homogeneous turbulence
Publisher	Cambridge University Press
Download/View statistics	View download statistics for this item

Download Statistics

Downloads

Downloads per month over past year

Related URLs

Deposit Details

Date Deposited:	10 May 2021 15:41	Date item deposited into CentAUR
Last Modified:	25 Jan 2025 00:19	Date item last modified

References

ANTONIA, R.A., SHAH, D.A. & BROWNE, L.W.B. 1987 The organized motion outside a turbulent wake. Phys. Fluids 30 (7), 2040–2045. BATCHELOR, G.K. 1953 The Theory of Homogeneous Turbulence. Cambridge University Press. BIRKHOFF, G. 1954 Fourier synthesis of homogeneous turbulence. Commun. Pure Appl. Maths 7 (1), 19–44. BISSET, D.K., HUNT, J.C.R. & ROGERS, M.M. 2002 The turbulent/non-turbulent interface bounding a far wake. J. Fluid Mech. 451, 383–410. BRADBURY, L.J.S. 1965 The structure of a self-preserving turbulent plane jet. J. Fluid Mech. 23 (1), 31–64. BRADSHAW, P. 1967 Irrotational fluctuations near a turbulent boundary layer. J. Fluid Mech. 27 (2), 209–230. CANUTO, C., HUSSAINI, M.Y., QUARTERONI, A. & ZANG, T.A. 1987 Spectral Methods in Fluid Dynamics. Springer-Verlag. CARRUTHERS, D.J. & HUNT, J.C.R. 1986 Velocity fluctuations near an interface between a turbulent region and a stably stratified layer. J. Fluid Mech. 165, 475–501. CIMARELLI, A., COCCONI, G., FROHNAPFEL, B. & ANGELIS, E.D. 2015 Spectral enstrophy budget in a shear-less flow with turbulent/non-turbulent interface. Phys. Fluids 27, 125106. DAVIDSON, P.A. 2004 Turbulence, An Introduction for Scientists and Engineers. Oxford University Press. EYINK, G.L. & THOMSON, D.J. 2000 Free decay of turbulence and breakdown of self-similarity. Phys. Fluids 12, 477–479. FABRIS, G. 1979 Conditional sampling study of the turbulent wake of a cylinder. Part 1. J. Fluid Mech. 94 (4), 673–709. ISHIDA, T., DAVIDSON, P.A. & KANEDA, Y. 2006 On the decay of isotropic turbulence. J. Fluid Mech. 564, 455–475. KOVASZNAY, L.S.G., KIBENS, V. & BLACKWELDER, R.F. 1970 Large-scale motion in the intermittent region of a turbulent boundary layer. J. Fluid Mech. 41 (2), 283–325. LESIEUR, M. 1997 Turbulence in Fluids. 3rd edn. Kluwer. OBERLACK, M. & ZIELENIEWICZ, A. 2013 Statistical symmetries and its impact on new decay modes and integral invariants of decaying turbulence. J. Turbul. 14 (2), 4–22. PEROT, B. & MOIN, P. 1995 Shear-free turbulent boundary layers. Part 1. Physical insights into near-wall turbulence. J. Fluid Mech. 295, 199–227. PHILLIPS, O.M. 1955 The irrotational motion outside a free turbulent boundary. Proc. Camb. Phil. Soc. 51, 220. POPE, S.B. 2000 Turbulent Flows. Cambridge University Press. SAFFMAN, P.G. 1967 The large-scale structure of homogeneous turbulence. J. Fluid Mech. 27, 581–593. DA SILVA, C.B., HUNT, J.C.R., EAMES, I. & WESTERWEEL, J. 2014 Interfacial layers between regions of different turbulent intensity. Annu. Rev. Fluid Mech. 46, 567–590. DA SILVA, C.B., DOS REIS, R.J.N. & PEREIRA, J.C.F. 2011 The intense vorticity structures near the turbulent/non-turbulent interface a jet. J. Fluid Mech. 685, 165–190. SILVA, T.S. & DA SILVA, C.B. 2017 The behaviour of the scalar gradient across the turbulent/non-turbulent interface in jets. Phys. Fluids 29, 085106. SILVA, T.S., ZECCHETTO, M. & DA SILVA, C.B. 2018 The scaling of the turbulent/non-turbulent interface at high reynolds numbers. J. Fluid Mech. 843, 156–179. SUNYACH, M. & MATHIEU, J. 1969 Zone de melange d’un jet plan fluctuations induites dans le cone a potentiel-intermittence. Intl J. Heat Mass Transfer 12 (12), 1679–1697. TAVEIRA, R.R. & DA SILVA, C.B. 2013 Kinetic energy budgets near the turbulent/nonturbulent interface in jets. Phys. Fluids 25, 015114. TEIXEIRA, M.A.C. & DA SILVA, C.B. 2012 Turbulence dynamics near a turbulent/non-turbulent interface. J. Fluid Mech. 695, 257–287. THOMAS, R.M. 1973 Conditional sampling and other measurements in a plane turbulent wake. J. Fluid Mech. 57 (3), 549–582. VASSILICOS, J.C. 2011 An infinity of possible invariants for decaying homogeneous turbulence. Phys. Lett. A 375 (6), 1010–1013. WATANABE, T., JAULINO, R., TAVEIRA, R., DA SILVA, C.B., NAGATA, K. & SAKAI, Y. 2017 Role of an isolated eddy near the turbulent/non-turbulent interface layer. Phys. Rev. Fluids 2, 094607. WATANABE, T., SAKAI, Y., NAGATA, K., ITO, Y. & HAYASE, T. 2014 Enstrophy and passive scalar transport near the turbulent/non-turbulent interface in a turbulent planar jet flow. Phys. Fluids 26, 105103. WESTERWEEL, J., FUKUSHIMA, C., PEDERSEN, J.M. & HUNT, J.C.R. 2005 Mechanics of the turbulent-nonturbulent interface of a jet. Phys. Rev. Lett. 95, 174501. WESTERWEEL, J., FUKUSHIMA, C., PEDERSEN, J.M. & HUNT, J.C.R. 2009 Momentum and scalar transport at the turbulent/non-turbulent interface of a jet. J. Fluid Mech. 631, 199–230. WILLIAMSON, J.H. 1980 Low-storage Runge–Kutta schemes. J. Comput. Phys. 35, 48–56. WYGNANSKI, I. & FIEDLER, H.E. 1970 The two-dimensional mixing region. J. Fluid Mech. 41 (2), 327–361.

University Staff: Request a correction | Centaur Editors: Update this record

Search Google Scholar