Skip to main content
    • Aa
    • Aa

Turbulence dynamics near a turbulent/non-turbulent interface

  • M. A. C. Teixeira (a1) and C. B. da Silva (a2)

The characteristics of the boundary layer separating a turbulence region from an irrotational (or non-turbulent) flow region are investigated using rapid distortion theory (RDT). The turbulence region is approximated as homogeneous and isotropic far away from the bounding turbulent/non-turbulent (T/NT) interface, which is assumed to remain approximately flat. Inviscid effects resulting from the continuity of the normal velocity and pressure at the interface, in addition to viscous effects resulting from the continuity of the tangential velocity and shear stress, are taken into account by considering a sudden insertion of the T/NT interface, in the absence of mean shear. Profiles of the velocity variances, turbulent kinetic energy (TKE), viscous dissipation rate (), turbulence length scales, and pressure statistics are derived, showing an excellent agreement with results from direct numerical simulations (DNS). Interestingly, the normalized inviscid flow statistics at the T/NT interface do not depend on the form of the assumed TKE spectrum. Outside the turbulent region, where the flow is irrotational (except inside a thin viscous boundary layer), decays as , where is the distance from the T/NT interface. The mean pressure distribution is calculated using RDT, and exhibits a decrease towards the turbulence region due to the associated velocity fluctuations, consistent with the generation of a mean entrainment velocity. The vorticity variance and display large maxima at the T/NT interface due to the inviscid discontinuities of the tangential velocity variances existing there, and these maxima are quantitatively related to the thickness of the viscous boundary layer (VBL). For an equilibrium VBL, the RDT analysis suggests that (where is the Kolmogorov microscale), which is consistent with the scaling law identified in a very recent DNS study for shear-free T/NT interfaces.

Corresponding author
Email address for correspondence:
Linked references
Hide All

This list contains references from the content that can be linked to their source. For a full set of references and notes please see the PDF or HTML where available.

1. K. Alvelius 1999 Random forcing of three-dimensional homogeneous turbulence. Phys. Fluids 11 (7), 18801889.

2. G. K. Batchelor & I. Proudman 1954 The effect of rapid distortion of a fluid in turbulent motion. Q. J. Mech. Appl. Maths 7, 83103.

4. P. Burattini , P. Lavoie & R. A. Antonia 2005 On the normalized turbulent energy dissipation rate. Phys. Fluids 17, 098103.

12. T. Ishihara , T. Gotoh & Y. Kaneda 2009 Study of high-Reynolds number isotropic turbulence by direct numerical simulation. Annu. Rev. Fluid Mech. 41, 165180.

16. C. B. da Silva 2009 The behaviour of subgrid-scale models near the turbulent/nonturbulent interface in jets. Phys. Fluids 21, 081702.

17. C. B. da Silva & J. C. F. Pereira 2008 Invariants of the velocity-gradient, rate-of-strain, and rate-of-rotation tensors across the turbulent/nonturbulent interface in jets. Phys. Fluids 20, 055101.

18. C. B. da Silva & R. N. Reis 2011 The role of coherent vortices near the turbulent/nonturbulent interface in a planar jet. Phil. Trans. R. Soc. Lond. A 369, 738753.

19. C. B. da Silva & R. R. Taveira 2010 The thickness of the t/nt interface is equal to the radius of the large vorticity structures near the edge of the shear layer. Phys. Fluids 22, 121702.

21. M. A. C. Teixeira & P. M. A. Miranda 1997 On the entrainment assumption in Schatzmann’s integral plume model. Appl. Sci. Res. 57, 1542.

23. D. Tordella , M. Iovieno & P. R. Bailey 2008 Sufficient condition for Gaussian departure in turbulence. Phys. Rev. E 77, 016309.

27. H. Wang & W. K. George 2002 The integral scale in homogeneous isotropic turbulence. J. Fluid Mech. 459, 429443.

28. J. Westerweel , C. Fukushima , J. M. Pedersen & J. C. R. Hunt 2005 Mechanics of the turbulent–nonturbulent interface of a jet. Phys. Rev. Lett. 95, 174501.

Recommend this journal

Email your librarian or administrator to recommend adding this journal to your organisation's collection.

Journal of Fluid Mechanics
  • ISSN: 0022-1120
  • EISSN: 1469-7645
  • URL: /core/journals/journal-of-fluid-mechanics
Please enter your name
Please enter a valid email address
Who would you like to send this to? *



Full text views

Total number of HTML views: 0
Total number of PDF views: 33 *
Loading metrics...

Abstract views

Total abstract views: 125 *
Loading metrics...

* Views captured on Cambridge Core between September 2016 - 26th May 2017. This data will be updated every 24 hours.