- Physical Review Journals
All JournalsPhysics Magazine
Access Provided by Xinjiang University

Physical Review Fluids

Export citation

Export citation

Choose format for download:

Download Citation
  • Access by Xinjiang University

Role of an isolated eddy near the turbulent/non-turbulent interface layer

T. Watanabe1,2,*, R. Jaulino2, R. R. Taveira2, C. B. da Silva1,2, K. Nagata1, and Y. Sakai3

  • 1Department of Aerospace Engineering, Nagoya University, 464-8603 Nagoya, Japan
  • 2LAETA, IDMEC, Instituto Superior Técnico, Universidade de Lisboa, Avenida Rovisco Pais, 1049-001 Lisboa, Portugal
  • 3Department of Mechanical Science and Engineering, Nagoya University, 464-8603 Nagoya, Japan

  • *watanabe.tomoaki@c.nagoya-u.jp
PDF

Phys. Rev. Fluids 2, 094607 – Published 25 September, 2017

DOI: https://doi.org/10.1103/PhysRevFluids.2.094607

Abstract

A simple analytical description for the effects of a single vortex near a turbulent/non-turbulent interface (TNTI) layer, based on a Burgers vortex (BV) model, is compared with results from direct numerical simulation (DNS) of shear-free turbulence. The BV model parameters are derived from the DNS data, and the model separates the entrainment as a two-stage process: (i) the strain imposed on the vortex draws non-turbulent fluid toward the irrotational boundary that separates the irrotational from the turbulent region, and afterwards (ii) the velocity associated with the vorticity field moves the entrained fluid toward the turbulent core region. The resulting model is able to predict the enstrophy dynamics, flow streamlines, and flow topology—such as the formation of the teardrop map in the invariants of the velocity gradient tensor—as well as the entrainment velocity. The BV model provides an interesting framework to analyze the small-scale “nibbling” eddy motions near the TNTI and allows the inclusion of the large-scale flow-dependent effects imposed by the strain rate, while it also links the entrainment characteristics to the eddy structure of the flow near TNTIs.

View figure in article

Physics Subject Headings (PhySH)

Article Text

References (33)

  1. C. B. da Silva, J. C. R. Hunt, I. Eames, and J. Westerweel, Interfacial layers between regions of different turbulence intensity, Annu. Rev. Fluid Mech. 46, 567 (2014).
  2. C. B. da Silva, R. R. Taveira, and G. Borrell, Characteristics of the turbulent/nonturbulent interface in boundary layers, jets and shear-free turbulence, J. Phys. Conf. Ser. 506, 012015 (2014).
  3. A. Attili, J. C. Cristancho, and F. Bisetti, Statistics of the turbulent/non-turbulent interface in a spatially developing mixing layer, J. Turbul. 15, 555 (2014).
  4. M. Gampert, J. Boschung, F. Hennig, M. Gauding, and N. Peters, The vorticity versus the scalar criterion for the detection of the turbulent/non-turbulent interface, J. Fluid Mech. 750, 578 (2014).
  5. G. Borrell and J. Jiménez, Properties of the turbulent/non-turbulent interface in boundary layers, J. Fluid Mech. 801, 554 (2008).
  6. J. Westerweel, C. Fukushima, J. M. Pedersen, and J. C. R. Hunt, Momentum and scalar transport at the turbulent/non-turbulent interface of a jet, J. Fluid Mech. 631, 199 (2009).
  7. M. Holzner and B. Lüthi, Laminar Superlayer at the Turbulence Boundary, Phys. Rev. Lett. 106, 134503 (2011).
  8. K. Chauhan, J. Philip, C. M. da Silva, N. Hutchins, and I. Marusic, The turbulent/non-turbulent interface and entrainment in a boundary layer, J. Fluid Mech. 742, 119 (2014).
  9. D. Mistry, J. Philip, J. R. Dawson, and I. Marusic, Entrainment at multi-scales across the turbulent/non-turbulent interface in an axisymmetric jet, J. Fluid Mech. 802, 690 (2016).
  10. T. Watanabe, C. B. da Silva, Y. Sakai, K. Nagata, and T. Hayase, Lagrangian properties of the entrainment across turbulent/non-turbulent interface layers, Phys. Fluids 28, 031701 (2016).
  11. C. B. da Silva, R. J. N. Dos Reis, and J. C. F. Pereira, The intense vorticity structures near the turbulent/non-turbulent interface in a jet, J. Fluid Mech. 685, 165 (2011).
  12. R. Jahanbakhshi, N. S. Vaghefi, and C. K. Madnia, Baroclinic vorticity generation near the turbulent/non-turbulent interface in a compressible shear layer, Phys. Fluids 27, 105105 (2015).
  13. T. Watanabe, C. B. da Silva, K. Nagata, and Y. Sakai, Geometrical aspects of turbulent/non-turbulent interfaces with and without mean shear, Phys. Fluids 29, 085105 (2017).
  14. J. Philip and I. Marusic, Large-scale eddies and their role in entrainment in turbulent jets and wakes, Phys. Fluids 24, 055108 (2012).
  15. M. A. C. Teixeira and C. B. da Silva, Turbulence dynamics near a turbulent/non-turbulent interface, J. Fluid Mech. 695, 257 (2012).
  16. P. A. Davidson, Turbulence: An Introduction for Scientists and Engineers (Oxford University Press, Oxford, U.K., 2004).
  17. R. R. Taveira and C. B. da Silva, Characteristics of the viscous superlayer in shear free turbulence and in planar turbulent jets, Phys. Fluids 26, 021702 (2014).
  18. T. Watanabe, Y. Sakai, K. Nagata, Y. Ito, and T. Hayase, Turbulent mixing of passive scalar near turbulent and non-turbulent interface in mixing layers, Phys. Fluids 27, 085109 (2015).
  19. R. R. Taveira, J. S. Diogo, D. C. Lopes, and C. B. da Silva, Lagrangian statistics across the turbulent-nonturbulent interface in a turbulent plane jet, Phys. Rev. E 88, 043001 (2013).
  20. T. Watanabe, Y. Sakai, K. Nagata, Y. Ito, and T. Hayase, Enstrophy and passive scalar transport near the turbulent/non-turbulent interface in a turbulent planar jet flow, Phys. Fluids 26, 105103 (2014).
  21. M. Wolf, M. Holzner, B. Lüthi, D. Krug, W. Kinzelbach, and A. Tsinober, Effects of mean shear on the local turbulent entrainment process, J. Fluid Mech. 731, 95 (2013).
  22. J. Jimenez and A. A. Wray, On the characteristics of vortex filaments in isotropic turbulence, J. Fluid Mech. 373, 255 (1998).
  23. A. Vincent and M. Meneguzzi, The dynamics of vorticity tubes in homogeneous turbulence, J. Fluid Mech. 258, 245 (1994).
  24. C. B. da Silva and J. C. F. Pereira, Invariants of the velocity-gradient, rate-of-strain, and rate-of-rotation tensors across the turbulent/nonturbulent interface in jets, Phys. Fluids 20, 055101 (2008).
  25. J. Martín, A. Ooi, M. S. Chong, and J. Soria, Dynamics of the velocity gradient tensor invariants in isotropic turbulence, Phys. Fluids 10, 2336 (1998).
  26. J. Soria, R. Sondergaard, B. J. Cantwell, M. S. Chong, and A. E. Perry, A study of the fine-scale motions of incompressible time-developing mixing layers, Phys. Fluids 6, 871 (1994).
  27. H. M. Blackburn, N. N. Mansour, and B. J. Cantwell, Topology of fine-scale motions in turbulent channel flow, J. Fluid Mech. 310, 269 (1996).
  28. J. Soria, A. Ooi, and M. S. Chong, Volume integrals of the QA−RA invariants of the velocity gradient tensor in incompressible flows, Fluid Dyn. Res. 19, 219 (1997).
  29. G. E. Elsinga and I. Marusic, Universal aspects of small-scale motions in turbulence, J. Fluid Mech. 662, 514 (2010).
  30. T. Watanabe, Y. Sakai, K. Nagata, Y. Ito, and T. Hayase, Vortex stretching and compression near the turbulent/nonturbulent interface in a planar jet, J. Fluid Mech. 758, 754 (2014).
  31. B. Ganapathisubramani, K. Lakshminarasimhan, and N. T. Clemens, Investigation of three-dimensional structure of fine scales in a turbulent jet by using cinematographic stereoscopic particle image velocimetry, J. Fluid Mech. 598, 141 (2008).
  32. J. Philip, I. Bermejo-Moreno, D. Chung, and I. Marusic, Characteristics of the entrainment velocity in a developing wake, in Proceedings of the Ninth International Symposium on Turbulence and Shear Flow Phenomena (TSFP-9), Melbourne, Australia (University of Melbourne, 2015), Vol, 3, paper 9C-5.
  33. T. Watanabe, J. J. Riley, and K. Nagata, Effects of stable stratification on turbulent/nonturbulent interfaces in turbulent mixing layers, Phys. Rev. Fluids 1, 044301 (2016).

Outline

Information

Phys. Rev. Fluids 2, 094607– Published 25 September, 2017
  • Received 10 December 2016

©2017 American Physical Society

Sign In to Your Journals Account

Filter

Filter

Article Lookup

Enter a citation