Hostname: page-component-745bb68f8f-grxwn Total loading time: 0 Render date: 2025-01-10T05:50:09.907Z Has data issue: false hasContentIssue false
  • English
  • Français

Free-stream coherent structures in a planar jet

Published online by Cambridge University Press:  05 January 2018

Kengo Deguchi Open the ORCID record for Kengo Deguchi [Opens in a new window]  and
Philip Hall
Kengo Deguchi*
Affiliation:
School of Mathematical Sciences, Monash University, Victoria 3800, Australia
Philip Hall
Affiliation:
School of Mathematical Sciences, Monash University, Victoria 3800, Australia Department of Mathematics, Imperial College London, South Kensington Campus, London SW7 2AZ, UK
*
†Email address for correspondence: [email protected]
Get access Rights & Permissions [Opens in a new window]

Abstract

The free-stream coherent structure theory developed by Deguchi & Hall (J. Fluid Mech., vol. 752, 2014, pp. 602–625), valid in the large-Reynolds-number asymptotic limit, is extended and applied to jet flows. It is shown that a nonlinear exact coherent structure can be supported at the edge of the jet, and the structure induces a much bigger streaky flow in the centre of the jet. The lambda-shaped vortices that characterise the coherent structure are qualitatively consistent with those seen in experimental observations. Here a planar incompressible jet is investigated for the sake of simplicity, but the structure we describe could be used as a basis of more complex theories for incompressible and compressible jets of practical importance.

JFM classification

Aerodynamics: Aerodynamics Aerodynamics: High-speed flow Instability: Nonlinear instability
Type
JFM Papers
Information
Journal of Fluid Mechanics , Volume 837 , 25 February 2018 , pp. 916 - 930
Copyright
© 2018 Cambridge University Press 

Access options

Get access to the full version of this content by using one of the access options below. (Log in options will check for institutional or personal access. Content may require purchase if you do not have access.)

References

Ball, C. G., Fellouah, H. & Pollard, A. 2012 The flow field in turbulent round free jets. Prog. Aerosp. Sci. 50, 1–26.10.1016/j.paerosci.2011.10.002Google Scholar
Bickley, W. G. 1937 The plane jet. Phil. Mag. 23, 727–731.Google Scholar
Clenshaw, C. W. & Elliott, D. 1960 A numerical treatment of the Orr–Sommerfeld equation in the case of a laminar jet. Q. J. Mech. Appl. Maths 13, 300–313.Google Scholar
Clever, R. M. & Busse, F. H. 1992 Three-dimensional convection in a horizontal fluid layer subjected to a constant shear. J. Fluid Mech. 234, 511–527.Google Scholar
Cvitanović, P. 2013 Recurrent flows: the clockwork behind turbulence. J. Fluid Mech. 726, 1–4.10.1017/jfm.2013.198Google Scholar
Deguchi, K. & Hall, P. 2014a Free-stream coherent structures in parallel boundary-layer flows. J. Fluid Mech. 752, 602–625.10.1017/jfm.2014.282Google Scholar
Deguchi, K. & Hall, P. 2014b Canonical exact coherent structures embedded in high Reynolds number flows. Phil. Trans. R. Soc. Lond. A 372, 20130352.Google Scholar
Deguchi, K. & Hall, P. 2015a Free-stream coherent structures in growing boundary layers: a link to near-wall streaks. J. Fluid Mech. 778, 451–484.10.1017/jfm.2015.314Google Scholar
Deguchi, K. & Hall, P. 2015b Asymptotic descriptions of oblique coherent states in shear flows. J. Fluid Mech. 782, 356–367.10.1017/jfm.2015.542Google Scholar
Deguchi, K. & Hall, P. 2017 The relationship between free-stream coherent structures and near-wall streaks at high Reynolds numbers. Phil. Trans. R. Soc. Lond. A 375, 20160078.Google Scholar
Deguchi, K., Hall, P. & Walton, A. G. 2013 The emergence of localized vortex–wave interaction states in plane Couette flow. J. Fluid Mech. 721, 58–85.10.1017/jfm.2013.27Google Scholar
Dempsey, L. J., Hall, P. & Deguchi, K. 2017 The excitation of Görtler vortices by free-stream coherent structures. J. Fluid Mech. 826, 60–96.10.1017/jfm.2017.380Google Scholar
Deo, R. C., Mi, J. & Nathan, G. J. 2008 The influence of Reynolds number on a plane jet. J. Fluid Mech. 20, 075108.Google Scholar
Fureby, C. & Grinstein, F. F. 2002 Large eddy simulation of high-Reynolds-number free and wall-bounded flows. J. Comput. Phys. 181, 68–97.10.1006/jcph.2002.7119Google Scholar
Gamard, S., Jung, D. & George, W. K. 2004 Downstream evolution of the most energetic modes in a turbulent axisymmetric jet at high Reynolds number. Part 2. The far-field region. J. Fluid Mech. 514, 205–230.Google Scholar
Gordeyev, S. V. & Thomas, F. O. 2000 Coherent structure in the turbulent planar jet. Part 1. Extraction of proper orthogonal decomposition eigenmodes and their self-similarity. J. Fluid Mech. 414, 145–194.10.1017/S002211200000848XGoogle Scholar
Gordeyev, S. V. & Thomas, F. O. 2002 Coherent structure in the turbulent planar jet. Part 2. Structural topology via POD eigenmode projection. J. Fluid Mech. 460, 349–380.10.1017/S0022112002008364Google Scholar
Gutmark, E. & Wygnanski, I. 1976 The planar turbulent jet. J. Fluid Mech. 73 (3), 465–495.10.1017/S0022112076001468Google Scholar
Hall, P. 1983 The linear development of Görtler vortices in growing boundary layers. J. Fluid Mech. 130, 41–58.10.1017/S0022112083000968Google Scholar
Hall, P. 1988 The nonlinear development of Görtler vortices in growing boundary layers. J. Fluid Mech. 193, 243–266.10.1017/S0022112088002137Google Scholar
Hall, P. & Sherwin, S. 2010 Streamwise vortices in shear flows: harbingers of transition and the skeleton of coherent structures. J. Fluid Mech. 661, 178–205.10.1017/S0022112010002892Google Scholar
Hall, P. & Smith, F. T. 1991 On strongly nonlinear vortex/wave interactions in boundary-layer transition. J. Fluid Mech. 227, 641–666.Google Scholar
Howard, L. N. 1959 Hydrodynamic stability of a jet. J. Math. Phys. 37, 283–298.10.1002/sapm1958371283Google Scholar
Iqbal, M. O. & Thomas, F. O. 2007 Coherent structure in a turbulent jet via a vector implementation of the proper orthogonal decomposition. J. Fluid Mech. 571, 281–326.Google Scholar
Itano, T. & Toh, S. 2001 The dynamics of bursting process in wall turbulence. J. Phys. Soc. Japan 70, 703–716.10.1143/JPSJ.70.703Google Scholar
Jung, D., Gamard, S. & George, W. K. 2004 Downstream evolution of the most energetic modes in a turbulent axisymmetric jet at high Reynolds number. Part 1. The near-field region. J. Fluid Mech. 514, 173–204.Google Scholar
Kawahara, G. & Kida, S. 2001 Periodic motion embedded in plane Couette turbulence: regeneration cycle and burst. J. Fluid Mech. 449, 291–300.Google Scholar
Kawahara, G., Uhlmann, M. & van Veen, L. 2012 The significance of simple invariant solutions in turbulent flows. Annu. Rev. Fluid Mech. 44, 203–225.Google Scholar
Kozlov, V. V., Grek, G. R., Löfdahl, L. L., Chernorai, V. G. & Litvinenko, M. V. 2002 Role of localised streamwise structures in the process of transition to turbulence in boundary layers and jets (review). J. Appl. Mech. Tech. Phys. 43 (2), 224–236.Google Scholar
Le Ribault, C., Sarkar, S. & Stanley, S. A. 1999 Large eddy simulation of a plane jet. Phys. Fluids 11 (10), 3069–3083.Google Scholar
Liepmann, D. & Morteza, G. 1992 The role of streamwise vorticity in the near-field entrainment of round jets. J. Fluid Mech. 245, 643–668.Google Scholar
de Lozar, A., Mellibovsky, M., Avila, M. & Hof, B. 2012 Edge state in pipe flow experiments. Phys. Rev. Lett. 108, 214502.10.1103/PhysRevLett.108.214502Google Scholar
Nagata, M. 1990 Three-dimensional finite-amplitude solutions in plane Couette flow: bifurcation from infinity. J. Fluid Mech. 217, 519–527.Google Scholar
Sakakibara, J. & Anzai, T. 2001 Chain-link-fence structures produced in a jet. Phys. Fluids 13 (6), 1541–1544.10.1063/1.1370391Google Scholar
Sato, H. 1960 The stability and transition of a two-dimensional jet. J. Fluid Mech. 7 (1), 53–80.Google Scholar
Schlichting, H. 1933 Laminare Strahlenausbreitung. Z. Angew. Math. Mech. 13, 260–263.10.1002/zamm.19330130403Google Scholar
Schlichting, H. 1979 Boundary-Layer Theory, 7th edn. McGraw-Hill.Google Scholar
Tatsumi, T. & Kakutani, T. 1958 The stability of a two-dimensional laminar jet. J. Fluid Mech. 4 (3), 261–275.Google Scholar
Thomas, F. O. & Chu, H. C. 1989 An experimental investigation of the transition of a planar jet: subharmonic suppression and upstream feedback. Phys. Fluids A 1, 1566–1587.10.1063/1.857333Google Scholar
Waleffe, F. 2001 Exact coherent structures in channel flow. J. Fluid Mech. 435, 93–102.10.1017/S0022112001004189Google Scholar