Hostname: page-component-669899f699-vbsjw Total loading time: 0 Render date: 2025-04-27T00:53:23.123Z Has data issue: false hasContentIssue false
  • English
  • Français

Transition induced by a bursting vortex ring in channel flow

Published online by Cambridge University Press:  08 May 2024

Boyuan Wang Open the ORCID record for Boyuan Wang [Opens in a new window]  and
Yue Yang Open the ORCID record for Yue Yang [Opens in a new window]
Boyuan Wang
Affiliation:
State Key Laboratory for Turbulence and Complex Systems, College of Engineering, Peking University, Beijing 100871, PR China
Yue Yang*
Affiliation:
State Key Laboratory for Turbulence and Complex Systems, College of Engineering, Peking University, Beijing 100871, PR China HEDPS-CAPT, Peking University, Beijing 100871, PR China
*
†Email address for correspondence: yyg@pku.edu.cn
Get access Rights & Permissions [Opens in a new window]

Abstract

We investigate the influence of vortices remote from the boundary on the near-wall flow dynamics in wall-bounded flows. A vortex ring with precisely controlled local twist is introduced into the outer layer of a channel flow at a moderate Reynolds number. We find that the minimum vorticity flux for triggering the transition to turbulence is significantly reduced from the initial disturbance of an untwisted vortex ring to that of a twisted ring. In particular, the latter disturbance can cause vortex bursting in the early transitional stage. The impact of vortex bursting on the transition process is characterised by the near-wall, wall-normal velocity with the rapid distortion theory. The wall-normal velocity grows during vortex bursting, and leads to streak formation and then the transition to turbulence. The notable wall-normal velocity is induced by the large di-vorticity generated in vortex bursting. We model the growing radial component of the di-vorticity in terms of the local twist, and demonstrate that its surge is due to the generation of highly twisted vortex lines in vortex bursting. Then, we derive that the generation of the di-vorticity in the outer layer enhances the wall-normal velocity in the inner layer via the Poisson equation with the image method and the multipole expansion. Thus, we elucidate that the vortex bursting can have an effect on the transition process.

JFM classification

Vortex Flows: Vortex dynamics Instability: Transition to turbulence Mathematical Foundations: Topological fluid dynamics
Type
JFM Papers
Information
Journal of Fluid Mechanics , Volume 986 , 10 May 2024 , A11
Check for updates
Copyright
© The Author(s), 2024. Published by 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.)

Article purchase

Temporarily unavailable

References

Adrian, R.J. 2007 Hairpin vortex organization in wall turbulence. Phys. Fluids 19, 041301.10.1063/1.2717527CrossRefGoogle Scholar
Adrian, R.J., Meinhart, C.D. & Tomkins, C.D. 2000 Vortex organization in the outer region of the turbulent boundary layer. J. Fluid Mech. 422, 1–54.CrossRefGoogle Scholar
Archer, P.J., Thomas, T.G. & Coleman, G.N. 2008 Direct numerical simulation of vortex ring evolution from the laminar to the early turbulent regime. J. Fluid Mech. 598, 201–226.10.1017/S0022112007009883CrossRefGoogle Scholar
Arendt, S., Fritts, D.C. & Andreassen, Ø. 1997 The initial value problem for Kelvin vortex waves. J. Fluid Mech. 344, 181–212.10.1017/S0022112097005958CrossRefGoogle Scholar
Blanco-Rodríguez, F.J. & Dizès, S.L. 2017 Curvature instability of a curved Batchelor vortex. J. Fluid Mech. 814, 397–415.10.1017/jfm.2017.34CrossRefGoogle Scholar
Boiko, A.V., Westin, K.J.A., Klingmann, B.G.B., Kozlov, V.V. & Alfredsson, P.H. 1994 Experiments in a boundary layer subjected to free stream turbulence. Part 2. The role of TS-waves in the transition process. J. Fluid Mech. 281, 219–245.CrossRefGoogle Scholar
Brandt, L. & Henningson, D.S. 2002 Transition of streamwise streaks in zero-pressure-gradient boundary layers. J. Fluid Mech. 472, 229–261.10.1017/S0022112002002331CrossRefGoogle Scholar
Canuto, C., Hussaini, M.Y., Quarteroni, A. & Zang, T.A. 1988 Spectral Methods in Fluid Dynamics. Springer.10.1007/978-3-642-84108-8CrossRefGoogle Scholar
Cheng, M., Lou, J. & Lim, T.T. 2010 Vortex ring with swirl: a numerical study. Phys. Fluids 22, 097101.CrossRefGoogle Scholar
Cuypers, Y., Maurel, A. & Petitjeans, P. 2003 Vortex burst as a source of turbulence. Phys. Rev. Lett. 91, 194502.CrossRefGoogle ScholarPubMed
Dazin, A., Dupont, P. & Stanislas, M. 2006 Experimental characterization of the instability of the vortex rings. Part 2. Non-linear phase. Exp. Fluids 41, 401–413.10.1007/s00348-006-0166-1CrossRefGoogle Scholar
Deissler, R.G. 2004 Effects of inhomogeneity and of shear flow in weak turbulent fields. Phys. Fluids 4, 1187–1198.10.1063/1.1706194CrossRefGoogle Scholar
Farrell, B.F. & Ioannou, P.J. 2012 Dynamics of streamwise rolls and streaks in turbulent wall-bounded shear flow. J. Fluid Mech. 708, 149–196.10.1017/jfm.2012.300CrossRefGoogle Scholar
Fransson, J.H.M., Matsubara, M. & Alfredsson, P.H. 2005 Transition induced by free-stream turbulence. J. Fluid Mech. 527, 1–25.10.1017/S0022112004002770CrossRefGoogle Scholar
Fukumoto, Y. & Hattori, Y. 2005 Curvature instability of a vortex ring. J. Fluid Mech. 526, 77–115.CrossRefGoogle Scholar
Haidari, A.H. & Smith, C.R. 1994 The generation and regeneration of single hairpin vortices. J. Fluid Mech. 277, 135–162.CrossRefGoogle Scholar
He, G.-S., Wang, J.-J., Pan, C., Feng, L.-H., Gao, Q. & Rinoshika, A. 2017 Vortex dynamics for flow over a circular cylinder in proximity to a wall. J. Fluid Mech. 812, 698–720.CrossRefGoogle Scholar
Hof, B., Juel, A. & Mullin, T. 2003 Scaling of the turbulence transition threshold in a pipe. Phys. Rev. Lett. 91, 244502.CrossRefGoogle Scholar
Hunt, J.C.R. & Durbin, P.A. 1999 Perturbed vortical layers and shear sheltering. Fluid Dyn. Res. 24, 375.CrossRefGoogle Scholar
Hussain, F. 1986 Coherent structures and turbulence. J. Fluid Mech. 173, 303–356.CrossRefGoogle Scholar
Jacobs, R.G. & Durbin, P.A. 2001 Simulations of bypass transition. J. Fluid Mech. 428, 185–212.CrossRefGoogle Scholar
Ji, L. & Van Rees, W.M. 2022 Bursting on a vortex tube with initial axial core-size perturbations. Phys. Rev. Fluids 7, 044704.CrossRefGoogle Scholar
John, D.J. 1998 Classical Electrodynamics, 3rd edn. Wiley.Google Scholar
Kerswell, R.R. 2002 Elliptical instability. Annu. Rev. Fluid Mech. 34, 83–113.CrossRefGoogle Scholar
Kim, J., Moin, P. & Moser, R. 1987 Turbulence statistics in fully developed channel flow at low Reynolds number. J. Fluid Mech. 177, 133–166.CrossRefGoogle Scholar
Kim, K., Adrian, R.J., Balachandar, S. & Sureshkumar, R. 2008 Dynamics of hairpin vortices and polymer-induced turbulent drag reduction. Phys. Rev. Lett. 100, 134504.CrossRefGoogle ScholarPubMed
Landahl, M.T. 1975 Wave breakdown and turbulence. SIAM J. Appl. Maths. 28 (4), 735–756.CrossRefGoogle Scholar
Landahl, M.T. 1980 A note on an algebraic instability of inviscid parallel shear flows. J. Fluid Mech. 98, 243–251.CrossRefGoogle Scholar
Luckring, J.M. 2019 The discovery and prediction of vortex flow aerodynamics. Aeronaut. J. 123, 729–804.CrossRefGoogle Scholar
Melander, M.V. & Hussain, F. 1994 Core dynamics on a vortex column. Fluid Dyn. Res. 13, 1–37.CrossRefGoogle Scholar
Moffatt, H.K. 1967 The interaction of turbulence with strong wind shear. In Proc. URSI-IUGG Int. Colloq. Atmos. Turbul. Radio Wave Propag., pp. 139–154. Nauka.Google Scholar
Mullin, T. 2011 Experimental studies of transition to turbulence in a pipe. Annu. Rev. Fluid Mech. 43, 1–24.CrossRefGoogle Scholar
Nazarenko, S., Kevlahan, N.K.-R. & Dubrulle, B. 1999 WKB theory for rapid distortion of inhomogeneous turbulence. J. Fluid Mech. 390, 325–348.CrossRefGoogle Scholar
Olsthoorn, J. & Dalziel, S.B. 2015 Vortex-ring-induced stratified mixing. J. Fluid Mech. 781, 113–126.CrossRefGoogle Scholar
Omrane, H.B., Ghedamsi, M. & Khenissy, S. 2016 Biharmonic equations under Dirichlet boundary conditions with supercritical growth. Adv. Nonlinear Stud. 16, 175–184.CrossRefGoogle Scholar
Peixinho, J. & Mullin, T. 2006 Decay of turbulence in pipe flow. Phys. Rev. Lett. 96, 094501.CrossRefGoogle ScholarPubMed
Philippe, R.S., Robert, D.M. & Michael, M.R. 1991 Spectral methods for the Navier–Stokes equations with one infinite and two periodic directions. J. Comput. Phys. 96, 297–324.Google Scholar
Ricco, P., Luo, J. & Wu, X. 2011 Evolution and instability of unsteady nonlinear streaks generated by free-stream vortical disturbances. J. Fluid Mech. 677, 1–38.CrossRefGoogle Scholar
Roach, G.F. 1982 Green's Functions. Cambridge University Press.Google Scholar
Rubin, Y., Wygnanski, I.J. & Haritonidis, J.H. 1980 Further observations on transition in a pipe. In Laminar-Turbulent Transition; Proc. IUTAM Symp. Stuggart, FRG, 1979 (ed. R. Eppler & F. Hussein), pp. 19–26. Springer.CrossRefGoogle Scholar
Saffman, P.G. 1981 Dynamics of vorticity. J. Fluid Mech. 106, 49–58.CrossRefGoogle Scholar
Sandham, N.D. & Kleiser, L. 1992 The late stages of transition to turbulence in channel flow. J. Fluid Mech. 245, 319–348.CrossRefGoogle Scholar
Saric, W.S., Reed, H.L. & Kerschen, E.J. 2002 Boundary-layer receptivity to freestream disturbances. Annu. Rev. Fluid Mech. 34, 291–319.CrossRefGoogle Scholar
Savill, A.M. 1987 Recent developments in rapid-distortion theory. Annu. Rev. Fluid Mech. 19, 531–573.CrossRefGoogle Scholar
Schlatter, P., Stolz, S. & Kleiser, L. 2004 LES of transitional flows using the approximate deconvolution model. Intl J. Heat Fluid Flow 25, 549–558.CrossRefGoogle Scholar
Schoppa, W. & Hussain, F. 2002 Coherent structure generation in near-wall turbulence. J. Fluid Mech. 453, 57–108.CrossRefGoogle Scholar
Serrin, J. 1959 Mathematical Principles of Classical Fluid Mechanics, pp. 125–263. Springer.Google Scholar
Shariff, K. & Leonard, A. 1992 Vortex rings. Annu. Rev. Fluid Mech. 24, 235–279.CrossRefGoogle Scholar
Shen, W., Yao, J., Hussain, F. & Yang, Y. 2022 Topological transition and helicity conversion of vortex knots and links. J. Fluid Mech. 943, A41.CrossRefGoogle Scholar
Shen, W., Yao, J., Hussain, F. & Yang, Y. 2023 Role of internal structures within a vortex in helicity dynamics. J. Fluid Mech. 970, A26.CrossRefGoogle Scholar
Sreenivasan, K.R. & Narasimha, R. 1978 Rapid distortion of axisymmetric turbulence. J. Fluid Mech. 84, 497–516.CrossRefGoogle Scholar
Wu, J.Z., Ma, H. & Zhou, M.-D. 2007 Vorticity and Vortex Dynamics. Springer.Google Scholar
Wu, X. 2019 Nonlinear theories for shear flow instabilities: physical insights and practical implications. Annu. Rev. Fluid Mech. 51, 451–485.CrossRefGoogle Scholar
Wu, X. 2023 New insights into turbulent spots. Annu. Rev. Fluid Mech. 55, 45–75.CrossRefGoogle Scholar
Wu, X., Jacobs, R.G., Hunt, J.C.R. & Durbin, P.A. 1999 Simulation of boundary layer transition induced by periodically passing wakes. J. Fluid Mech. 398, 109–153.CrossRefGoogle Scholar
Xiong, S. & Yang, Y. 2019 Construction of knotted vortex tubes with the writhe-dependent helicity. Phys. Fluids 31, 047101.CrossRefGoogle Scholar
Xu, J., Liu, J., Zhang, Z. & Wu, X. 2023 Spatial–temporal transformation for primary and secondary instabilities in weakly non-parallel shear flows. J. Fluid Mech. 959, A21.CrossRefGoogle Scholar
Yang, Y. & Pullin, D.I. 2011 Geometric study of Lagrangian and Eulerian structures in turbulent channel flow. J. Fluid Mech. 674, 67–92.CrossRefGoogle Scholar
Zaki, T.A. 2013 From streaks to spots and on to turbulence: exploring the dynamics of boundary layer transition. Flow Turbul. Combust. 91, 451–473.CrossRefGoogle Scholar
Zaki, T.A. & Durbin, P.A. 2005 Mode interaction and the bypass route to transition. J. Fluid Mech. 531, 85–111.CrossRefGoogle Scholar
Zhao, Y., Xiong, S., Yang, Y. & Chen, S. 2018 Sinuous distortion of vortex surfaces in the lateral growth of turbulent spots. Phys. Rev. Fluids 3, 074701.CrossRefGoogle Scholar
Zhao, Y., Yang, Y. & Chen, S. 2016 Evolution of material surfaces in the temporal transition in channel flow. J. Fluid Mech. 793, 840–876.CrossRefGoogle Scholar
Zhong, X. & Wang, X. 2012 Direct numerical simulation on the receptivity, instability, and transition of hypersonic boundary layers. Annu. Rev. Fluid Mech. 44, 527–561.CrossRefGoogle Scholar
Zhou, J., Adrian, R.J. & Balachandar, S. 1996 Autogeneration of near-wall vortical structures in channel flow. Phys. Fluids 8, 288–290.CrossRefGoogle Scholar
Zhou, J., Adrian, R.J., Balachandar, S. & Kendall, T.M. 1999 Mechanisms for generating coherent packets of hairpin vortices in channel flow. J. Fluid Mech. 387, 353–396.CrossRefGoogle Scholar