Hostname: page-component-76fb5796d-5g6vh Total loading time: 0 Render date: 2024-04-25T21:10:51.073Z Has data issue: false hasContentIssue false
  • English
  • Français

Flow structures in spanwise rotating plane Poiseuille flow based on thermal analogy

Published online by Cambridge University Press:  23 December 2021

Shengqi Zhang ,
Zhenhua Xia Open the ORCID record for Zhenhua Xia [Opens in a new window]  and
Shiyi Chen
Shengqi Zhang
Affiliation:
State Key Laboratory for Turbulence and Complex Systems, Peking University, Beijing 100871, PR China
Zhenhua Xia*
Affiliation:
Department of Engineering Mechanics, Zhejiang University, Hangzhou 310027, PR China
Shiyi Chen
Affiliation:
State Key Laboratory for Turbulence and Complex Systems, Peking University, Beijing 100871, PR China Department of Mechanics and Aerospace Engineering, Southern University of Science and Technology, Shenzhen 518055, PR China
*
†Email address for correspondence: xiazh@zju.edu.cn
Get access Rights & Permissions [Opens in a new window]

Abstract

The analogy between rotating shear flow and thermal convection suggests the existence of plumes, inertial waves and plume currents in plane Poiseuille flow under spanwise rotation. The existence of these flow structures is examined with the results of three-dimensional and two-dimensional three-component direct numerical simulations. The dynamics of plumes near the unstable side is embodied in a truncated exponential distribution of turbulent fluctuations. For large rotation numbers, inertial waves are identified near the stable side, and these can be used to explain the abnormal flow statistics, such as the large root-mean-square of the streamwise velocity fluctuation and the nearly negligible Reynolds shear stress. For small or medium rotation numbers, plumes generated from the unstable side form large-scale plume currents and the patterns of the plume currents show different capabilities in scalar transport.

JFM classification

Convection: Buoyancy-driven instability Turbulent Flows: Rotating turbulence
Type
JFM Papers
Information
Journal of Fluid Mechanics , Volume 933 , 25 February 2022 , A24
Check for updates
Copyright
© The Author(s), 2021. 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.)

References

REFERENCES

Berkooz, G., Holmes, P. & Lumley, J.L. 1993 The proper orthogonal decomposition in the analysis of turbulent flows. Annu. Rev. Fluid Mech. 25 (1), 539–575.CrossRefGoogle Scholar
Bradshaw, P. 1969 The analogy between streamline curvature and buoyancy in turbulent shear flow. J. Fluid Mech. 36 (1), 177–191.CrossRefGoogle Scholar
Brethouwer, G. 2016 Linear instabilities and recurring bursts of turbulence in rotating channel flow simulations. Phys. Rev. Fluids 1 (5), 054404.CrossRefGoogle Scholar
Brethouwer, G. 2017 Statistics and structure of spanwise rotating turbulent channel flow at moderate Reynolds numbers. J. Fluid Mech. 828, 424–458.CrossRefGoogle Scholar
Brethouwer, G. 2018 Passive scalar transport in rotating turbulent channel flow. J. Fluid Mech. 844, 297–322.CrossRefGoogle Scholar
Brethouwer, G. 2019 Influence of spanwise rotation and scalar boundary conditions on passive scalar transport in turbulent channel flow. Phys. Rev. Fluids 4 (1), 014602.CrossRefGoogle Scholar
Brethouwer, G., Schlatter, P., Duguet, Y., Henningson, D.S. & Johansson, A.V. 2014 Recurrent bursts via linear processes in turbulent environments. Phys. Rev. Lett. 112 (14), 144502.CrossRefGoogle ScholarPubMed
Dai, Y.-J., Huang, W.-X. & Xu, C.-X. 2016 Effects of Taylor–Görtler vortices on turbulent flows in a spanwise-rotating channel. Phys. Fluids 28 (11), 115104.CrossRefGoogle Scholar
Greenspan, H.P. 1968 The Theory of Rotating Fluids. CUP Archive.Google Scholar
Greenspan, H.P. 1969 On the non-linear interaction of inertial modes. J. Fluid Mech. 36 (2), 257–264.CrossRefGoogle Scholar
Grundestam, O., Wallin, S. & Johansson, A.V. 2008 Direct numerical simulations of rotating turbulent channel flow. J. Fluid Mech. 598, 177–199.CrossRefGoogle Scholar
He, G., Jin, G. & Yang, Y. 2017 Space-time correlations and dynamic coupling in turbulent flows. Annu. Rev. Fluid Mech. 49, 51–70.CrossRefGoogle Scholar
Hsieh, A. & Biringen, S. 2016 The minimal flow unit in complex turbulent flows. Phys. Fluids 28 (12), 125102.CrossRefGoogle Scholar
Huang, Y., Xia, Z., Wan, M., Shi, Y. & Chen, S. 2019 Hysteresis behavior in spanwise rotating plane Couette flow with varying rotation rates. Phys. Rev. Fluids 4 (5), 052401.CrossRefGoogle Scholar
Huisman, S.G., Van Der Veen, R.C., Sun, C. & Lohse, D. 2014 Multiple states in highly turbulent Taylor–Couette flow. Nat. Commun. 5 (1), 3820.CrossRefGoogle ScholarPubMed
Jain, A.K. 2010 Data clustering: 50 years beyond K-means. Pattern Recogn. Lett. 31 (8), 651–666.CrossRefGoogle Scholar
Jakirlic, S., Hanjalic, K. & Tropea, C. 2002 Modeling rotating and swirling turbulent flows: a perpetual challenge. AIAA J. 40 (10), 1984–1996.CrossRefGoogle Scholar
Johnston, J.P. 1998 Effects of system rotation on turbulence structure: a review relevant to turbomachinery flows. Intl J. Rotating Mach. 4 (2), 97–112.CrossRefGoogle Scholar
Johnston, J.P., Halleent, R.M. & Lezius, D.K. 1972 Effects of spanwise rotation on the structure of two-dimensional fully developed turbulent channel flow. J. Fluid Mech. 56 (3), 533–557.CrossRefGoogle Scholar
Kristoffersen, R. & Andersson, H.I. 1993 Direct simulations of low-Reynolds-number turbulent flow in a rotating channel. J. Fluid Mech. 256, 163–197.CrossRefGoogle Scholar
Lecoanet, D., Le Bars, M., Burns, K.J., Vasil, G.M., Brown, B.P., Quataert, E. & Oishi, J.S. 2015 Numerical simulations of internal wave generation by convection in water. Phys. Rev. E 91 (6), 063016.CrossRefGoogle ScholarPubMed
Liu, N.-S. & Lu, X.-Y. 2007 Direct numerical simulation of spanwise rotating turbulent channel flow with heat transfer. Intl J. Numer. Meth. Fluids 53 (11), 1689–1706.CrossRefGoogle Scholar
Maciel, Y., Picard, D., Yan, G., Gleyzes, C. & Dumas, G. 2003 Fully developed turbulent channel flow subject to system rotation. AIAA Paper 2003-4153.CrossRefGoogle Scholar
Matsubara, M. & Alfredsson, P.H. 1996 Experimental study of heat and momentum transfer in rotating channel flow. Phys. Fluids 8 (11), 2964–2973.CrossRefGoogle Scholar
Nagano, Y. & Hattori, H. 2003 Direct numerical simulation and modelling of spanwise rotating channel flow with heat transfer. J. Turbul. 4, N10.CrossRefGoogle Scholar
Nakabayashi, K. & Kitoh, O. 1996 Low Reynolds number fully developed two-dimensional turbulent channel flow with system rotation. J. Fluid Mech. 315, 1–29.CrossRefGoogle Scholar
Nakabayashi, K. & Kitoh, O. 2005 Turbulence characteristics of two-dimensional channel flow with system rotation. J. Fluid Mech. 528, 355–377.CrossRefGoogle Scholar
Ostilla-Mónico, R., Van Der Poel, E.P., Verzicco, R., Grossmann, S. & Lohse, D. 2014 Exploring the phase diagram of fully turbulent Taylor–Couette flow. J. Fluid Mech. 761, 1–26.CrossRefGoogle Scholar
Sacco, F., Verzicco, R. & Ostilla-Mónico, R. 2019 Dynamics and evolution of turbulent Taylor rolls. J. Fluid Mech. 870, 970–987.CrossRefGoogle Scholar
Schmid, P.J. 2010 Dynamic mode decomposition of numerical and experimental data. J. Fluid Mech. 656, 5–28.CrossRefGoogle Scholar
Tanaka, M., Kida, S., Yanase, S. & Kawahara, G. 2000 Zero-absolute-vorticity state in a rotating turbulent shear flow. Phys. Fluids 12 (8), 1979–1985.CrossRefGoogle Scholar
Taylor, G.I. 1938 The spectrum of turbulence. Proc. R. Soc. Lond. A 164 (919), 476–490.CrossRefGoogle Scholar
Toppaladoddi, S. & Wettlaufer, J.S. 2018 Penetrative convection at high Rayleigh numbers. Phys. Rev. Fluids 3 (4), 043501.CrossRefGoogle Scholar
Towne, A., Schmidt, O.T. & Colonius, T. 2018 Spectral proper orthogonal decomposition and its relationship to dynamic mode decomposition and resolvent analysis. J. Fluid Mech. 847, 821–867.CrossRefGoogle Scholar
Turner, J.S. 1979 Buoyancy Effects in Fluids. Cambridge University Press.Google Scholar
Van Der Poel, E.P., Ostilla-Mónico, R., Donners, J. & Verzicco, R. 2015 A pencil distributed finite difference code for strongly turbulent wall-bounded flows. Comput. Fluids 116, 10–16.CrossRefGoogle Scholar
van der Veen, R.C.A., Huisman, S.G., Merbold, S., Harlander, U., Egbers, C., Lohse, D. & Sun, C. 2016 Taylor–Couette turbulence at radius ratio $\eta =0.5$: scaling, flow structures and plumes. J. Fluid Mech. 799, 334–351.CrossRefGoogle Scholar
Visscher, J., Andersson, H.I., Barri, M., Didelle, H., Viboud, S., Sous, D. & Sommeria, J. 2011 A new set-up for PIV measurements in rotating turbulent duct flows. Flow Meas. Instrum. 22 (1), 71–80.CrossRefGoogle Scholar
Waleffe, F. 1993 Inertial transfers in the helical decomposition. Phys. Fluids A 5 (3), 677–685.CrossRefGoogle Scholar
Wallace, J.M. & Dickinson, R.E. 1972 Empirical orthogonal representation of time series in the frequency domain. Part I: theoretical considerations. J. Appl. Meteorol. Clim. 11 (6), 887–892.2.0.CO;2>CrossRefGoogle Scholar
Wallin, S., Grundestam, O. & Johansson, A.V. 2013 Laminarization mechanisms and extreme-amplitude states in rapidly rotating plane channel flow. J. Fluid Mech. 730, 193–219.CrossRefGoogle Scholar
Wang, Q., Zhou, Q., Wan, Z.-H. & Sun, D.-J. 2019 a Penetrative turbulent Rayleigh–Bénard convection in two and three dimensions. J. Fluid Mech. 870, 718–734.CrossRefGoogle Scholar
Wang, Y., He, X. & Tong, P. 2019 b Turbulent temperature fluctuations in a closed Rayleigh–Bénard convection cell. J. Fluid Mech. 874, 263–284.CrossRefGoogle Scholar
Wen, J., Zhang, W.-Y., Ren, L.-Z., Bao, L.-Y., Dini, D., Xi, H.-D. & Hu, H.-B. 2020 Controlling the number of vortices and torque in Taylor–Couette flow. J. Fluid Mech. 901, A30.CrossRefGoogle Scholar
Xia, Z., Brethouwer, G. & Chen, S. 2018 a High-order moments of streamwise fluctuations in a turbulent channel flow with spanwise rotation. Phys. Rev. Fluids 3 (2), 022601.CrossRefGoogle Scholar
Xia, Z., Shi, Y., Cai, Q., Wan, M. & Chen, S. 2018 b Multiple states in turbulent plane Couette flow with spanwise rotation. J. Fluid Mech. 837, 477–490.CrossRefGoogle Scholar
Xia, Z., Shi, Y. & Chen, S. 2016 Direct numerical simulation of turbulent channel flow with spanwise rotation. J. Fluid Mech. 788, 42–56.CrossRefGoogle Scholar
Yang, Y.-T. & Wu, J.-Z. 2012 Channel turbulence with spanwise rotation studied using helical wave decomposition. J. Fluid Mech. 692, 137–152.CrossRefGoogle Scholar
Zhang, S., Chen, X., Xia, Z., Xi, H.-D., Zhou, Q. & Chen, S. 2021 Stabilizing/destabilizing the large-scale circulation in turbulent Rayleigh–Bénard convection with sidewall temperature control. J. Fluid Mech. 915, A14.CrossRefGoogle Scholar
Zhang, S., Xia, Z., Shi, Y. & Chen, S. 2019 A two-dimensional-three-component model for spanwise rotating plane Poiseuille flow. J. Fluid Mech. 880, 478–496.CrossRefGoogle Scholar
Zhang, Y.-Z., Sun, C., Bao, Y. & Zhou, Q. 2018 How surface roughness reduces heat transport for small roughness heights in turbulent Rayleigh–Bénard convection. J. Fluid Mech. 836, R2.CrossRefGoogle Scholar
Zhu, X., Stevens, R.J.A.M., Shishkina, O., Verzicco, R. & Lohse, D. 2019 $Nu\sim Ra^{1/2}$ scaling enabled by multiscale wall roughness in Rayleigh–Bénard turbulence. J. Fluid Mech. 869, R4.CrossRefGoogle Scholar

Zhang et al. supplementary movie 1

Contour of $u'$ in the $y-z$ plane from the 2-D case at $Re_\tau=180, Ro_\tau=5$. The dashed and dash-dotted lines denote the horizontal locations at $y=y_1$ and $y=y_2$ with $N_b(y_1)=0.1N_b(-1)$ and $N_b(y_2)=0.1N_b(1)$ respectively.

Download Zhang et al. supplementary movie 1(Video)
Video 8 MB

Zhang et al. supplementary movie 2

Contour of $u'$ in the $y-z$ plane from the 2-D case at $Re_\tau=180, Ro_\tau=40$. The dashed and dash-dotted lines denote the horizontal locations at $y=y_1$ and $y=y_2$ with $N_b(y_1)=0.1N_b(-1)$ and $N_b(y_2)=0.1N_b(1)$ respectively.

Download Zhang et al. supplementary movie 2(Video)
Video 8.1 MB

Zhang et al. supplementary movie 3

Contour of $u'$ in the $y-z$ plane at $x=0$ from the 3-D case at $Re_\tau=180, Ro_\tau=5$. The dashed and dash-dotted lines denote the horizontal locations at $y=y_1$ and $y=y_2$ with $N_b(y_1)=0.1N_b(-1)$ and $N_b(y_2)=0.1N_b(1)$ respectively.

Download Zhang et al. supplementary movie 3(Video)
Video 8.2 MB

Zhang et al. supplementary movie 4

Contour of $u'$ in the $y-z$ plane at $x=0$ from the 3-D case at $Re_\tau=180, Ro_\tau=40$. The dashed and dash-dotted lines denote the horizontal locations at $y=y_1$ and $y=y_2$ with $N_b(y_1)=0.1N_b(-1)$ and $N_b(y_2)=0.1N_b(1)$ respectively.

Download Zhang et al. supplementary movie 4(Video)
Video 8.4 MB
Supplementary material: PDF

Zhang et al. supplementary material

Captions for movies 1-4

Download Zhang et al. supplementary material(PDF)
PDF 13.3 KB