Publikationsserver der Universitätsbibliothek Marburg
Titel:Momentum Transport in Rotating Shear Turbulence
Autor:Brauckmann, Hannes Jörn
Weitere Beteiligte: Eckhardt, Bruno (Prof. Dr.)
Veröffentlicht:2016
URI:https://archiv.ub.uni-marburg.de/diss/z2016/0238
URN: urn:nbn:de:hebis:04-z2016-02383
DOI: https://doi.org/10.17192/z2016.0238
DDC:530 Physik
Titel (trans.):Impulstransport in rotierender Scherturbulenz
Publikationsdatum:2016-06-14
Lizenz:https://rightsstatements.org/vocab/InC-NC/1.0/

Dokument

Schlagwörter:
Physics, Strömungsmechanik, Rotating turbulence, Taylor-Couette-Strömung, Turbulenz, Fluid mechanics, Direct numerical simulations, Physik, Taylor-Couette flow

Summary:
In turbulent shear flows, the interaction of vortices with a solid surface determines the drag exerted by the fluid. In many practical examples, wall curvature or additional body forces influence the flow and consequently change the drag. Therefore, understanding the connection between the turbulent motion and the drag force (or torque) represents an important task for fluid dynamics research. We study this connection in Taylor-Couette flow, the motion of a fluid between two independently rotating concentric cylinders, which serves as a fundamental model system to analyse the effects of wall curvature and system rotation on the turbulence and angular momentum transport resulting in the torque. Differential rotation, mean rotation and curvature of the cylinders can be varied independently by means of the shear Reynolds number Re_S, rotation number R_Ω and radius ratio η. Because of its large parameter space, the Taylor-Couette flow shows a variety of turbulent phenomena that we study in direct numerical simulations using a spectral method. Furthermore, we introduce physical models to explain the observed turbulent behaviour.

Bibliographie / References

  1. Esser, A. & Grossmann, S. (1996). Analytic expression for Taylor-Couette stability boundary. Phys. Fluids 8: 1814-1819 (cit. on pp. 6, 43, 79, 85, 86, 90, 95).
  2. Paoletti, M. S., van Gils, D. P. M., Dubrulle, B., Sun, C., Lohse, D. & Lathrop, D. P. (2012). Angular momentum transport and turbulence in laboratory models of Keplerian flows. Astron. Astrophys. 547: A64 (cit. on pp. 26, 33, 55, 62, 81).
  3. Paoletti, M. S. & Lathrop, D. P. (2011). Angular momentum transport in turbulent flow between independently rotating cylinders. Phys. Rev. Lett. 106: 024501 (cit. on pp. 3, 9, 26, 33-36, 40, 41, 45, 48, 62, 103, 104).
  4. Tong, P., Goldburg, W. I., Huang, J. S. & Witten, T. A. (1990). Anisotropy in turbulent drag reduction. Phys. Rev. Lett. 65: 2780-2783 (cit. on p. 12).
  5. Coles, D. (1967). A note on Taylor instability in circular Couette flow. J. Appl. Mech. 34: 529-534 (cit. on p. 5).
  6. Moser, R. D., Moin, P. & Leonard, A. (1983). A spectral numerical method for the Navier-Stokes equations with applications to TaylorCouette flow. J. Comput. Phys. 52: 524-544 (cit. on p. 15).
  7. Prandtl, L. (1905). Über Flüssigkeitsbewegung bei sehr kleiner Reibung. Verhandlungen des III. Int. Math. Kongress, Heidelberg 1904. B. G. Teubner, 484-491 (cit. on p. 10).
  8. Nagata, M. (1986). Bifurcations in Couette flow between almost corotating cylinders. J. Fluid Mech. 169: 229-250 (cit. on pp. 5, 6).
  9. Koschmieder, E. L. (1993). Bénard cells and Taylor vortices. Cambridge University Press (cit. on pp. 3, 24, 35).
  10. Ostilla-Mónico, R., van der Poel, E. P., Verzicco, R., Grossmann, S. & Lohse, D. (2014b). Boundary layer dynamics at the transition between the classical and the ultimate regime of Taylor-Couette flow. Phys. Fluids 26: 015114 (cit. on pp. 80, 92, 93, 95).
  11. Van Driest, E. R. & Blumer, C. B. (1963). Boundary layer transition: Freestream turbulence and pressure gradient effects. AIAA J. 1: 1303- 1306 (cit. on p. 90).
  12. Busse, F. H. (1970). Bounds for turbulent shear flow. J. Fluid Mech. 41: 219- 240 (cit. on p. 8).
  13. Van den Berg, T. H., van Gils, D. P. M., Lathrop, D. P. & Lohse, D. (2007). Bubbly turbulent drag reduction is a boundary layer effect. Phys. Rev. Lett. 98: 084501 (cit. on p. 12).
  14. Gibson, J. F. (2012). Channelflow: A spectral Navier-Stokes simulator in C++. Tech. rep. U. New Hampshire (cit. on p. 28).
  15. Boyd, J. P. (2000). Chebyshev and Fourier spectral methods. 2nd ed. Dover Publications (cit. on pp. 16, 18, 22).
  16. Tokgöz, S. (2014). Coherent structures in Taylor-Couette flow: Experimental investigation. PhD thesis. Delft University of Technology (cit. on p. 11).
  17. Barri, M. & Andersson, H. I. (2010). Computer experiments on rapidly rotating plane Couette flow. Commun. Comput. Phys. 7: 683-717 (cit. on p. 52).
  18. Howard, L. N. (1966). Convection at high Rayleigh number. Applied Mechanics. Springer, 1109-1115 (cit. on pp. 10, 79, 83).
  19. Mallock, A. (1888). Determination of the viscosity of water. Proc. R. Soc. London A 45: 126-132 (cit. on p. 2).
  20. Dubrulle, B. (1993). Differential rotation as a source of angular momentum transfer in the solar nebula. Icarus 106: 59-76 (cit. on p. 59).
  21. Dong, S. & Zheng, X. (2011). Direct numerical simulation of spiral turbulence. J. Fluid Mech. 668: 150-173 (cit. on p. 35).
  24. Bilson, M. & Bremhorst, K. (2007). Direct numerical simulation of turbulent Taylor-Couette flow. J. Fluid Mech. 579: 227-270 (cit. on pp. 29, 45, 75).
  25. Brauckmann, H. J. & Eckhardt, B. (2013a). Direct numerical simulations of local and global torque in Taylor-Couette flow up to Re = 30 000. J. Fluid Mech. 718: 398-427 (cit. on pp. 3, 9, 11, 16, 20, 21, 24, 26, 28, 30, 31, 33, 35, 36, 40, 49, 52, 54, 65, 71, 104, 117).
  26. Bottin, S., Daviaud, F., Manneville, P. & Dauchot, O. (1998). Discontinuous transition to spatiotemporal intermittency in plane Couette flow. Europhys. Lett. 43: 171-176 (cit. on p. 3).
  27. Taylor, G. I. (1935). Distribution of velocity and temperature between concentric rotating cylinders. Proc. R. Soc. London A 151: 494-512 (cit. on pp. 69, 71, 82, 83).
  28. Avila, M., Meseguer, A. & Marques, F. (2006). Double Hopf bifurcation in corotating spiral Poiseuille flow. Phys. Fluids 18: 064101 (cit. on p. 16).
  29. Van den Berg, T. H., Luther, S., Lathrop, D. P. & Lohse, D. (2005). Drag reduction in bubbly Taylor-Couette turbulence. Phys. Rev. Lett. 94: 044501 (cit. on p. 12).
  30. Fenstermacher, P. R., Swinney, H. L. & Gollub, J. P. (1979). Dynamical instabilities and the transition to chaotic Taylor vortex flow. J. Fluid Mech. 94: 103-128 (cit. on p. 3).
  31. Martínez-Arias, B., Peixinho, J., Crumeyrolle, O. & Mutabazi, I. (2014). Effect of the number of vortices on the torque scaling in Taylor-Couette flow. J. Fluid Mech. 748: 756-767 (cit. on pp. 11, 65).
  32. Ostilla-Mónico, R., Verzicco, R. & Lohse, D. (2015). Effects of the computational domain size on direct numerical simulations of TaylorCouette turbulence with stationary outer cylinder. Phys. Fluids 27: 025110 (cit. on pp. 24, 25, 28).
  33. Doering, C. R. & Constantin, P. (1992). Energy dissipation in shear driven turbulence. Phys. Rev. Lett. 69: 1648-1651 (cit. on p. 8).
  34. Goharzadeh, A. & Mutabazi, I. (2001). Experimental characterization of intermittency regimes in the Couette-Taylor system. Eur. Phys. J. B 19: 157-162 (cit. on p. 3).
  35. Hiwatashi, K., Alfredsson, P. H., Tillmark, N. & Nagata, M. (2007). Experimental observations of instabilities in rotating plane Couette flow. Phys. Fluids 19: 048103 (cit. on p. 6).
  36. Kitoh, O. & Umeki, M. (2008). Experimental study on large-scale streak structure in the core region of turbulent plane Couette flow. Phys. Fluids 20: 025107 (cit. on p. 11).
  37. Mallock, A. (1896). Experiments on fluid viscosity. Philos. Trans. R. Soc. London A 187: 41-56 (cit. on p. 2).
  38. Donnelly, R. J. & Fultz, D. (1960). Experiments on the stability of viscous flow between rotating cylinders. II. Visual observations. Proc. R. Soc. London A 258: 101-123 (cit. on pp. 43, 85).
  39. Tillmark, N. & Alfredsson, P. H. (1992). Experiments on transition in plane Couette flow. J. Fluid Mech. 235: 89-102 (cit. on p. 3).
  40. Van Atta, C. (1966). Exploratory measurements in spiral turbulence. J. Fluid Mech. 25: 495-512 (cit. on pp. 3, 10, 35).
  41. Ostilla-Mónico, R., van der Poel, E. P., Verzicco, R., Grossmann, S. & Lohse, D. (2014c). Exploring the phase diagram of fully turbulent Taylor-Couette flow. J. Fluid Mech. 761: 1-26 (cit. on pp. 3, 27, 47, 66).
  42. Cox, S. M. & Matthews, P. C. (2002). Exponential time differencing for stiff systems. J. Comput. Phys. 176: 430-455 (cit. on p. 16).
  43. Meseguer, A., Mellibovsky, F., Avila, M. & Marques, F. (2009a). Families of subcritical spirals in highly counter-rotating Taylor-Couette flow. Phys. Rev. E 79: 036309 (cit. on p. 16).
  44. Hof, B., Westerweel, J., Schneider, T. M. & Eckhardt, B. (2006). Finite lifetime of turbulence in shear flows. Nature 443: 59-62 (cit. on p. 3).
  45. Andereck, C. D., Liu, S. S. & Swinney, H. L. (1986). Flow regimes in a circular Couette system with independently rotating cylinders. J. Fluid Mech. 164: 155-183 (cit. on pp. 3, 4, 6, 35).
  46. Tsukahara, T., Tillmark, N. & Alfredsson, P. H. (2010). Flow regimes in a plane Couette flow with system rotation. J. Fluid Mech. 648: 5-33 (cit. on p. 6).
  47. Eckhardt, B., Grossmann, S. & Lohse, D. (2007a). Fluxes and energy dissipation in thermal convection and shear flows. Europhys. Lett. 78: 24001 (cit. on pp. 8, 57).
  48. Duguet, Y., Schlatter, P. & Henningson, D. S. (2010). Formation of turbulent patterns near the onset of transition in plane Couette flow. J. Fluid Mech. 650: 119-129 (cit. on p. 3).
  49. Blasius, H. (1908). Grenzschichten in Flüssigkeiten mit kleiner Reibung. Z. Math. Phys. 56: 1-37 (cit. on p. 10).
  50. Ahlers, G., Grossmann, S. & Lohse, D. (2009). Heat transfer and large scale dynamics in turbulent Rayleigh-Bénard convection. Rev. Mod. Phys. 81: 503-537 (cit. on pp. 45, 66).
  51. Avila, K. & Hof, B. (2013). High-precision Taylor-Couette experiment to study subcritical transitions and the role of boundary conditions and size effects. Rev. Sci. Instrum. 84: 065106 (cit. on p. 3).
  52. Grossmann, S., Lohse, D. & Sun, C. (2016). High-Reynolds number Taylor-Couette turbulence. Annu. Rev. Fluid Mech. 48: 53-80 (cit. on p. 12).
  53. Smits, A. J., McKeon, B. J. & Marusic, I. (2011). High-Reynolds number wall turbulence. Annu. Rev. Fluid Mech. 43: 353-375 (cit. on p. 11).
  54. Chandrasekhar, S. (1961). Hydrodynamic and Hydromagnetic Stability. 1st ed. Clarendon Press (cit. on pp. 11, 38, 42, 71, 79, 88, 95).
  55. Heinrichs, W. (1989). Improved condition number for spectral methods. Math. Comput. 53: 103-119 (cit. on p. 16).
  56. Ravelet, F., Delfos, R. & Westerweel, J. (2010). Influence of global rotation and Reynolds number on the large-scale features of a turbulent Taylor-Couette flow. Phys. Fluids 22: 055103 (cit. on pp. 3, 11, 47, 51, 55, 62, 68).
  57. Meseguer, A., Mellibovsky, F., Avila, M. & Marques, F. (2009b). Instability mechanisms and transition scenarios of spiral turbulence in TaylorCouette flow. Phys. Rev. E 80: 046315 (cit. on pp. 3, 16, 35).
  58. Brauckmann, H. J. & Eckhardt, B. (2013b). Intermittent boundary layers and torque maxima in Taylor-Couette flow. Phys. Rev. E 87: 033004 (cit. on pp. 11, 27, 35, 38, 39, 51, 52, 60, 64-66, 68, 76, 79, 81, 103, 117).
  59. Monty, J. P., Stewart, J. A., Williams, R. C. & Chong, M. S. (2007). Largescale features in turbulent pipe and channel flows. J. Fluid Mech. 589: 147-156 (cit. on p. 11).
  60. Prigent, A., Grégoire, G., Chaté, H., Dauchot, O. & van Saarloos, W. (2002). Large-scale finite-wavelength modulation within turbulent shear flows. Phys. Rev. Lett. 89: 014501 (cit. on p. 3).
  61. Boersma, B. J. (2015). Large scale motions in the direct numerical simulation of turbulent pipe flow. Direct and Large-Eddy Simulation IX. Springer, 243-249 (cit. on p. 11).
  62. Meseguer, A. & Trefethen, L. N. (2003). Linearized pipe flow to Reynolds number 107. J. Comput. Phys. 186: 178-197 (cit. on p. 15).
  63. Burin, M. J., Schartman, E. & Ji, H. (2010). Local measurements of turbulent angular momentum transport in circular Couette flow. Exp. Fluids 48: 763-769 (cit. on pp. 3, 75).
  64. Eckhardt, B. & Yao, D. (1995). Local stability analysis along Lagrangian paths. Chaos, Solitons & Fractals 5: 2073-2088 (cit. on pp. 59, 60).
  65. Huisman, S. G., Scharnowski, S., Cierpka, C., Kähler, C. J., Lohse, D. & Sun, C. (2013). Logarithmic boundary layers in strong Taylor-Couette turbulence. Phys. Rev. Lett. 110: 264501 (cit. on pp. 10, 23).
  66. Ahlers, G., Bodenschatz, E., Funfschilling, D., Grossmann, S., He, X., Lohse, D., Stevens, R. J. A. M. & Verzicco, R. (2012). Logarithmic temperature profiles in turbulent Rayleigh-Bénard convection. Phys. Rev. Lett. 109: 114501 (cit. on p. 70).
  67. Prigent, A., Grégoire, G., Chaté, H. & Dauchot, O. (2003). Longwavelength modulation of turbulent shear flows. Physica D 174: 100-113 (cit. on p. 3).
  68. Barcilon, A., Brindley, J., Lessen, M. & Mobbs, F. R. (1979). Marginal instability in Taylor-Couette flows at a very high Taylor number. J. Fluid Mech. 94: 453-463 (cit. on p. 35).
  69. Brauckmann, H. J. & Eckhardt, B. (2016). Marginally stable and turbulent boundary layers in low-curvature Taylor-Couette flow. Manuscript in preparation (cit. on p. 118).
  70. Lellep, G. M. (2015). Marginally stable velocity profiles in Taylor-Couette flow. Bachelor thesis. Philipps-Universität Marburg (cit. on p. 101).
  71. Avila, M., Belisle, M. J., Lopez, J. M., Marques, F. & Saric, W. S. (2008). Mode competition in modulated Taylor-Couette flow. J. Fluid Mech. 601: 381-406 (cit. on p. 16).
  72. Dubrulle, B. & Hersant, F. (2002). Momentum transport and torque scaling in Taylor-Couette flow from an analogy with turbulent convection. Eur. Phys. J. B 26: 379-386 (cit. on pp. 8, 9, 57).
  73. Brauckmann, H. J., Salewski, M. & Eckhardt, B. (2016). Momentum transport in Taylor-Couette flow with vanishing curvature. J. Fluid Mech. 790: 419-452 (cit. on pp. 26, 51, 118).
  74. Huisman, S. G., van der Veen, R. C. A., Sun, C. & Lohse, D. (2014). Multiple states in highly turbulent Taylor-Couette flow. Nat. Commun. 5: 3820 (cit. on pp. 11, 24, 27, 35, 47, 66).
  75. Avila, M. (2008). Nonlinear dynamics of mode competition in annular flows. PhD thesis. Polytechnic University of Catalonia (cit. on pp. 15, 16).
  76. Orszag, S. A. & Israeli, M. (1974). Numerical simulation of viscous incompressible flows. Annu. Rev. Fluid Mech. 6: 281-318 (cit. on p. 22).
  77. Meseguer, A. & Mellibovsky, F. (2007). On a solenoidal Fourier-Chebyshev spectral method for stability analysis of the Hagen-Poiseuille flow. Appl. Numer. Math. 57: 920-938 (cit. on pp. 15, 16).
  78. Rayleigh, L. (1917). On the dynamics of revolving fluids. Proc. R. Soc. London A 93: 148-154 (cit. on pp. 42, 71, 82, 84).
  79. Jeong, J. & Hussain, F. (1995). On the identification of a vortex. J. Fluid Mech. 285: 69-94 (cit. on p. 37).
  80. Ruelle, D. & Takens, F. (1971). On the nature of turbulence. Commun. Math. Phys. 20: 167-192 (cit. on p. 3).
  81. Andersson, P., Berggren, M. & Henningson, D. S. (1999). Optimal disturbances and bypass transition in boundary layers. Phys. Fluids 11: 134- 150 (cit. on p. 90).
  82. Ostilla, R., Stevens, R. J. A. M., Grossmann, S., Verzicco, R. & Lohse, D. (2013). Optimal Taylor-Couette flow: direct numerical simulations. J. Fluid Mech. 719: 14-46 (cit. on pp. 5, 9, 18, 26, 30-32, 40, 49, 52, 54, 71).
  83. Ostilla-Mónico, R., Huisman, S. G., Jannink, T. J. G., Van Gils, D. P. M., Verzicco, R., Grossmann, S., Sun, C. & Lohse, D. (2014a). Optimal Taylor-Couette flow: radius ratio dependence. J. Fluid Mech. 747: 1-29 (cit. on pp. 48, 51, 52, 63-65, 73, 77, 101).
  84. Barcilon, A. & Brindley, J. (1984). Organized structures in turbulent Taylor-Couette flow. J. Fluid Mech. 143: 429-449 (cit. on pp. 9, 10, 79, 93, 95).
  85. Malkus, W. V. R. (1956). Outline of a theory of turbulent shear flow. J. Fluid Mech. 1: 521-539 (cit. on pp. 10, 79).
  86. Oertel, H., ed. (2010). Prandtl-Essentials of Fluid Mechanics. Vol. 158. Applied Mathematical Sciences. Springer New York (cit. on p. 79).
  87. Stevens, R. J. A. M., Verzicco, R. & Lohse, D. (2010). Radial boundary layer structure and Nusselt number in Rayleigh-Bénard convection. J. Fluid Mech. 643: 495-507 (cit. on p. 18).
  88. Kerr, R. M. (1996). Rayleigh number scaling in numerical convection. J. Fluid Mech. 310: 139-179 (cit. on p. 70).
  89. 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: 144502 (cit. on p. 11).
  90. Schultz, M. P. & Flack, K. A. (2013). Reynolds-number scaling of turbulent channel flow. Phys. Fluids 25: 025104 (cit. on pp. 9, 10).
  91. Eckmann, J.-P. (1981). Roads to turbulence in disipative dynamical systems. Rev. Mod. Phys. 53: 643-654 (cit. on p. 3).
  92. Lezius, D. K. & Johnston, J. P. (1976). Roll-cell instabilities in rotating laminar and turbulent channel flows. J. Fluid Mech. 77: 153-175 (cit. on p. 6).
  93. Shi, L., Avila, M. & Hof, B. (2013). Scale invariance at the onset of turbulence in Couette flow. Phys. Rev. Lett. 110: 204502 (cit. on p. 3).
  94. Eckhardt, B., Grossmann, S. & Lohse, D. (2000). Scaling of global momentum transport in Taylor-Couette and pipe flow. Eur. Phys. J. B 18: 541-544 (cit. on p. 9).
  95. Daly, C. A., Schneider, T. M., Schlatter, P. & Peake, N. (2014). Secondary instability and tertiary states in rotating plane Couette flow. J. Fluid Mech. 761: 27-61 (cit. on p. 6).
  96. Marcus, P. S. (1984a). Simulation of Taylor-Couette flow. Part 1. Numerical methods and comparison with experiment. J. Fluid Mech. 146: 45-64 (cit. on pp. 7, 15, 17, 18, 56).
  97. Meseguer, A., Avila, M., Mellibovsky, F. & Marques, F. (2007). Solenoidal spectral formulations for the computation of secondary flows in cylindrical and annular geometries. Eur. Phys. J. Spec. Top. 146: 249-259 (cit. on p. 15).
  98. Tokgoz, S., Elsinga, G. E., Delfos, R. & Westerweel, J. (2012). Spatial resolution and dissipation rate estimation in Taylor-Couette flow for tomographic PIV. Exp. Fluids 53: 561-583 (cit. on p. 4).
  99. Racina, A. & Kind, M. (2006). Specific power input and local micromixing times in turbulent Taylor-Couette flow. Exp. Fluids 41: 513-522 (cit. on pp. 30, 31).
  100. Schmid, P. J. & Henningson, D. S. (2001). Stability and Transition in Shear Flows. Vol. 142. Applied Mathematical Sciences. Springer (cit. on p. 90).
  101. Dubrulle, B., Dauchot, O., Daviaud, F., Longaretti, P.-Y., Richard, D. & Zahn, J.-P. (2005). Stability and turbulent transport in Taylor-Couette flow from analysis of experimental data. Phys. Fluids 17: 095103 (cit. on pp. 4-6, 9, 26, 33, 36, 54, 55, 62, 76, 79, 81, 82, 91, 98, 103).
  102. Riecke, H. & Paap, H.-G. (1986). Stability and wave-vector restriction of axisymmetric Taylor vortex flow. Phys. Rev. A 33: 547-553 (cit. on p. 24).
  103. Avila, M., Marques, F., Lopez, J. M. & Meseguer, A. (2007). Stability control and catastrophic transition in a forced Taylor-Couette system. J. Fluid Mech. 590: 471-496 (cit. on p. 16).
  104. Taylor, G. I. (1923). Stability of a viscous liquid contained between two rotating cylinders. Philos. Trans. R. Soc. London A 223: 289-343 (cit. on pp. 2, 4, 24, 43, 79, 85).
  105. Reynolds, W. C. & Tiederman, W. G. (1967). Stability of turbulent channel flow, with application to Malkus's theory. J. Fluid Mech. 27: 253-272 (cit. on p. 79).
  106. Tritton, D. J. (1992). Stabilization and destabilization of turbulent shear flow in a rotating fluid. J. Fluid Mech. 241: 503-523 (cit. on p. 71).
  107. Tsukahara, T. (2011). Structures and turbulent statistics in a rotating plane Couette flow. J. Phys. Conf. Ser. 318: 022024 (cit. on pp. 51, 52).
  108. Daviaud, F., Hegseth, J. & Bergé, P. (1992). Subcritical transition to turbulence in plane Couette flow. Phys. Rev. Lett. 69: 2511-2514 (cit. on p. 3).
  109. Donnelly, R. J. (1991). Taylor-Couette flow: The early days. Phys. Today 44: 32-39 (cit. on p. 2).
  110. Tilgner, A., Belmonte, A. & Libchaber, A. (1993). Temperature and velocity profiles of turbulent convection in water. Phys. Rev. E 47: R2253 (cit. on p. 70).
  111. Brown, E. & Ahlers, G. (2007). Temperature gradients, and search for non-Boussinesq effects, in the interior of turbulent Rayleigh-Bénard convection. Europhys. Lett. 80: 14001 (cit. on p. 70).
  112. Malkus, W. V. R. (1983). The amplitude of turbulent shear flow. Pure Appl. Geophys. 121: 391-400 (cit. on p. 79).
  113. Bradshaw, P. (1969). The analogy between streamline curvature and buoyancy in turbulent shear flow. J. Fluid Mech. 36: 177-191 (cit. on p. 71).
  114. Malkus, W. V. R. (1954). The heat transport and spectrum of thermal turbulence. Proc. R. Soc. London A 225: 196-212 (cit. on pp. 10, 79, 83, 95).
  115. Fardin, M. A., Perge, C. & Taberlet, N. (2014). "The hydrogen atom of fluid dynamics" - introduction to the Taylor-Couette flow for soft matter scientists. Soft Matter 10: 3523-3535 (cit. on p. 3).
  116. Reynolds, W. C. & Hussain, A. K. M. F. (1972). The mechanics of an organized wave in turbulent shear flow. Part 3. Theoretical models and comparisons with experiments. J. Fluid Mech. 54: 263-288 (cit. on p. 66).
  117. Swinney, H. L. & Gollub, J. P. (1978). The transition to turbulence. Phys. Today 31: 41-49 (cit. on p. 3).
  118. Jones, C. A. (1985). The transition to wavy Taylor vortices. J. Fluid Mech. 157: 135-162 (cit. on p. 15).
  119. Nagata, M. (1990). Three-dimensional finite-amplitude solutions in plane Couette flow: bifurcation from infinity. J. Fluid Mech. 217: 519-527 (cit. on p. 6).
  120. Brauckmann, H. J. (2011). Torque calculations for Taylor-Couette flow. Masters thesis. Philipps-Universität Marburg (cit. on pp. 18, 21, 24, 117).
  121. Merbold, S., Brauckmann, H. J. & Egbers, C. (2013). Torque measurements and numerical determination in differentially rotating wide gap Taylor-Couette flow. Phys. Rev. E 87: 023014 (cit. on pp. 3, 26, 30, 32, 33, 35, 41, 42, 48, 60, 65, 117).
  122. Eckhardt, B., Grossmann, S. & Lohse, D. (2007b). Torque scaling in turbulent Taylor-Couette flow between independently rotating cylinders. J. Fluid Mech. 581: 221-250 (cit. on pp. 7-9, 29, 42, 56).
  123. Van Gils, D. P. M., Huisman, S. G., Bruggert, G.-W., Sun, C. & Lohse, D. (2011). Torque scaling in turbulent Taylor-Couette flow with co- and counterrotating cylinders. Phys. Rev. Lett. 106: 024502 (cit. on pp. 3, 9, 26, 33, 35, 36, 40, 54, 62, 103, 104).
  124. Borrero-Echeverry, D., Schatz, M. F. & Tagg, R. (2010). Transient turbulence in Taylor-Couette flow. Phys. Rev. E 81: 025301 (cit. on p. 3).
  125. Faisst, H. & Eckhardt, B. (2000). Transition from the Couette-Taylor system to the plane Couette system. Phys. Rev. E 61: 7227-7230 (cit. on pp. 6, 48, 55).
  126. Coles, D. (1965). Transition in circular Couette flow. J. Fluid Mech. 21: 385- 425 (cit. on pp. 3, 10, 24, 35).
  127. Lathrop, D. P., Fineberg, J. & Swinney, H. L. (1992a). Transition to sheardriven turbulence in Couette-Taylor flow. Phys. Rev. A 46: 6390-6405 (cit. on pp. 3, 8, 9, 11, 26, 36, 65, 80, 93, 95, 96).
  128. Couette, M. (1890). Études sur le frottement des liquides. Ann. Chim. Phys., Ser. VI 21: 433-510 (cit. on p. 2).
  129. Hersant, F., Dubrulle, B. & Huré, J.-M. (2005). Turbulence in circumstellar disks. Astron. Astrophys. 429: 531-542 (cit. on p. 6).
  130. Colovas, P. W. & Andereck, C. D. (1997). Turbulent bursting and spatiotemporal intermittency in the counterrotating Taylor-Couette system. Phys. Rev. E 55: 2736-2741 (cit. on p. 35).
  131. Coughlin, K. & Marcus, P. S. (1996). Turbulent bursts in Couette-Taylor flow. Phys. Rev. Lett. 77: 2214-2217 (cit. on pp. 11, 27, 35, 38, 42, 44).
  132. Smith, G. P. & Townsend, A. A. (1982). Turbulent Couette flow between concentric cylinders at large Taylor numbers. J. Fluid Mech. 123: 187-217 (cit. on pp. 10, 69, 73, 82, 83).
  133. Lathrop, D. P., Fineberg, J. & Swinney, H. L. (1992b). Turbulent flow between concentric rotating cylinders at large Reynolds number. Phys. Rev. Lett. 68: 1515-1518 (cit. on pp. 3, 9, 36, 80, 93, 95).
  134. Brethouwer, G., Duguet, Y. & Schlatter, P. (2012). Turbulent-laminar coexistence in wall flows with Coriolis, buoyancy or Lorentz forces. J. Fluid Mech. 704: 137-172 (cit. on pp. 10, 51).
  135. Tuckerman, L. S., Kreilos, T., Schrobsdorff, H., Schneider, T. M. & Gibson, J. F. (2014). Turbulent-laminar patterns in plane Poiseuille flow. Phys. Fluids 26: 114103 (cit. on p. 3).
  136. Hultmark, M., Vallikivi, M., Bailey, S. C. C. & Smits, A. J. (2012). Turbulent pipe flow at extreme Reynolds numbers. Phys. Rev. Lett. 108: 094501 (cit. on p. 10).
  137. Avsarkisov, V., Hoyas, S., Oberlack, M. & García-Galache, J. P. (2014). Turbulent plane Couette flow at moderately high Reynolds number. J. Fluid Mech. 751: R1 (cit. on pp. 10, 11).
  138. Bech, K. H. & Andersson, H. I. (1997). Turbulent plane Couette flow subject to strong system rotation. J. Fluid Mech. 347: 289-314 (cit. on pp. 52, 73).
  139. Salewski, M. & Eckhardt, B. (2015). Turbulent states in plane Couette flow with rotation. Phys. Fluids 27: 045109 (cit. on pp. 8, 28, 58, 62, 65).
  140. Greidanus, A. J., Delfos, R., Tokgoz, S. & Westerweel, J. (2015). Turbulent Taylor-Couette flow over riblets: drag reduction and the effect of bulk fluid rotation. Exp. Fluids 56: 107 (cit. on p. 12).
  141. Koschmieder, E. L. (1979). Turbulent Taylor vortex flow. J. Fluid Mech. 93: 515-527 (cit. on p. 35).
  142. Nicodemus, R., Grossmann, S. & Holthaus, M. (1997a). Variational bound on energy dissipation in plane Couette flow. Phys. Rev. E 56: 6774- 6786 (cit. on p. 9).
  143. Nicodemus, R., Grossmann, S. & Holthaus, M. (1997b). Variational bound on energy dissipation in turbulent shear flow. Phys. Rev. Lett. 79: 4170-4173 (cit. on p. 9).
  144. Doering, C. R. & Constantin, P. (1994). Variational bounds on energy dissipation in incompressible flows: Shear flow. Phys. Rev. E 49: 4087- 4099 (cit. on p. 9).
  145. Grossmann, S., Lohse, D. & Sun, C. (2014). Velocity profiles in strongly turbulent Taylor-Couette flow. Phys. Fluids 26: 025114 (cit. on p. 10).
  146. Lewis, G. S. & Swinney, H. L. (1999). Velocity structure functions, scaling, and transitions in high-Reynolds-number Couette-Taylor flow. Phys. Rev. E 59: 5457-5467 (cit. on pp. 3, 9, 11, 26, 30, 31, 65, 70, 73, 80, 82, 83, 93, 95).
  147. Gol'dshtik, M. A., Sapozhnikov, V. A. & Shtern, V. N. (1970). Verification of the Malkus hypothesis regarding the stability of turbulent flows. Fluid Dyn. 5: 863-867 (cit. on p. 79).
  148. Komminaho, J., Lundbladh, A. & Johansson, A. V. (1996). Very large structures in plane turbulent Couette flow. J. Fluid Mech. 320: 259-285 (cit. on p. 51).
  149. Gibson, J. F., Halcrow, J. & Cvitanovi c´, P. (2008). Visualizing the geometry of state space in plane Couette flow. J. Fluid Mech. 611: 107-130 (cit. on p. 28).
  150. Demay, Y., Iooss, G. & Laure, P. (1992). Wave patterns in the small gap Couette-Taylor problem. Eur. J. Mech. B/Fluids 11: 621-634 (cit. on p. 6).
  151. King, G. P., Li, Y., Lee, W., Swinney, H. L. & Marcus, P. S. (1984). Wave speeds in wavy Taylor-vortex flow. J. Fluid Mech. 141: 365-390 (cit. on pp. 9, 10, 79, 83, 85, 89, 93, 95, 96, 99).
  152. Suryadi, A., Segalini, A. & Alfredsson, P. H. (2014). Zero absolute vorticity: Insight from experiments in rotating laminar plane Couette flow. Phys. Rev. E 89: 033003 (cit. on pp. 52, 72, 73).

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