Abstract
We report on velocity fluctuations and the fluctuation-driven radial transport of angular momentum in turbulent circular Couette flow. Our apparatus is short (cylinder height to gap width ratio Γ ~ 2) and of relatively high wall curvature (ratio of cylinder radii η ~ 0.35). Fluctuation levels and the mean specific angular momentum are found to be roughly constant over radius, in accordance with previous studies featuring narrower gaps. Synchronized dual beam Laser Doppler Velocimetry (2D LDV) is used to directly measure the r − θ Reynolds stress component as a function of Reynolds number (Re), revealing approximate scalings in the non-dimensional angular momentum transport that confirm previous measurements of torque in similar flows. 2D LDV further allows for a decomposition of the turbulent transport to assess the relative roles of fluctuation intensity and r − θ cross-correlation. We find that the increasing angular momentum transport with Re is due to intensifying absolute fluctuation levels accompanied by a slightly weakening cross-correlation.
Similar content being viewed by others
References
Andereck CD, Liu SS, Swinney HL (1986) Flow regimes in a circular Couette system with independently rotating cylinders. J Fluid Mech 164:155
Barcilon A, Brindley J (1984) Organized structures in turbulent Taylor–Couette flow. J Fluid Mech 143:429 (data by F. R. Mobbs)
Bilgen E, Boulos R (1973) Functional dependence of torque coefficient of coaxial cylinders on gap width and Reynolds numbers. Trans ASME J Fluids Eng 95:122
Bilson M, Bremhorst K (2007) Direct numerical simulation of turbulent Taylor–Couette flow. J Fluid Mech 579:227
Burin MJ et al (2006) Reduction of Ekman circulation in Taylor–Couette flow. Exp Fluids 40:962
Burin MJ, Schartman E, Ji H (2008) Studies of turbulent angular momentum transport in Taylor–Couette flow via 2D laser doppler velocimetry. J Phys Conf Ser 137:012020
Cole JA (1976) Taylor-vortex instability and annulus length effects. J Fluid Mech 75:1
Couette M (1890) Etude sur le frottement des liquids. Ann Chim Phys 21:433
Doering CR, Constantin P (1992) Energy dissipation in shear driven turbulence. Phys Rev Lett 69:1648
Dong S (2007) Direct numerical simulation of turbulent Taylor–Couette flow. J Fluid Mech 587:373
Donnelly RJ, Simon NJ (1960) An empirical torque relation for supercritical flow between rotating cylinders. J Fluid Mech 7:26 with an appendix by Batchelor G
Eckhardt B, Grossman S, Lohse D (2007) Torque scaling in turbulent Taylor–Couette flow between independently rotating cylinders. J Fluid Mech 581:221
Ji H, Burin MJ, Schartman E, Goodman J (2006) Hydrodynamic turbulence cannot transport angular momentum effectively in astrophysical disks. Nature 444:343
Kageyama A et al (2004) Numerical and experimental investigation of circulation in short cylinders. J Phys Soc Jpn 73:2424
Koga JK, Koschmieder EL (1989) Taylor vortices in short fluid columns. Phys Fluids A 1:1475
Lathrop D, Fineberg J, Swinney HL (1992a) Transition to shear-driven turbulence in Taylor–Couette flow. Phys Rev A 46:6390
Lathrop D, Fineberg J, Swinney HL (1992b) Turbulent flow between concentric rotating cylinders at large Reynolds number. Phys Rev Lett 68:1515
Lewis GS, Swinney HL (1999) Velocity structure functions, scaling, and transitions in high-Reynolds-number Couette–Taylor flow. Phys Rev E 59:5457
Lücke M, Mihelcic M, Wingerarth K, Pfister G (1984) Flow in a small annulus between concentric cylinders. J Fluid Mech 140:343
Mallock A (1896) Experiments on fluid viscosity. Phil Trans R Soc Lond A 187:41
Marie L, Daviaud F (2004) Experimental measurement of the scale-by-scale momentum transport budget in a turbulent shear flow. Phys Fluids 16:457
Panton RL (1992) Scaling laws for the angular momentum of a completely turbulent Couette flow. C R Acad Sci Paris Ser II 315:1467
Racina A, Kind M (2006) Specific power input and local micromixing times in turbulent Taylor–Couette flow. Exp Fluids 41:513
Roberts PH (1965) Experiments on the stability of viscous flow between rotating cylinders. VI. Finite-amplitude experiments. Proc. Roy. Soc. Lon. 283:531 (in an appendix from Donnelly RJ, Schwarz KW)
Schartman E, Ji H, Burin MJ (2009) Development of a Couette–Taylor flow device with active minimization of secondary circulation. Rev Sci Inst 80:1–024501
Shankar PN, Kumar M (1994) Experimental determination of the kinetic viscosity of glycerol‐water mixtures. Proc R Soc Lond A 444:573
Smith GP, Townsend AA (1982) Turbulent Couette flow between concentric cylinders at large Taylor numbers. J Fluid Mech 123:7
Taylor GI (1923) Stability of a viscous liquid contained between two rotating cylinders. Phil Trans R Soc Lond A 223:289
Taylor GI (1935) Distribution of velocity and temperature between concentric rotating cylinders. Proc R Soc Lond A 151:494
Taylor GI (1936) Fluid friction between rotating cylinders. I. Torque measurements. Proc R Soc Lond A 157:546
Tong P et al (1990) Anisotropy in turbulent drag reduction. Phys Rev Lett 65:2780
Wendt F (1933) Turbulente Strömungen zswischen zwei rotierenden konaxialen zylindern. Ing Arch 4:577
Acknowledgement
The LDV system used in this work was leased from Dantec Dynamics, Inc.
Author information
Authors and Affiliations
Corresponding author
Rights and permissions
About this article
Cite this article
Burin, M.J., Schartman, E. & Ji, H. Local measurements of turbulent angular momentum transport in circular Couette flow. Exp Fluids 48, 763–769 (2010). https://doi.org/10.1007/s00348-009-0756-9
Received:
Revised:
Accepted:
Published:
Issue Date:
DOI: https://doi.org/10.1007/s00348-009-0756-9