Hostname: page-component-586b7cd67f-t7fkt Total loading time: 0 Render date: 2024-12-01T03:32:57.483Z Has data issue: false hasContentIssue false

Boundary-layer turbulence in experiments on quasi-Keplerian flows

Published online by Cambridge University Press:  15 March 2017

Jose M. Lopez*
Affiliation:
Institute of Fluid Mechanics, Friedrich-Alexander-Universität Erlangen-Nürnberg, 91058 Erlangen, Germany Departament de Física Aplicada, Univ. Politècnica de Catalunya, Barcelona 08034, Spain Institute of Science and Technology, 3400 Klosterneuburg, Austria
Marc Avila
Affiliation:
Institute of Fluid Mechanics, Friedrich-Alexander-Universität Erlangen-Nürnberg, 91058 Erlangen, Germany Center of Applied Space Technology and Microgravity, University of Bremen, 28359 Bremen, Germany
*
Email address for correspondence: [email protected]

Abstract

Most flows in nature and engineering are turbulent because of their large velocities and spatial scales. Laboratory experiments on rotating quasi-Keplerian flows, for which the angular velocity decreases radially but the angular momentum increases, are however laminar at Reynolds numbers exceeding one million. This is in apparent contradiction to direct numerical simulations showing that in these experiments turbulence transition is triggered by the axial boundaries. We here show numerically that as the Reynolds number increases, turbulence becomes progressively confined to the boundary layers and the flow in the bulk fully relaminarizes. Our findings support that turbulence is unlikely to occur in isothermal constant-density quasi-Keplerian flows.

Type
Papers
Copyright
© 2017 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

Avila, M. 2012 Stability and angular-momentum transport of fluid flows between corotating cylinders. Phys. Rev. Lett. 108, 124501.Google Scholar
Avila, M., Grimes, M., Lopez, J. M. & Marques, F. 2008 Global endwall effects on centrifugally stable flows. Phys. Fluids 20, 104104.Google Scholar
Balbus, S. A. 2003 Enhanced angular momentum transport in accretion disks. Annu. Rev. Astron. Astrophys. 41 (1), 555597.Google Scholar
Balbus, S. A. & Hawley, J. F. 1998 Instability, turbulence, and enhanced transport in accretion disks. Rev. Mod. Phys. 70, 153.Google Scholar
Brauckmann, H. J. & Eckhardt, B. 2013 Direct numerical simulations of local and global torque in Taylor–Couette flow up to Re = 30 000. J. Fluid Mech. 718, 398427.Google Scholar
Dubrulle, B., Dauchot, O., Daviaud, F., Longaretti, P.-Y., Richard, D. & Zahn, J.-P. 2005a Stability and turbulent transport in Taylor–Couette flow from analysis of experimental data. Phys. Fluids 17 (9), 095103.Google Scholar
Dubrulle, B., Marié, L., Normand, C., Richard, D., Hersant, F. & Zahn, J.-P. 2005b A hydrodynamic shear instability in stratified disks. Astron. Astrophys. 429, 113.Google Scholar
Edlund, E. M. & Ji, H. 2014 Nonlinear stability of laboratory quasi-Keplerian flows. Phys. Rev. E 89, 021004.Google Scholar
Edlund, E. M. & Ji, H. 2015 Reynolds number scaling of the influence of boundary layers on the global behavior of laboratory quasi-Keplerian flows. Phys. Rev. E 92, 043005.Google Scholar
Fricke, K. 1968 Instabilität stationärer rotation in sternen. Z. Astrophys. 68, 317344.Google Scholar
Goldreich, P. & Schubert, G. 1967 Differential rotation in stars. Astrophys. J. 150, 571587.Google Scholar
Hollerbach, R. & Fournier, A. 2004 End-effects in rapidly rotating cylindrical Taylor–Couette flow. In MHD Couette Flows: Experiments and Models, AIP Conference Proceedings, vol. 733, pp. 114121.Google Scholar
Hughes, S. & Randriamampianina, A. 1998 An improved projection scheme applied to pseudospectral methods for the incompressible Navier–Stokes equations. Intl J. Numer. Meth. Fluids 28, 501521.Google Scholar
Ji, H. & Balbus, S. 2013 Angular momentum transport in astrophysics and in the lab. Phys. Today 66 (8), 2733.Google Scholar
Ji, H., Burin, M., Schartman, E. & Goodman, J. 2006 Hydrodynamic turbulence cannot transport angular momentum effectively in astrophysical disks. Nature 444 (7117), 343346.Google Scholar
Johnson, B. M. & Gammie, C. F. 2006 Nonlinear stability of thin, radially stratified disks. Astrophys. J. 636 (1), 63.CrossRefGoogle Scholar
Kerswell, R. 2015 Instability driven by boundary inflow across shear: a way to circumvent Rayleigh’s stability criterion in accretion disks? J. Fluid Mech. 784, 619663.Google Scholar
Klahr, H. & Bodenheimer, P. 2003 Turbulence in accretion disks: vorticity generation and angular momentum transport via the global baroclinic instability. Astrophys. J. 582 (2), 869.Google Scholar
Le Bars, M. & Le Gal, P. 2007 Experimental analysis of the stratorotational instability in a cylindrical Couette flow. Phys. Rev. Lett. 99 (6), 064502.Google Scholar
Leclercq, C., Partridge, J. L., Augier, P., Dalziel, S. B. & Kerswell, R. R. 2016 Using stratification to mitigate end effects in quasi-Keplerian Taylor–Couette flow. J. Fluid Mech. 791, 608630.Google Scholar
Le Dizès, S. & Riedinger, X. 2010 The strato-rotational instability of Taylor–Couette and Keplerian flows. J. Fluid Mech. 660, 147161.Google Scholar
Lesur, G. & Latter, H. 2016 On the survival of zombie vortices in protoplanetary discs. Mon. Not. R. Astron. Soc. 462, 45494554.Google Scholar
Lin, D. N. C. & Papaloizou, J. 1980 On the structure and evolution of the primordial solar nebula. Mon. Not. R. Astron. Soc. 191 (1), 3748.Google Scholar
Lin, D. N. C. & Pringle, J. E. 1987 A viscosity prescription for a self-gravitating accretion disc. Mon. Not. R. Astron. Soc. 225 (3), 607613.Google Scholar
Lopez, J. M. & Marques, F. 2015 Dynamics of axially localized states in Taylor–Couette flows. Phys. Rev. E 91, 053011.Google Scholar
Lopez, J. M., Marques, F. & Avila, M. 2015 Conductive and convective heat transfer in fluid flows between differentially heated and rotating cylinders. Intl J. Heat Mass Transfer 90, 959967.Google Scholar
Lopez, J. M. & Shen, J. 1998 An efficient spectral-projection method for the Navier–Stokes equations in cylindrical geometries I. Axisymmetric cases. J. Comput. Phys. 139, 308326.Google Scholar
Marcus, P., Pei, S., Jiang, C., Barranco, J., Hassanzadeh, P. & Lecoanet, D. 2015 Zombie vortex instability. I. A purely hydrodynamic instability to resurrect the dead zones of protoplanetary disks. Astrophys. J. 808 (1), 87.Google Scholar
Maretzke, S., Hof, B. & Avila, M. 2014 Transient growth in linearly stable Taylor–Couette flows. J. Fluid Mech. 742, 254290.Google Scholar
Mercader, I., Batiste, O. & Alonso, A. 2010 An efficient spectral code for incompressible flows in cylindrical geometries. Comput. Fluids 39, 215224.Google Scholar
Miesch, M., Matthaeus, W., Brandenburg, A., Petrosyan, A., Pouquet, A., Cambon, C., Jenko, F., Uzdensky, D., Stone, J., Tobias, S. et al. 2015 Large-eddy simulations of magnetohydrodynamic turbulence in heliophysics and astrophysics. Space Sci. Rev. 194 (1), 97137.Google Scholar
Molemaker, M. J., McWilliams, J. C. & Yavneh, I. 2001 Instability and equilibration of centrifugally stable stratified Taylor–Couette flow. Phys. Rev. Lett. 86 (23), 5270.Google Scholar
Nelson, R. P., Gressel, O. & Umurhan, O. M. 2013 Linear and non-linear evolution of the vertical shear instability in accretion discs. Mon. Not. R. Astron. Soc. 435 (3), 26102632.Google Scholar
Nordsiek, F., Huisman, S. G., van der Veen, R. C. A., Sun, C., Lohse, D. & Lathrop, D. P. 2015 Azimuthal velocity profiles in Rayleigh-stable Taylor–Couette flow and implied axial angular momentum transport. J. Fluid Mech. 774, 342362.Google Scholar
Obabko, A., Cattaneo, F. & Fischer, P. 2008 The influence of horizontal boundaries on Ekman circulation and angular momentum transport in a cylindrical annulus. Phys. Scr. T132, 014029.Google Scholar
Paoletti, M. S. & Lathrop, D. P. 2011 Angular momentum transport in turbulent flow between independently rotating cylinders. Phys. Rev. Lett. 106 (2), 024501.Google Scholar
Paoletti, M., van Gils, D. P., Dubrulle, B., Sun, C., Lohse, D. & Lathrop, D. 2012 Angular momentum transport and turbulence in laboratory models of Keplerian flows. Astron. Astrophys. 547, A64.Google Scholar
Petersen, M., Julien, K. & Stewart, G. 2007 Baroclinic vorticity production in protoplanetary disks. Astrophys. J. 658, 12361251.Google Scholar
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 (5), 055103.CrossRefGoogle Scholar
Rayleigh, Lord 1917 On the dynamics of revolving fluids. Proc. R. Soc. Lond. A 93 (648), 148154.Google Scholar
Richard, D. & Zahn, J.-P. 1999 Turbulence in differentially rotating flows. What can be learned from the Couette–Taylor experiment. Astron. Astrophys. 347, 734738.Google Scholar
Riedinger, X., Le Dizès, S. & Meunier, P. 2011 Radiative instability of the flow around a rotating cylinder in a stratified fluid. J. Fluid Mech. 672, 130146.Google Scholar
Ryu, D. & Goodman, J. 1992 Convective instability in differentially rotating disks. Astrophys. J. 388, 438450.Google Scholar
Schartman, E., Ji, H., Burin, M. J. & Goodman, J. 2012 Stability of quasi-Keplerian shear flow in a laboratory experiment. Astron. Astrophys. 543, A94.Google Scholar
Shalybkov, D. & Rüdiger, G. 2005 Stability of density-stratified viscous Taylor–Couette flows. Astron. Astrophys. 438 (2), 411417.Google Scholar
Shi, L., Rampp, M., Hof, B. & Avila, M. 2015 A hybrid MPI-OpenMP parallel implementation for pseudospectral simulations with application to Taylor–Couette flow. Comput. Fluids 106, 111.Google Scholar
Toomre, A. 1964 On the gravitational stability of a disk of stars. Astrophys. J. 139, 12171238.Google Scholar
Turner, N. J., Fromang, S., Gammie, C., Klahr, H., Lesur, G., Wardle, M. & Bai, X. N. 2014 Transport and Accretion in Planet-Forming Disks. Arizona University Press.Google Scholar
Urpin, V. & Brandenburg, A. 1998 Magnetic and vertical shear instabilities in accretion discs. Mon. Not. R. Astron. Soc. 294, 399.Google Scholar