- Open Access
Effect of split endcaps on the flow dynamics in a tall Taylor-Couette setup
Phys. Rev. Fluids 11, 014606 – Published 26 January, 2026
DOI: https://doi.org/10.1103/1fm1-b1f7
Abstract
The effects of axial boundaries or endcaps are of fundamental interest in many Taylor-Couette (TC) flow experiments. A main challenge in those experiments has been to minimize these effects, which can substantially alter the flow structure compared to the axially unbounded idealized case. Therefore, understanding and disentangling the influence of endcaps on the TC flow dynamics is essential for the unambiguous interpretation of experimental results, particularly when other dynamical processes (instabilities) in TC flows are involved. In this paper, we study the hydrodynamic evolution of a quasi-Keplerian TC flow in the presence of split endcaps for experimentally relevant high Reynolds numbers, , up to , which are larger than those considered in related previous studies. At these , the flow deviates from the ideal TC flow profile without endcaps, resulting in about deviation in angular velocity at the midheight of the cylinder. Aside from turbulent fluctuations caused by shearing instability near the endcaps, the bulk flow remains nearly axially independent and exhibits overall Rayleigh stability. We characterize the scalings of the Ekman and Stewartson layer sizes with as well as examine the effect of the ratio of the outer to inner cylinders' angular velocities on the flow. The implications of these findings for ongoing magnetorotational instability (MRI) experiments based on the similar axially bounded TC setup are also discussed. Specifically, it is shown that when imposing a constant axial magnetic field in all the considered configurations, the flow profile modified by the endcaps lowers the critical threshold for the onset of MRI that in turn can facilitate its emergence and detection in those experiments.
Physics Subject Headings (PhySH)
Article Text
References (50)
- H. Ji, M. Burin, E. Schartman, and J. Goodman, Hydrodynamic turbulence cannot transport angular momentum effectively in astrophysical disks, Nature (London) 444, 343 (2006).
- M. Avila, Stability and angular-momentum transport of fluid flows between corotating cylinders, Phys. Rev. Lett. 108, 124501 (2012).
- J. M. Lopez and M. Avila, Boundary-layer turbulence in experiments on quasi-Keplerian flows, J. Fluid Mech. 817, 21 (2017).
- H. Ji and J. Goodman, Taylor-Couette flow for astrophysical purposes, Philos. Trans. R. Soc. A 381, 20220119 (2023).
- D. Feldmann, D. Borrero-Echeverry, M. J. Burin, K. Avila, and M. Avila, Routes to turbulence in Taylor–Couette flow, Philos. Trans. R. Soc. A 381, 20220114 (2023).
- E. P. Velikhov, Stability of an ideally conducting liquid flowing between rotating cylinders in a magnetic field, Zh. Eksp. Teor. Fiz. 36, 1398 (1959) [Sov. JETP 9, 995 (1959)].
- S. A. Balbus and J. F. Hawley, A powerful local shear instability in weakly magnetized disks. I. Linear analysis, Astrophys. J. 376, 214 (1991).
- R. J. Tayler, The adiabatic stability of stars containing magnetic fields—I. Toroidal fields, Mon. Not. R. Astron. Soc. 161, 365 (1973).
- G. Rüdiger, M. Gellert, R. Hollerbach, M. Schultz, and F. Stefani, Stability and instability of hydromagnetic Taylor-Couette flows, Phys. Rep. 741, 1 (2018).
- A. Kageyama, H. Ji, J. Goodman, F. Chen, and E. Shoshan, Numerical and experimental investigation of circulation in short cylinders, J. Phys. Soc. Jpn. 73, 2424 (2004).
- F. Stefani, G. Gerbeth, T. Gundrum, R. Hollerbach, J. Priede, G. Rüediger, and J. Szklarski, Helical magnetorotational instability in a Taylor-Couette flow with strongly reduced ekman pumping, Phys. Rev. E 80, 066303 (2009).
- R. Hollerbach and A. Fournier, End-effects in rapidly rotating cylindrical Taylor-Couette flow, in MHD Couette Flows: Experiments and Models, edited by R. Rosner, G. Rüdiger, and A. Bonanno, American Institute of Physics Conference Series Vol. 733 (American Institute of Physics, College Park, MD, 2004), pp. 114–121.
- J. Goodman and H. Ji, Magnetorotational instability of dissipative Couette flow, J. Fluid Mech. 462, 365 (2002).
- G. Rüdiger, M. Schultz, and D. Shalybkov, Linear magnetohydrodynamic Taylor-Couette instability for liquid sodium, Phys. Rev. E 67, 046312 (2003).
- A. Mishra, G. Mamatsashvili, and F. Stefani, From helical to standard magnetorotational instability: Predictions for upcoming liquid sodium experiments, Phys. Rev. Fluids 7, 064802 (2022).
- G. Rüdiger and M. Schultz, The gap-size influence on the excitation of magnetorotational instability in cylindric Taylor-Couette flows, J. Plasma Phys. 90, 905900105 (2024).
- H. Ji, J. Goodman, and A. Kageyama, Magnetorotational instability in a rotating liquid metal annulus, Mon. Not. R. Astron. Soc. 325, L1 (2001).
- M. J. Burin, H. Ji, E. Schartman, R. Cutler, P. Heitzenroeder, W. Liu, L. Morris, and S. Raftopolous, Reduction of ekman circulation within Taylor-Couette flow, Exp. Fluids 40, 962 (2006).
- E. Schartman, H. Ji, and M. J. Burin, Development of a Couette-Taylor flow device with active minimization of secondary circulation, Rev. Sci. Instrum. 80, 024501 (2009).
- E. Schartman, H. Ji, M. J. Burin, and J. Goodman, Stability of quasi-Keplerian shear flow in a laboratory experiment, Astron. Astrophys. 543, A94 (2012).
- E. M. Edlund and H. Ji, Nonlinear stability of laboratory quasi-Keplerian flows, Phys. Rev. E 89, 021004(R) (2014).
- E. M. Edlund and H. Ji, Reynolds number scaling of the influence of boundary layers on the global behavior of laboratory quasi-Keplerian flows, Phys. Rev. E 92, 043005 (2015).
- L. Shi, B. Hof, M. Rampp, and M. Avila, Hydrodynamic turbulence in quasi-Keplerian rotating flows, Phys. Fluids 29, 044107 (2017).
- M. S. Paoletti and D. P. Lathrop, Angular momentum transport in turbulent flow between independently rotating cylinders, Phys. Rev. Lett. 106, 024501 (2011).
- M. S. Paoletti, D. P. M. van Gils, B. Dubrulle, C. Sun, D. Lohse, and D. P. Lathrop, Angular momentum transport and turbulence in laboratory models of Keplerian flows, Astron. Astrophys. 547, A64 (2012).
- F. Nordsiek, S. G. Huisman, R. C. A. van der Veen, C. Sun, D. Lohse, and D. P. Lathrop, Azimuthal velocity profiles in Rayleigh-stable Taylor-Couette flow and implied axial angular momentum transport, J. Fluid Mech. 774, 342 (2015).
- F. Stefani, A. Gailitis, G. Gerbeth, A. Giesecke, T. Gundrum, G. Rüdiger, M. Seilmayer, and T. Vogt, The DRESDYN project: Liquid metal experiments on dynamo action and magnetorotational instability, Geophys. Astrophys. Fluid Dyn. 113, 51 (2019).
- G. Wendt, Potentialtheoretische Behandlung des Wehneltzylinders, Ann. Phys. 409, 445 (1933).
- D. Coles, Transition in circular Couette flow, J. Fluid Mech. 21, 385 (1965).
- D. Richard and J.-P. Zahn, Turbulence in differentially rotating flows. What can be learned from the Couette-Taylor experiment, Astron. Astrophys. 347, 734 (1999).
- J. Szklarski, Reduction of boundary effects in the spiral MRI experiment PROMISE, Astron. Nachr. 328, 499 (2007).
- C. Gissinger, J. Goodman, and H. Ji, The role of boundaries in the magnetorotational instability, Phys. Fluids 24, 074109 (2012).
- D. Choi, F. Ebrahimi, K. J. Caspary, E. P. Gilson, J. Goodman, and H. Ji, Nonaxisymmetric simulations of the Princeton magnetorotational instability experiment with insulating and conducting axial boundaries, Phys. Rev. E 100, 033116 (2019).
- H. M. Blackburn and S. J. Sherwin, Formulation of a Galerkin spectral element-Fourier method for three-dimensional incompressible flows in cylindrical geometries, J. Comput. Phys. 197, 759 (2004).
- H. M. Blackburn, D. Lee, T. Albrecht, and J. Singh, CSemtex: A spectral element-fourier solver for the incompressible Navier-Stokes equations in cylindrical or Cartesian coordinates, Comput. Phys. Commun. 245, 106804 (2019).
- A. Mishra, G. Mamatsashvili, and F. Stefani, Nonaxisymmetric modes of magnetorotational and possible hydrodynamical instabilities in the upcoming DRESDYN-MRI experiments: Linear and nonlinear dynamics, Phys. Rev. Fluids 9, 033904 (2024).
- Greenspan, The Theory of Rotating Fluids (Cambridge University Press, Cambridge, 1968).
- Since the flow is approximately symmetric around the midheight , the radial profiles in the lower half of the cylinders are similar.
- K. Stewartson, On almost rigid rotations, J. Fluid Mech. 3, 17 (1957).
- W. Liu, Magnetized ekman layer and stewartson layer in a magnetized Taylor-Couette flow, Phys. Rev. E 77, 056314 (2008).
- J. Szklarski and G. Rüdiger, Ekman-Hartmann layer in a magnetohydrodynamic Taylor-Couette flow, Phys. Rev. E 76, 066308 (2007).
- A. I. Vooren, The Stewartson layer of a rotating disk of finite radius, J. Eng. Math. 26, 131 (1992).
- A. Mishra, G. Mamatsashvili, V. Galindo, and F. Stefani, Convective, absolute and global azimuthal magnetorotational instabilities, J. Fluid Mech. 922, R4 (2021).
- A. Mishra, G. Mamatsashvili, M. Seilmayer, and F. Stefani, One-winged butterflies: Mode selection for azimuthal magnetorotational instability by thermal convection, J. Fluid Mech. 992, R1 (2024).
- Y. Wang, F. Ebrahimi, H. Lu, J. Goodman, E. P. Gilson, and H. Ji, Observation of nonaxisymmetric standard magnetorotational instability induced by a free-shear layer, Phys. Rev. Lett. 134, 135101 (2025).
- Y. Wang, E. P. Gilson, F. Ebrahimi, J. Goodman, and H. Ji, Observation of axisymmetric standard magnetorotational instability in the laboratory, Phys. Rev. Lett. 129, 115001 (2022).
- Y. Wang, E. P. Gilson, F. Ebrahimi, J. Goodman, K. J. Caspary, H. W. Winarto, and H. Ji, Identification of a non-axisymmetric mode in laboratory experiments searching for standard magnetorotational instability, Nat. Commun. 13, 4679 (2022).
- J.-L. Guermond, R. Laguerre, J. Léorat, and C. Nore, Nonlinear magnetohydrodynamics in axisymmetric heterogeneous domains using a Fourier/finite element technique and an interior penalty method, J. Comput. Phys. 228, 2739 (2009).
- C. Nore, D. C. Quiroz, L. Cappanera, and J.-L. Guermond, Direct numerical simulation of the axial dipolar dynamo in the Von Kármán sodium experiment, Europhys. Lett. 114, 65002 (2016).
- H. W. Winarto, H. Ji, J. Goodman, F. Ebrahimi, E. P. Gilson, and Y. Wang, Parameter space mapping of the Princeton magnetorotational instability experiment, Phys. Rev. E 102, 023113 (2020).