Upper bound on angular momentum transport in Taylor-Couette flow

Zijing Ding and Elena Marensi
Phys. Rev. E 100, 063109 – Published 24 December 2019

Abstract

We investigate the upper bound on angular momentum transport in Taylor-Couette flow theoretically and numerically by a one-dimensional background field method. The flow is bounded between a rotating inner cylinder of radius Ri and a fixed outer cylinder of radius Ro. A variational problem is formulated and solved by a pseudo-time-stepping method up to a Taylor number Ta=109. The angular momentum transport, characterized by a Nusselt number Nu, is bounded by NucTa1/2, where the prefactor c depends on the radius ratio η=Ri/Ro. Three typical radius ratios are investigatedi.e., η=0.5,0.714,and0.909, and the corresponding prefactors c=0.0049,0.0075,and0.0086 are found to improve (lower) the rigorous upper bounds by Doering and Constantin [C. Doering and P. Constantin, Phys. Rev. Lett. 69, 1648 (1992)] and Constantin [P. Constantin, SIAM Rev. 36, 73 (1994)] by at least one order of magnitude. Furthermore, we show, via an inductive bifurcation analysis, that considering a three-dimensional background velocity field is unable to lower the bound.

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  • Received 6 July 2019

DOI:https://doi.org/10.1103/PhysRevE.100.063109

©2019 American Physical Society

Physics Subject Headings (PhySH)

Fluid Dynamics

Authors & Affiliations

Zijing Ding*

  • Department of Applied Mathematics and Theoretical Physics, University of Cambridge, Cambridge CB3 0WA, England, United Kingdom

Elena Marensi

  • School of Mathematics and Statistics, University of Sheffield, Sheffield S3 7RH, England, United Kingdom

  • *z.ding@damtp.cam.ac.uk

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Vol. 100, Iss. 6 — December 2019

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