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 and a fixed outer cylinder of radius . A variational problem is formulated and solved by a pseudo-time-stepping method up to a Taylor number . The angular momentum transport, characterized by a Nusselt number Nu, is bounded by , where the prefactor depends on the radius ratio . Three typical radius ratios are investigatedi.e., , and the corresponding prefactors 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.
2 More- Received 6 July 2019
DOI:https://doi.org/10.1103/PhysRevE.100.063109
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