Upper bound on angular momentum transport in Taylor-Couette flow

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 R-i and a fixed outer cylinder of radius R-o. A variational problem is formulated and solved by a pseudo-time-stepping method up to a Taylor number Ta = 10(9). The angular momentum transport, characterized by a Nusselt number Nu, is bounded by Nu <= cTa(1/2), where the prefactor c depends on the radius ratio eta = R-i/R-o. Three typical radius ratios are investigatedi.e., eta = 0.5, 0.714, and 0.909, and the corresponding prefactors c = 0.0049, 0.0075, and 0.0086 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.