Optimal Taylor-Couette turbulence

Physics – Fluid Dynamics

Scientific paper

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26 pages, 22 figures

Scientific paper

Strongly turbulent Taylor-Couette flow with independently rotating inner (IC) and outer cylinder (OC) with a radius ratio of {\eta} = 0.716 is experimentally studied. From global torque measurements we analyze the dimensionless angular velocity (AV) flux Nu_{\omega}(Ta, a) as a function of the Taylor number Ta and the AV ratio a = -{\omega}_o/{\omega}_i in the large Taylor number regime from 10^11 to 10^13. We analyze the data with the common power law ansatz for the dimensionless AV transport flux Nu_{\omega}(Ta, a) = f(a)*Ta^{\gamma}, with an amplitude f(a) and an exponent {\gamma}. The data are consistent with one exponent {\gamma} = 0.39\pm0.03 for all a. The amplitude of the AV flux f(a) = Nu_{\omega}(Ta, a)/Ta^0.39 is measured to be maximal at slight counter-rotation, namely at an AV ratio of a_opt = 0.368\pm0.001. This value is theoretically interpreted as the result of a competition between the destabilizing IC rotation and the stabilizing but shear-enhancing OC counter-rotation. -- With the help of laser Doppler anemometry we provide AV profiles and in particular identify the radial position r_n of the neutral line, defined by <{\omega}(r_n)>_t = 0 for fixed height z. For these large Ta-values the ratio a_opt = 0.368 is distinguished by a zero AV gradient in the bulk. While for moderate counter-rotation 0 < a < a_opt the neutral line still remains close to the OC and the probability distribution function (PDF) of the bulk AV is observed to be mono-modal, for stronger counter-rotation a > a_opt the neutral line is pushed inwards towards the IC; in this regime the PDF of the bulk AV becomes bi-modal, reflecting intermittent bursts of turbulent structures beyond the neutral line into the outer flow domain, which otherwise is stabilized by the counter-rotating OC. Finally, a hypothesis is offered allowing a unifying view and consistent interpretation for all these various results.

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