Optimal Taylor-Couette turbulence

Abstract

Strongly turbulent Taylor-Couette flow with independently rotating inner and outer cylinders with a radius ratio of η= 0.716 is experimentally studied. From global torque measurements, we analyse the dimensionless angular velocity flux Nu_ω(Ta, a) as a function of the Taylor number Ta and the angular velocity ratio a = -ω_o/ω_i in the large-Taylor-number regime 10^{11} \lesssim Ta \lesssim 10^{13}. We analyse the data with the common power-law ansatz for the dimensionless angular velocity transport flux Nu_ω(Ta, a) = f(a)Ta^γ, with an amplitude f(a) and an exponent γ. The data are consistent with one effective exponent γ= 0.39\pm0.03 for all a. The amplitude of the angular velocity flux f(a) = Nu_ω(Ta, a)/Ta^0.39 is measured to be maximal at slight counter-rotation, namely at an angular velocity ratio of a_opt = 0.33\pm0.04. This value is theoretically interpreted as the result of a competition between the destabilizing inner cylinder rotation and the stabilizing but shear-enhancing outer cylinder counter-rotation. With the help of laser Doppler anemometry, we provide angular velocity profiles and identify the radial position r_n of the neutral line. While for moderate counter-rotation -0.40 ω_i \lesssim ω_o < 0, the neutral line still remains close to the outer cylinder and the probability distribution function (p.d.f.) of the bulk angular velocity is observed to be monomodal. For stronger counter-rotation the neutral line is pushed inwards towards the inner cylinder; in this regime the p.d.f. of the bulk angular velocity becomes bimodal, reflecting intermittent bursts of turbulent structures beyond the neutral line into the outer flow domain, which otherwise is stabilized by the counter-rotating outer cylinder. Finally, a hypothesis is offered allowing a unifying view for all these various results.