Optimal Taylor-Couette turbulence

Strongly turbulent Taylor-Couette flow with independently rotating inner and outer cylinders with a radius ratio of eta = 0.716 is experimentally studied. From global torque measurements, we analyse the dimensionless angular velocity flux Nu(omega)(Ta, a) as a function of the Taylor number T a and the angular velocity ratio a = -omega(o)/omega(i) in the large-Taylor-number regime 10(11) less than or similar to Ta less than or similar to 10(13) and well off the inviscid stability borders (Rayleigh lines) a = -eta(2) for co-rotation and a = infinity for counter-rotation. We analyse the data with the common power-law ansatz for the dimensionless angular velocity 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 effective exponent gamma = 0.39 +/- 0.03 for all a, but we discuss a possible a dependence in the co- and weakly counter-rotating regimes. The amplitude of the angular velocity flux f(a) Nu(omega)(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 +/- 0.04, i.e. along the line omega(o) = -0.33 omega(i). 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 in particular identify the radial position r(n) of the neutral line, defined by (t) = 0 for fixed height z. For these large Ta values, the ratio a approximate to 0.40, which is close to a(opt) = 0.33, is distinguished by a zero angular velocity gradient partial derivative omega/partial derivative r = 0 in the bulk. While for moderate counter-rotation -0.40 omega(i) less than or similar to omega(o) < 0, the neutral line still remains close to the outer cylinder and the probability distribution function 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 probability distribution function 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 and consistent interpretation for all these various results.