Optimal Taylor–Couette flow: radius ratio dependence

Taylor–Couette flow with independently rotating inner ( i ) and outer ( o ) cylinders is explored numerically and experimentally to determine the effects of the radius ratio on the system response. Numerical simulations reach Reynolds numbers of up to Rei=9.5 x 10^3 and Re0= 5 x 10^3 , corresponding to Taylor numbers of up to Ta=10^8 for four different radius ratios n=ri/ro between 0.5 and 0.909. The experiments, performed in the Twente Turbulent Taylor–Couette ( T^3C ) set-up, reach Reynolds numbers of up to Rei= 2 x 10^6 and Reo= 1.5 x 10^6 , corresponding to Ta= 5 x 10^12 for n=.714--0.909 . Effective scaling laws for the torque J^w(Ta) are found, which for sufficiently large driving Ta are independent of the radius ratio n . As previously reported for n=0.714 , optimum transport at a non-zero Rossby number Ro=ri|wi-wo|/ ]2(ro-ri)wo] is found in both experiments and numerics. Here Ro(opt) is found to depend on the radius ratio and the driving of the system. At a driving in the range between Ta~3 x 10^8 and Ta~10^10 , Ro(opt) saturates to an asymptotic n -dependent value. Theoretical predictions for the asymptotic value of Ro(opt) are compared to the experimental results, and found to differ notably. Furthermore, the local angular velocity profiles from experiments and numerics are compared, and a link between a flat bulk profile and optimum transport for all radius ratios is reported