Taylor-Couette turbulence

Figure 1: The Taylor-Couette system consists of two coaxial cylinders of length L. The inner cylinder has the radius r_i and the angular velocity ω_i, while the outer cylinder has the radius r_o and the angular velocity ω_o. Figure from Ref [1].

We [1] numerically simulated turbulent Taylor-Couette flow for independently rotating inner and outer cylinders, focusing on the analogy with turbulent Rayleigh-Bénard flow. Reynolds numbers up to Re_i = 8 x 10³ and Re_o = ±4 x 10³ are reached for the inner and outer cylinders, respectively, corresponding to Taylor numbers Ta up to 10⁸. Effective scaling laws for the torque and other system responses are found, see figure 2. Experiments with the Twente Turbulent Taylor-Couette (T³C) setup and with a similar facility in Maryland at very high Reynolds numbers have revealed optimum transport at a non-zero rotation-rate ratio a = -ω_o / ω_i of about a_opt = 0.33. For large enough Ta in the numerically accessible range we also find optimum transport at non-zero counter-rotation. The position of this maximum shifts with the driving, reaching a_opt = 0.15 for Ta = 2.5 x 10⁷. This is consistent with the experimental result that a_opt becomes approximately independent of the driving strength at sufficiently large Reynolds numbers. In addition, we investigated the angular-velocity profiles and visualized the flow structures in the different regimes.

Figure 2: Left panel show the Absolute (Nu_ω) number and the right panel the compensated (Nu_ω / Ta^0.21) Nusselt number versus Ta for η=r_i/r_o=5/7. Experiments (dots) and the numerics agree in shape, but there is a slight shift between the data, which we attribute to the different boundary conditions in the lateral direction. Figure from Ostilla-Mónico et al. (2013).