Effect of roll number on the statistics of turbulent Taylor-Couette flow

A series of direct numerical simulations in large computational domains has been performed in order to probe the spatial feature robustness of the Taylor rolls in turbulent Taylor-Couette flow. The latter is the flow between two coaxial independently rotating cylinders of radius r(i) and r(o), respectively. Large axial aspect ratios Gamma = 7-8 [with Gamma = L/(r(o) - r(i)), and L the axial length of the domain] and a simulation with Gamma = 14 were used in order to allow the system to select the most unstable wave number and to possibly develop multiple states. The radius ratio was taken as eta = r(i)/r(o) = 0.909, the inner cylinder Reynolds number was fixed to Re-i = 3.4 x 10(4), and the outer cylinder was kept stationary, resulting in a frictional Reynolds number of Re-tau approximate to 500, except for the Gamma = 14 simulation where Re-i = 1.5 x 104 and Re-tau approximate to 240. The large-scale rolls were found to remain axially pinned for all simulations. Depending on the initial conditions, stable solutions with different number of rolls n(r) and roll wavelength lambda(z) were found for Gamma = 7. The effect of lambda(z) and nr on the statistics was quantified. The torque and mean flow statistics were found to be independent of both lambda(z) and n(r), while the velocity fluctuations and energy spectra showed some box-size dependence. Finally, the axial velocity spectra were found to have a very sharp dropoff for wavelengths larger than lambda(z), while for the small wavelengths they collapse.