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 $\mathrm{\Gamma }=7–8$ [with $\mathrm{\Gamma }=L/(r_o-r_i)$, and $L$ the axial length of the domain] and a simulation with $\mathrm{\Gamma }=14$ 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 ${\text{Re}}_i=3.4\times {10}^4$, and the outer cylinder was kept stationary, resulting in a frictional Reynolds number of ${\text{Re}}_{\tau }\approx 500$, except for the $\mathrm{\Gamma }=14$ simulation where ${\text{Re}}_i=1.5\times {10}^4$ and ${\text{Re}}_{\tau }\approx 240$. 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 $\mathrm{\Gamma }=7$. The effect of ${\lambda }_z$ and $n_r$ 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.

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• Taylor-Couette system
• Turbulence