Effect of roll number on the statistics of 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 ri and ro, respectively. Large axial aspect ratios ?=7–8 [with ?=L/(ro?ri), and L the axial length of the domain] and a simulation with ?=14were 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 ?=ri/ro= 0.909, the inner cylinder Reynolds number was fixed to Rei=3.4×10^4, and the outer cylinder was kept stationary, resulting in a frictional Reynolds number of Re??500, except for the ?=14simulation where Rei=1.5×10^4 and Re??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 nrand roll wavelength ?z were found for ?=7.The effect of ?z and nron the statistics was quantified. The torque and mean flow statistics were found to be independent of both ?z and nr, 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 ?z, while for the small wavelengths they collapse