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 Γ=7–8 [with Γ=L/(r o −r i ) , and L the axial length of the domain] and a simulation with Γ=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 η=r i /r o =0.909 , the inner cylinder Reynolds number was fixed to Re i =3.4×10 4 , and the outer cylinder was kept stationary, resulting in a frictional Reynolds number of Re τ ≈500 , except for the Γ=14 simulation where Re i =1.5×10 4 and Re τ ≈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 λ z were found for Γ=7 . The effect of λ z and n r on the statistics was quantified. The torque and mean flow statistics were found to be independent of both λ 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 λ z , while for the small wavelengths they collapse.