The effect of roll number on the statistics of turbulent Taylor-Couette flow

Abstract

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 (TC) 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 wavenumber 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 $Re_i=3.4\cdot10^4$, and the outer cylinder was kept stationary, resulting in a frictional Reynolds number of $Re_\tau\approx500$, except for the $\Gamma=14$ simulation where $Re_i=1.5\cdot10^4$ and $Re_\tau\approx240$. 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 $n_r$ 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 was found to have a very sharp drop off for wavelengths larger than $\lambda_z$, while for the small wavelengths they collapse.