Effects of the computational domain size on direct numerical simulations of Taylor-Couette turbulence with stationary outer cylinder

摘要

In search for the cheapest but still reliable numerical simulation, asystematic study on the effect of the computational domain ("box") size ondirect numerical simulations of Taylor-Couette flow was performed. Four boxes,with varying azimuthal and axial extents were used. The radius ratio betweenthe inner cylinder and the outer cylinder was fixed to $\eta=r_i/r_o=0.909$,and the outer was kept stationary, while the inner rotated at a Reynolds number$Re_i=10^5$. Profiles of mean and fluctuation velocities are compared, as wellas autocorrelations and velocity spectra. The smallest box is found toaccurately reproduce the torque and mean azimuthal velocity profiles of largerboxes, while having smaller values of the fluctuations than the larger boxes.The axial extent of the box directly reflects on the Taylor-rolls and plays acrucial role on the correlations and spectra. The azimuthal extent is alsofound to play a significant role, as larger boxes allow for azimuthal wave-likepatterns in the Taylor rolls to develop, which affects the statistics in thebulk region. For all boxes studied, the spectra does not reach a boxindependent maximum.