Direct numerical simulation of turbulent Taylor-Couette flow with grooved walls

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We present direct numerical simulations of Taylor-Couette flow with grooved walls up to inner cylinder Reynolds number of $Re_i=3.76\times10^4$, corresponding to Taylor number of $Ta=2.15\times10^9$. The simulations are performed at a fixed radius ratio $\eta=r_i/r_o=0.714$. The grooves are axisymmetric V-shaped obstacles attached to the wall with a tip angle of $90^\circ$. Results are compared with the smooth wall case in order to investigate the effects of the grooved walls. In particular, we focus on the effective scaling laws for torque, boundary layers and flow structures. With increasing $Ta$, the boundary layer thickness finally becomes smaller than the groove height. When this happens, the plumes are ejected from tips of the grooves and a secondary circulation between the grooves is formed. This is associated with a sharp increase of the torque and thus the effective scaling law for the torque becomes much steeper. Further increasing $Ta$ does not result in an additional slope increases. Instead, the effective scaling law saturates to the same ``ultimate'' regime effective exponents seen for smooth walls.