Torque scaling in turbulent Taylor-Couette flow with independently rotating cylinders

We present experimental studies of the turbulent flow of water between independently rotating cylinders. The Taylor-Couette system is capable of both strong turbulence ($Re > 2 \times 10^6$) and rapid rotation. The torque required to drive the inner cylinder and the wall shear stress at the outer boundary are precisely measured as a function of the two angular velocities $\Omega_1$ and $\Omega_2$. We find that the dynamics, which are fully determined by the Reynolds number $Re$ and Rossby number $Ro = \Omega_1 - \Omega_2/\Omega_2$, are different in four different regions of the ($\Omega_1, \Omega_2$) parameter space. Our measurements allow us to estimate the skin friction coefficient $c_f$. We compare our measurements of $c_f$ with those of previous experiments and discuss the potential relevance for angular momentum transport in astrophysical flows.