Large-eddy simulation of Taylor-Couette flow at relatively large Reynolds number

We present large-eddy simulations (LES) of the incompressible Navier-Stokes equations for Taylor-Couette flow at relatively high Reynolds numbers. The ratio of the two co-axial cylinder diameters is fixed as $\eta = R_i/R_o = 0.909$ with $R_i,R_o$ the inner and outer cylinder radii respectively. The outer cylinder is stationary while the inner cylinder rotates with constant angular velocity $\Omega_i$, leading to the driving Reynolds number $Re_i= (R_o-R_i)\,R_i \Omega_i /\nu$ with $\nu$ the kinematic viscosity of the Newtonian fluid. Wall-resolved LES is implemented using the stretched-vortex, sub-grid scale model with $Re_i$ in the range $10^5 - 3 \times 10^6$. We develop an empirical flow model for the $Re_{\tau_i} = F(\eta,Re_i)$ relationship where $Re_{\tau_i} = u_{\tau_i}\,(R_o -R_i)/(2\nu)$ is the inner-cylinder friction Reynolds number. Comparison of the model behavior with experimental data [van Gils \textit{et al.}, \textit{PRL}, 106, (2011), van Gils \textit{et al.}, \textit{J. Fluid Mech.},706, (2012), Merbold \textit{et al.}, \textit{Phys. Rev. E},87, (2013) ], direct numerical simulation [Ostilla M\'onico \textit{et al.}, \textit{J. Fluid Mech.}, 788, (2016)] and the present LES will be discussed.