Direct numerical simulations of Taylor–Couette flow for vanishingly small inner cylinders

Weinvestigate turbulent Taylor–Couette flow between two concentric cylinders, where the inner cylinder of radius ri rotates while the outer one of radius ro remains stationary. Using direct numerical simulations, we examine how varying the radius ratio η =ri/ro from η =0.714 down to 0.0244 affects the flow characteristics at low to moderate Reynolds numbers. Our results show significant changes in the flow structures and statistics in the limit of a vanishingly small inner radius. The turbulent kinetic energy, scaled with the friction velocity at the inner cylinder, does not exhibit a self-similar scaling; instead, it decreases with decreasing η. The turbulent kinetic energy budgets reveal that the locations of peak production and total dissipation are independent of η, whereas their amplitudes decrease as η increases. The pressure–velocity correlation near the inner cylinder is large for small η and its amplitude decreases with increasing η, while the turbulent transport term exhibits the opposite trend. Numerical simulations for η ⩽0.5 show that, for our specific set-up, a rather good collapse of the distribution of the normalised torque versus the Taylor number (Ta) is obtained when the latter is defined according to Chandrasekhar (Hydrodynamic and Hydromagnetic Stability, Oxford Univ. Press, 1961), with a tendency towards a Ta1/3 regime at sufficiently large Ta.