DNS of Taylor–Couette flow between counter-rotating cylinders at small radius ratio

A counter-rotating Taylor–Couette flow with relatively small radius ratios of $$\eta = 0.2$$ –0.5 was investigated over a wide range of the Reynolds number, from laminar to turbulent regime, by means of three-dimensional direct numerical simulations. We investigated the $$\eta $$ dependence of the flow structure and determined a critical value between $$\eta =0.2$$ and 0.3, below which, the stable outer cylinder side exhibited a modal structure that was different from the Taylor-vortex flow on the inner side. At $$\eta \ge 0.3$$ , the Taylor-vortex on the unstable inner side dominated the entire flow field between the cylinders, whose footprints were observed in the vicinity of the outer cylinder wall. However, for $$\eta =0.2$$ , the influence from the inner side was limited up to the centre of the cylinder gap. Moreover, on the stable outer cylinder side, there appeared a modal structure that was axially homogeneous, azimuthally periodic, and similar to the Tollmien–Schlichting instability wave. As the Reynolds number increased with a fixed $$\eta =0.2$$ , the modal structure changed its azimuthal wavenumber and thickened radially in the wall unit. Although the Reynolds shear stress on the outer side remained approximately zero, the intensity of the velocity fluctuations was comparable to the Taylor-vortex flows in the central part.