Direct numerical simulations of spiral Taylor-Couette turbulence

We perform direct numerical simulations of spiral turbulent Taylor-Couette (TC) flow for 400 6 Rei 6 1200 and 2000 6 Reo 6 1000, i.e. counter-rotation. The aspect ratio D height =gap width of the domain is 42 6 6 125, with periodic boundary conditions in the axial direction, and the radius ratio D ri =ro D 0:91. We show that, with decreasing Rei or with decreasing Reo, the formation of a turbulent spiral from an initially `featureless turbulent' flow can be described by the phenomenology of the Ginzburg-Landau equations, similar as seen in the experimental findings of Prigent et al. (Phys. Rev. Lett., vol. 89, 2002, 014501) for TC flow at D 0 :98 an D 430 and in numerical simulations of oblique turbulent bands in plane Couette flow by Rolland & Manneville (Eur. Phys. J., vol. 80, 2011, pp. 529-544). We therefore conclude that the Ginzburg-Landau description also holds when curvature effects play a role, and that the finite-wavelength instability is not a consequence of the no-slip boundary conditions at the upper and lower plates in the experiments. The most unstable axial wavelength z;c=d 41 in our simulations differs from findings in Prigent et al., where z;c =d 32, and so we conclude that z;c depends on the radius ratio . Furthermore, we find that the turbulent spiral is stationary in the reference frame of the mean velocity in the gap, rather than the mean velocity of the two rotating cylinders.