Direct numerical simulations of spiral Taylor–Couette turbulence. (25th March 2020)

• Record Type: Journal Article
• Authors: Berghout, Pieter; Dingemans, Rick J.; Zhu, Xiaojue; Verzicco, Roberto; Stevens, Richard J. A. M.; van Saarloos, Wim; Lohse, Detlef
• Is Part Of: Journal of fluid mechanics. Volume 887(2020)
• Publication Date: 2020-03-25
• Subjects: Taylor–Couette flow, -- pattern formation, -- rotating turbulence; Fluid mechanics -- Periodicals; 532.005
• DOI: 10.1017/jfm.2020.33
• Languages: English
• ISSNs: 0022-1120

Abstract

Abstract : Abstract : We perform direct numerical simulations of spiral turbulent Taylor–Couette (TC) flow for $400\leqslant Re_{i}\leqslant 1200$ and $-2000\leqslant Re_{o}\leqslant -1000$, i.e. counter-rotation. The aspect ratio $\unicode[STIX]{x1D6E4}=\text{height}/\text{gap width}$ of the domain is $42\leqslant \unicode[STIX]{x1D6E4}\leqslant 125$, with periodic boundary conditions in the axial direction, and the radius ratio $\unicode[STIX]{x1D702}=r_{i}/r_{o}=0.91$ . We show that, with decreasing $Re_{i}$ or with decreasing $Re_{o}$, 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 $\unicode[STIX]{x1D702}=0.98$ an $\unicode[STIX]{x1D6E4}=430$ 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 $\unicode[STIX]{x1D706}_{z, c}/d\approx 41$ in our simulations differs from findings in Prigent et al., where $\unicode[STIX]{x1D706}_{z, c}/d\approx 32$, and so we conclude that $\unicode[STIX]{x1D706}_{z, c}$ depends on the radius ratio $\unicode[STIX]{x1D702}$ . 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.