Mean structure of the supercritical turbulent spiral in Taylor–Couette flow

The large-scale laminar/turbulent spiral patterns that appear in the linearly unstable regime of counter-rotating Taylor–Couette flow are investigated from a statistical perspective by means of direct numerical simulation. Unlike the vast majority of previous numerical studies, we analyse the flow in periodic parallelogram-annular domains, following a coordinate change that aligns one of the parallelogram sides with the spiral pattern. The domain size, shape and spatial resolution have been varied and the results compared with those in a sufficiently large computational orthogonal domain with natural axial and azimuthal periodicity. We find that a minimal parallelogram of the right tilt significantly reduces the computational cost without notably compromising the statistical properties of the supercritical turbulent spiral. Its mean structure, obtained from extremely long time integrations in a co-rotating reference frame using the method of slices, bears remarkable similarity with the turbulent stripes observed in plane Couette flow, the centrifugal instability playing only a secondary route. This article is part of the theme issue ‘Taylor–Couette and related flows on the centennial of Taylor’s seminal Philosophical transactions paper (Part 2). KD’s research was supported by Australian Research Council Discovery Early Career Researcher Award (DE170100171). BW, RA, FM and AM research was supported by the Spanish Ministerio de Economía y Competitividad (grant numbers FIS2016-77849-R and FIS2017-85794-P) and Ministerio de Ciencia e Innovación (grant number PID2020-114043GB-I00), and the Generalitat de Catalunya (grant 2017-SGR-785). BW’s research was also supported by the Chinese Scholarship Council (grant CSC No. 201806440152). FM is a Serra-Húnter Fellow.