/* DATA DESCRIPTION: Citation: Feldmann, Daniel; Borrero-Echeverry, Daniel; Burin, Michael J; Avila, Kerstin; Avila, Marc (2023): Routes to turbulence in Taylor–Couette flow [dataset]. PANGAEA, https://doi.org/10.1594/PANGAEA.955328 Abstract: Fluid flows between rotating concentric cylinders exhibit two distinct routes to turbulence. In flows dominated by inner-cylinder rotation, a sequence of linear instabilities leads to temporally chaotic dynamics as the rotation speed is increased. The resulting flow patterns occupy the whole system and sequentially lose spatial symmetry and coherence in the transition process. In flows dominated by outercylinder rotation, the transition is abrupt and leads directly to turbulent flow regions that compete with laminar ones. We here review the main features of these two routes to turbulence. Bifurcation theory rationalises the origin of temporal chaos in both cases. However, the catastrophic transition of flows dominated by outer-cylinder rotation can only be understood by accounting for the spatial proliferation of turbulent regions with a statistical approach. We stress the role of the rotation number (the ratio of Coriolis to inertial forces) and show that it determines the lower border for the existence of intermittent laminar-turbulent patterns. Keyword(s): dynamical systems; pattern formation; transition to turbulence Related to: Feldmann, Daniel; Borrero-Echeverry, Daniel; Burin, Michael J; Avila, Kerstin; Avila, Marc (accepted): Routes to turbulence in Taylor-Couette flow. arXiv, https://doi.org/10.48550/arXiv.2209.04921 Parameter(s): Binary Object (Binary) * PI: Feldmann, Daniel (https://orcid.org/0000-0002-6585-2875, daniel.feldmann@zarm.uni-bremen.de) Figure (Fig) * PI: Feldmann, Daniel (https://orcid.org/0000-0002-6585-2875, daniel.feldmann@zarm.uni-bremen.de) Title (Title) * PI: Feldmann, Daniel (https://orcid.org/0000-0002-6585-2875, daniel.feldmann@zarm.uni-bremen.de) Binary Object (File Size) [Bytes] (Binary (Size)) * PI: Feldmann, Daniel (https://orcid.org/0000-0002-6585-2875, daniel.feldmann@zarm.uni-bremen.de) File name (File name) * PI: Feldmann, Daniel (https://orcid.org/0000-0002-6585-2875, daniel.feldmann@zarm.uni-bremen.de) Variable (Variable) * PI: Feldmann, Daniel (https://orcid.org/0000-0002-6585-2875, daniel.feldmann@zarm.uni-bremen.de) File format (File format) * PI: Feldmann, Daniel (https://orcid.org/0000-0002-6585-2875, daniel.feldmann@zarm.uni-bremen.de) Description (Description) * PI: Feldmann, Daniel (https://orcid.org/0000-0002-6585-2875, daniel.feldmann@zarm.uni-bremen.de) License: Creative Commons Attribution 4.0 International (CC-BY-4.0) (URI: https://creativecommons.org/licenses/by/4.0/) Status: Curation Level: Enhanced curation (URI: https://wiki.pangaea.de/wiki/Curation_levels) * Processing Level: PANGAEA data processing level 2 (URI: https://wiki.pangaea.de/wiki/Processing_levels#PANGAEA_data_processing_level_2) Size: 122 data points Files: All files referred to in data matrix can be downloaded in one go as ZIP or TAR (PANGAEA user account required). To download single files, use the filename from data matrix appended to "https://download.pangaea.de/dataset/955328/files/". */ Binary Fig Title Binary (Size) [Bytes] File name Variable File format Description codeFigures.tar.gz Figures source code 13.1 MBytes codeFigures.tar.gz Python, LaTeX Source code (Python, LaTeX) to reproduce figures shown in the paper codeSimulations.tar.gz Simulations source code 3.8 GBytes codeSimulations.tar.gz Fortran, C, binary Source code, parameter files and initial conditions to reproduce/continue direct numerical simulations shown in the paper dataSimNeutralStabilityCurve.tar.gz 1 Neutral stability curve 13.1 kBytes dataSimNeutralStabilityCurve.tar.gz Reynolds numbers (Re_o, Re_i) binary (npy) Data from stability analysis to reproduce the neutral stability curve in terms of the inner/outer cylinder Reynolds number, i.e. the set of dimensionless control parameter of the Taylor-Couette system as defined on p. 3 in Feldmann et al 2023 dataSimFlowFieldsSupercrit.tar.gz 2a,b,c,d Flow fields for supercritical route 6.9 GBytes dataSimFlowFieldsSupercrit.tar.gz Velocity (u) and pressure (p) fields binary (HDF5) Flow field data to reproduce contour plots, instantaneous three-dimensional snapshots of the velocity field (u) in cylindrical coordinates, i.e. u = [u_r, u_theta, u_z], and pressure field (p) for different Re_i and stationary outer cylinder (Re_o=0) dataSimReNuSupercrit.tar.gz 2e Supercritical bifurcation diagram 1.1 kBytes dataSimReNuSupercrit.tar.gz Reynolds (Re_i) and Nusselt (Nu_i) numbers binary (npy) Reynolds (Re_i) and Nusselt (Nu_i) numbers at the inner cylinder wall to reproduce the supercritical bifurcation diagram, data for different flow states at different Re_i and stationary outer cylinder (Re_o=0), the Nusselt number represents the normalised torque as defined on p. 7 in Feldmann et al. 2023 dataSimVeloTimeSeries.tar.gz 2f Velocity time series for supercritical route 35.2 MBytes dataSimVeloTimeSeries.tar.gz Radial velocity (u_r) over time (t) binary (npy) Time series data of the radial velocity component (u_r) measured at mid-gap position between the inner and outer cylinder dataSimNuTimeSeries.tar.gz 2g Nusselt time series for supercritical route 5.1 MBytes dataSimNuTimeSeries.tar.gz Torque Nusselt numbers (Nu_i) over time (t) binary (npy) Time series data of the torque measured at the inner cylinder in terms of the inner cylinder Nusselt number (Nu_i) as defined onp. 7 in Feldmann et al 2023 dataSimNuSpectraSupercrit.tar.gz 2h-k Nusselt spectra for supercritical route 43.5 MBytes dataSimNuSpectraSupercrit.tar.gz Nusselt spectra (FFT(Nu_i)) over wave number (kappa) binary (npy) Fourier spectrum of the inner cylinder Nusselt number (torque) time series data, in terms of abs(FFT(Nu_i(t)))^2 versus wave number (kappa_t) in units of one over viscous time units (i.e. nu/d^2) dataSimFlowFieldsSTC.tar.gz 3a Spatio-temporally chaotic flow field 1.9 GBytes dataSimFlowFieldsSTC.tar.gz Velocity (u) and pressure (p) fields binary (HDF5) Flow field data to reproduce contour plot, instantaneous three-dimensional snapshot of the velocity field (u) in cylindrical coordinates, i.e. u = [u_r, u_theta, u_z], and pressure field (p) from DNS in a large domain dataSimNuSpectraSTC.tar.gz 3b Nusselt spectra for onset of spatio-temporal chaos 389.6 kBytes dataSimNuSpectraSTC.tar.gz Nusselt spectra (FFT(Nu_i)) over wave number (kappa_t) binary (npy) Fourier spectrum of the inner cylinder Nusselt number (torque) time series data, in terms of abs(FFT(Nu_i(t)))^2 versus wave number (kappa_t) in units of one over viscous time units (i.e. nu/d^2) dataSimEnergySpectraSTC.tar.gz 3c Modal energy for onset of spatio-temporal chaos 16.5 kBytes dataSimEnergySpectraSTC.tar.gz Modal kinetic energy (E) over wave number (kappa_z) binary (npy) Kinetic energy (E) contained per axial wave number (kappa_z) for Re_i=250 extracted from two DNS in a small and a large domain dataExpFlowFieldsSpirals.tar.gz 4a,c-h Spiral turbulence in experiments 27.3 MBytes dataExpFlowFieldsSpirals.tar.gz Flow field visualisation (photograph) png, mp4 Photographs and videos from flow field visualisation in Taylor-Couette flow experiments at different outer cylinder Reynolds numbers (Re_o) and fixed inner cylinder (Re_i=0) published in Burin & Czarnocki J. Fluid Mech. 2012 dataSimFlowFieldsSpirals.tar.gz 4b Spiral turbulence in simulations 6.1 GBytes dataSimFlowFieldsSpirals.tar.gz Flow fied, velocity (u_r, u_theta, u_z), pressure (p) binary (HDF5) Flow field data to reproduce contour plot, instantaneous three-dimensional snapshot of the velocity field (u) in cylindrical coordinates, i.e. u = [u_r, u_theta, u_z], and pressure field (p) from DNS in a large domain with stationary inner cylinder and Re_o=4500 dataExpReiReoSpirals.tar.gz 5a Stability/hysteresis diagram for spiral turbulence 869 Bytes dataExpReiReoSpirals.tar.gz Reynolds numbers (Re_o, Re_i) binary (npy) Data from linear theory and experiments to reproduce the stability/hysteresis curves in terms of the inner/outer cylinder Reynolds number, i.e. the set of dimensionless control parameter of the Taylor-Couette system as defined on p. 3 in Feldmann et al 2023 dataExpFlowFieldsSpirals.tar.gz 5b,c Supercritical spiral turbulence 27.3 MBytes dataExpFlowFieldsSpiralsSupercritical.tar.gz Flow field visualistion png, pdf Photographs from flow field visualisation in counter-rotating Taylor-Couette flow experiments at (Re_i = 700, Re_o = -700) and (Re_i = 600, RE_o = -1000) as published in Avila & Hof Entropy 2022 dataExpReiReoLaminarisation.tar.gz 6 Laminarisation boundary of turbulent spots 105.7 kBytes dataExpReiReoLaminarisation.tar.gz Reynolds numbers (Re_o, Re_i) binary (npy) Data from experiments and a few simulation to reproduce the laminarisation boundary of turbulent spots in terms of the inner/outer cylinder Reynolds number, the conversion from (Re_i, Re_o) to (Re_S, R_Omega) is done in the corresponding python script in codeFigures dataExpTurbulentLifetimes.tar.gz 7 Lifetime of turbulent episodes 2.5 kBytes dataExpTurbulentLifetimes.tar.gz Duration of turbulent episodes (t_turb) binary (npy) Duration of turbulent episodes (t_turb) in terms of convective time units in Taylor-Couette flow experiments with Re o = 8106 and stationary inner cylinder (Re_i = 0) published in Borrero-Echeverry et al. Phys. Rev E. 2010 dataSimOnsetChaoticTransients.tar.gz 8 Onset of chaotic transients 60 kBytes dataSimOnsetChaoticTransients.tar.gz Kinetic energy (E_cf), Reynolds number (Re) binary (npy) Onset of chaotic transients in plane Couette flow. Kinetic energy contained in the cross-flow components versus Reynolds number. Data kindly provided by Tobias Kreilos; Kreilos & Eckhardt, Periodic orbits near onset of chaos in plane Couette flow, Chaos 22, 047505, 2012.