@article{19730, abstract = {Feigenbaum universality is shown to occur in subcritical shear flows. Our testing ground is the counter-rotation regime of the Taylor–Couette flow, where numerical calculations are performed within a small periodic domain. The accurate computation of up to the seventh period-doubling bifurcation, assisted by a purposely defined Poincaré section, has enabled us to reproduce the two Feigenbaum universal constants with unprecedented accuracy in a fluid flow problem. We have further devised a method to predict the bifurcation diagram up to the accumulation point of the cascade based on the detailed inspection of just the first few period-doubling bifurcations. Remarkably, the method is applicable beyond the accumulation point, with predictions remaining valid, in a statistical sense, for the chaotic dynamics that follows.}, author = {Wang, Baoying and Ayats López, Roger and Deguchi, K. and Meseguer, A. and Mellibovsky, F.}, issn = {1469-7645}, journal = {Journal of Fluid Mechanics}, publisher = {Cambridge University Press}, title = {{Feigenbaum universality in subcritical Taylor-Couette flow}}, doi = {10.1017/jfm.2025.278}, volume = {1010}, year = {2025}, } @article{19732, abstract = {The transition to chaos in the subcritical regime of counter-rotating Taylor–Couette flow is investigated using a minimal periodic domain capable of sustaining coherent structures. Following a Feigenbaum cascade, the dynamics is found to be remarkably well approximated by a simple discrete map that admits rigorous proof of its chaotic nature. The chaotic set that arises for the map features densely distributed periodic points that are in one-to-one correspondence with unstable periodic orbits (UPOs) of the Navier–Stokes system. This supports the increasingly accepted view that UPOs may serve as the backbone of turbulence and, indeed, we demonstrate that it is possible to reconstruct every statistical property of chaotic fluid flow from UPOs.}, author = {Wang, Baoying and Ayats López, Roger and Deguchi, K. and Meseguer, A. and Mellibovsky, F.}, issn = {1469-7645}, journal = {Journal of Fluid Mechanics}, publisher = {Cambridge University Press}, title = {{Mathematically established chaos and forecast of statistics with recurrent patterns in Taylor-Couette flow}}, doi = {10.1017/jfm.2025.151}, volume = {1011}, year = {2025}, } @article{14754, abstract = {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 role.}, author = {Wang, B. and Mellibovsky, F. and Ayats López, Roger and Deguchi, K. and Meseguer, A.}, issn = {1471-2962}, journal = {Philosophical Transactions of the Royal Society A}, keywords = {General Physics and Astronomy, General Engineering, General Mathematics}, number = {2246}, publisher = {The Royal Society}, title = {{Mean structure of the supercritical turbulent spiral in Taylor–Couette flow}}, doi = {10.1098/rsta.2022.0112}, volume = {381}, year = {2023}, } @article{12137, abstract = {We investigate the local self-sustained process underlying spiral turbulence in counter-rotating Taylor–Couette flow using a periodic annular domain, shaped as a parallelogram, two of whose sides are aligned with the cylindrical helix described by the spiral pattern. The primary focus of the study is placed on the emergence of drifting–rotating waves (DRW) that capture, in a relatively small domain, the main features of coherent structures typically observed in developed turbulence. The transitional dynamics of the subcritical region, far below the first instability of the laminar circular Couette flow, is determined by the upper and lower branches of DRW solutions originated at saddle-node bifurcations. The mechanism whereby these solutions self-sustain, and the chaotic dynamics they induce, are conspicuously reminiscent of other subcritical shear flows. Remarkably, the flow properties of DRW persist even as the Reynolds number is increased beyond the linear stability threshold of the base flow. Simulations in a narrow parallelogram domain stretched in the azimuthal direction to revolve around the apparatus a full turn confirm that self-sustained vortices eventually concentrate into a localised pattern. The resulting statistical steady state satisfactorily reproduces qualitatively, and to a certain degree also quantitatively, the topology and properties of spiral turbulence as calculated in a large periodic domain of sufficient aspect ratio that is representative of the real system.}, author = {Wang, B. and Ayats López, Roger and Deguchi, K. and Mellibovsky, F. and Meseguer, A.}, issn = {1469-7645}, journal = {Journal of Fluid Mechanics}, keywords = {Mechanical Engineering, Mechanics of Materials, Condensed Matter Physics, Applied Mathematics}, publisher = {Cambridge University Press}, title = {{Self-sustainment of coherent structures in counter-rotating Taylor–Couette flow}}, doi = {10.1017/jfm.2022.828}, volume = {951}, year = {2022}, } @article{12146, abstract = {In this paper, we explore the stability and dynamical relevance of a wide variety of steady, time-periodic, quasiperiodic, and chaotic flows arising between orthogonally stretching parallel plates. We first explore the stability of all the steady flow solution families formerly identified by Ayats et al. [“Flows between orthogonally stretching parallel plates,” Phys. Fluids 33, 024103 (2021)], concluding that only the one that originates from the Stokesian approximation is actually stable. When both plates are shrinking at identical or nearly the same deceleration rates, this Stokesian flow exhibits a Hopf bifurcation that leads to stable time-periodic regimes. The resulting time-periodic orbits or flows are tracked for different Reynolds numbers and stretching rates while monitoring their Floquet exponents to identify secondary instabilities. It is found that these time-periodic flows also exhibit Neimark–Sacker bifurcations, generating stable quasiperiodic flows (tori) that may sometimes give rise to chaotic dynamics through a Ruelle–Takens–Newhouse scenario. However, chaotic dynamics is unusually observed, as the quasiperiodic flows generally become phase-locked through a resonance mechanism before a strange attractor may arise, thus restoring the time-periodicity of the flow. In this work, we have identified and tracked four different resonance regions, also known as Arnold tongues or horns. In particular, the 1 : 4 strong resonance region is explored in great detail, where the identified scenarios are in very good agreement with normal form theory. }, author = {Wang, B. and Ayats López, Roger and Meseguer, A. and Marques, F.}, issn = {1089-7666}, journal = {Physics of Fluids}, keywords = {Condensed Matter Physics, Fluid Flow and Transfer Processes, Mechanics of Materials, Computational Mechanics, Mechanical Engineering}, number = {11}, publisher = {AIP Publishing}, title = {{Phase-locking flows between orthogonally stretching parallel plates}}, doi = {10.1063/5.0124152}, volume = {34}, year = {2022}, }