These pattern modifications are attributable to low-frequency velocity modulations, which arise from the simultaneous propagation of two opposing spiral wave modes. This paper investigates the low-frequency modulations and spiral pattern changes of the SRI, employing direct numerical simulations to examine the influence of Reynolds numbers, stratification, and container geometry. The parameter study demonstrates that modulations manifest as a secondary instability, not present across all SRI unstable states. The TC model's relationship to star formation processes in accretion discs makes the findings quite intriguing. This piece, part of a special issue dedicated to Taylor-Couette and related flows, marks a century since Taylor's landmark Philosophical Transactions publication.
A study of the critical instability modes of viscoelastic Taylor-Couette flow is conducted, with one rotating cylinder and a fixed one, using both linear stability analysis and experimental methods. The viscoelastic nature of the Rayleigh circulation criterion reveals how polymer solution elasticity can generate flow instability, even when the Newtonian counterpart remains stable. Rotating the inner cylinder alone yields experimental evidence of three critical modes: stationary axisymmetric vortices, or Taylor vortices, at low elasticity; standing waves, often termed ribbons, at intermediate elasticity values; and disordered vortices (DV) for high elasticity. Rotating the outer cylinder while the inner cylinder is held still, and with substantial elasticity, critical modes exhibit a DV form. The theoretical and experimental results are in good accord, subject to the accurate determination of the polymer solution's elasticity. Blebbistatin manufacturer This article is included in the special issue 'Taylor-Couette and related flows' dedicated to the centennial of Taylor's original Philosophical Transactions paper (Part 2).
The flow of fluid between rotating concentric cylinders showcases two distinct pathways leading to turbulence. When inner-cylinder rotation prevails, a cascade of linear instabilities results in temporally chaotic behavior as rotational velocity escalates. Throughout the system, the resulting flow patterns evolve, exhibiting a sequential loss of spatial symmetry and coherence during the transition. Outer-cylinder rotation-induced flows exhibit a swift and abrupt transition into turbulent flow regions that actively contend with laminar ones. In this review, we examine the key attributes of these two pathways to turbulence. Both cases of temporal chaos are fundamentally explained by the principles of bifurcation theory. In contrast, the disastrous change in the flow, dominated by the rotation of the outer cylinder, can only be elucidated by employing a statistical methodology to assess the spatial dispersion of turbulent zones. The rotation number, the ratio of Coriolis to inertial forces, dictates the lowest possible value for the existence of intermittent laminar-turbulent flow patterns. The centennial of Taylor's Philosophical Transactions paper is marked by this theme issue's second part, specifically focusing on Taylor-Couette and related flows.
Taylor-Couette flow provides a classic example for examining the dynamics of Taylor-Gortler instability, the centrifugal instability, and the vortices they induce. Flow over curved surfaces or geometries is a traditional indicator of TG instability. Computational results demonstrate the presence of vortex structures akin to those of TG near the walls in both lid-driven cavity and Vogel-Escudier flow systems. The VE flow, originating from a rotating lid (the top lid) within a cylindrical enclosure, contrasts with the LDC flow, generated within a square or rectangular chamber by a lid's linear motion. Blebbistatin manufacturer Phase space diagrams, reconstructed, reveal the appearance of these vortical structures, showing TG-like vortices in both flow types, occurring within chaotic regions. The emergence of these vortices in the VE flow correlates with the onset of instability in the side-wall boundary layer at high [Formula see text]. The VE flow, in a series of events, progresses from a steady state at low [Formula see text] to a chaotic state. Contrary to VE flows, within LDC flows, the absence of curved boundaries reveals TG-like vortices during the initiation of instability when the flow is in a limit cycle. The LDC flow's journey from a steady state into a chaotic state included a stage of periodic oscillation. Cavities exhibiting different aspect ratios are scrutinized in both flow scenarios for the manifestation of TG-like vortices. In the second part of the 'Taylor-Couette and related flows' special issue, this article highlights the importance of Taylor's landmark Philosophical Transactions paper from a century ago.
Taylor-Couette flow, characterized by stable stratification, has garnered significant interest due to its exemplary role in understanding the complex interactions of rotation, stable stratification, shear, and container boundaries. This fundamental system has potential implications for geophysical and astrophysical phenomena. This article offers a comprehensive assessment of current knowledge on this subject, identifies key areas requiring further investigation, and outlines prospective directions for future research. In the thematic section dedicated to Taylor-Couette and related flows, this article appears, specifically in Part 2, celebrating the centennial of Taylor's landmark Philosophical Transactions paper.
A numerical investigation examines the Taylor-Couette flow of concentrated, non-colloidal suspensions, featuring a rotating inner cylinder and a stationary outer cylinder. Cylindrical annuli with a radius ratio of 60 (annular gap to particle radius) are used to study suspensions with bulk particle volume fractions b = 0.2 and 0.3. The outer radius is 1/0.877 times the size of the inner radius. Suspension-balance models and rheological constitutive laws are utilized in the execution of numerical simulations. To discern the flow patterns stemming from suspended particles, the Reynolds number of the suspension, calculated using the bulk particle volume fraction and inner cylinder's rotational speed, is manipulated up to a value of 180. Beyond the realm of wavy vortex flow in a semi-dilute suspension, modulated flow patterns emerge at high Reynolds numbers. Therefore, the circular Couette flow transforms into ribbon-like structures, followed by spiral vortex flow, wavy spiral vortex flow, wavy vortex flow, and culminating in a modulated wavy vortex flow, specifically in concentrated suspensions. Moreover, an assessment of the friction and torque coefficients for the suspension mechanisms is undertaken. The torque on the inner cylinder is noticeably enhanced by the presence of suspended particles, which simultaneously reduces the friction coefficient and the pseudo-Nusselt number. Specifically, the coefficients diminish within the stream of denser suspensions. This article forms part 2 of the 'Taylor-Couette and related flows' theme issue, a special celebration of a century since Taylor's seminal paper in Philosophical Transactions.
Statistical analyses of the large-scale laminar/turbulent spiral patterns appearing in the linearly unstable regime of counter-rotating Taylor-Couette flow are conducted using direct numerical simulations. Our methodology, unlike previous numerical approaches, examines the flow within periodic parallelogram-annular domains, leveraging a coordinate adjustment that aligns a parallelogram side with the spiral pattern. Variations in domain size, shape, and spatial resolution were implemented, and the outcomes were juxtaposed with those derived from a substantially extensive computational orthogonal domain exhibiting inherent axial and azimuthal periodicity. The application of a minimal parallelogram, precisely angled, demonstrably reduces the computational burden without compromising the statistical properties of the supercritical turbulent spiral. The mean structure, ascertained through the analysis of extremely extended time integrations in a co-rotating reference frame employing the method of slices, bears a striking similarity to the turbulent stripes observed in plane Couette flow, with centrifugal instability playing a substantially lesser part. The 'Taylor-Couette and related flows' theme issue, part 2, features this article, marking a century since Taylor's landmark Philosophical Transactions paper.
A Cartesian analysis of the Taylor-Couette system is provided in the limiting case of a vanishing gap between coaxial cylinders. The ratio [Formula see text], between the inner and outer cylinder angular velocities, plays a crucial role in shaping the axisymmetric flow. Our numerical stability study shows a remarkable alignment with previous studies for the critical Taylor number, [Formula see text], for the start of axisymmetric instability. Blebbistatin manufacturer The Taylor number, denoted by [Formula see text], is expressible as [Formula see text], in which the rotation number, [Formula see text], and the Reynolds number, [Formula see text], calculated in the Cartesian coordinate system, are derived from the average and the difference between [Formula see text] and [Formula see text]. Within the region denoted by [Formula see text], instability arises, and the product of [Formula see text] and [Formula see text] remains finite. Furthermore, a numerical code was developed by us to compute nonlinear axisymmetric flows. When [Formula see text], the mean flow distortion in the axisymmetric flow is found to be antisymmetrical across the gap; an additional symmetric part of the mean flow distortion is present concurrently when [Formula see text]. The analysis also demonstrates that for any finite [Formula see text], all flows with [Formula see text] will gravitate towards the [Formula see text] axis, effectively re-creating the plane Couette flow system when the gap vanishes. This article forms part of a two-part theme issue, 'Taylor-Couette and related flows,' observing the centennial of Taylor's seminal Philosophical Transactions paper.