Rotating concentric cylinders' fluid flow demonstrates two clearly differentiated routes to turbulence. Dominated by inner-cylinder rotation, a progression of linear instabilities culminates in temporally chaotic dynamics as the rotational speed ascends. Sequential loss of spatial symmetry and coherence is evident in the resulting flow patterns that occupy the entire system during the transition. The transition to turbulent flow regions, competing with laminar flow, is direct and abrupt in flows characterized by outer-cylinder rotation. Herein, we survey the defining characteristics of these two routes to turbulence. Temporal chaos in both instances is attributable to the mechanisms of bifurcation theory. However, the catastrophic shift in flows, dominated by outer-cylinder rotation, necessitates a statistical treatment of the spatial expansion of turbulent areas. We posit that the rotation number, the fraction of Coriolis to inertial forces, sets the lower limit for the manifestation of intermittent laminar-turbulent flow. Marking the centennial of Taylor's Philosophical Transactions paper, this theme issue's second part delves into Taylor-Couette and related flow phenomena.

To understand Taylor-Gortler (TG) instability, centrifugal instability, and the accompanying vortices, the Taylor-Couette flow serves as a crucial benchmark. Flow over curved surfaces or geometric forms is a common factor in the occurrence of TG instability. PX-478 supplier A computational investigation validates the existence of TG-like near-wall vortex structures within the Vogel-Escudier and lid-driven cavity flow paradigms. A rotating lid, situated at the top of a circular cylinder, induces the VE flow, distinctly different from the LDC flow generated by a linearly moving lid inside a square or rectangular cavity. By investigating reconstructed phase space diagrams, we identify the emergence of these vortical configurations, notably observing TG-like vortices in both flow systems' chaotic states. The VE flow showcases these vortices when the side-wall boundary layer instability occurs at significant [Formula see text] values. PX-478 supplier Observations reveal that the VE flow, initially steady at low [Formula see text], transitions into a chaotic state through a series of events. Unlike VE flows, LDC flows, devoid of curved boundaries, display TG-like vortices at the onset of instability within a limit cycle flow. From a steady state, the LDC flow demonstrated a periodic oscillatory pattern before ultimately entering a chaotic state. Cavities with varying aspect ratios are assessed in both flow patterns to find if TG-like vortices are present. This article, forming part 2 of the special theme issue on Taylor-Couette and related flows, is a tribute to Taylor's seminal Philosophical Transactions paper marking its centennial.

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. Our analysis of the current literature on this subject includes a review of existing knowledge, a summary of open questions, and a proposal for future research directions. Within the commemorative theme issue 'Taylor-Couette and related flows,' dedicated to the centennial of Taylor's seminal Philosophical Transactions paper (Part 2), this article is included.

Numerical analysis investigates Taylor-Couette flow in concentrated, non-colloidal suspensions, wherein a rotating inner cylinder interacts with a stationary outer cylinder. The study focuses on suspensions of bulk particle volume fraction b = 0.2 and 0.3, which are contained within cylindrical annuli with a radius ratio of 60 (annular gap to particle radius). A comparison of the inner radius to the outer radius results in a ratio of 0.877. Suspension-balance models and rheological constitutive laws are utilized in the execution of numerical simulations. The influence of suspended particles on flow patterns is examined by systematically changing the Reynolds number of the suspension, a quantity linked to the bulk particle volume fraction and the rotational speed of the inner cylinder, up to 180. In high-Reynolds-number flows of semi-dilute suspensions, modulated flow patterns, distinct from wavy vortex flows, appear. 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. Furthermore, the friction and torque coefficients of the suspensions are calculated. PX-478 supplier The presence of suspended particles demonstrably boosted the torque on the inner cylinder, while concurrently diminishing both the friction coefficient and the pseudo-Nusselt number. Specifically, the coefficients diminish within the stream of denser suspensions. Celebrating the centennial of Taylor's influential Philosophical Transactions paper, this article is part of the 'Taylor-Couette and related flows' theme issue, segment 2.

Using direct numerical simulation, a statistical investigation is performed on the large-scale laminar or turbulent spiral patterns found in the linearly unstable counter-rotating Taylor-Couette flow. 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. The spectrum of domain sizes, shapes, and resolutions was investigated, and the corresponding findings were benchmarked against outcomes from a computationally expansive orthogonal domain with innate axial and azimuthal periodicity. We found that precisely tilting a minimal parallelogram effectively reduces the computational effort, maintaining the supercritical turbulent spiral's statistical characteristics. Using the method of slices on extremely long time integrations in a co-rotating frame, the mean structure exhibits a significant resemblance to the turbulent stripes observed in plane Couette flow, with the centrifugal instability contributing less significantly. Marking the centennial of Taylor's seminal Philosophical Transactions paper, this article forms part of the 'Taylor-Couette and related flows' theme issue (Part 2).

The Taylor-Couette system is represented in Cartesian coordinates in the limit where the gap between the coaxial cylinders approaches zero. The ratio [Formula see text] of the angular velocities of the inner and outer cylinders, respectively, directly influences the axisymmetric flow's characteristics. Previous investigations concerning the critical Taylor number, [Formula see text], for axisymmetric instability's onset exhibit remarkable consistency with our numerical stability study. The Taylor number, mathematically defined as [Formula see text], can be decomposed into [Formula see text], where the rotation number, [Formula see text], and the Reynolds number, [Formula see text], within the Cartesian space, are directly calculated based on the average and the difference between [Formula see text] and [Formula see text]. Instability is present in the region [Formula see text], where the product of [Formula see text] and [Formula see text] maintains a finite magnitude. We also developed a numerical procedure for computing nonlinear axisymmetric flows. Examination of the axisymmetric flow reveals that the mean flow distortion is antisymmetrical across the gap if [Formula see text], accompanied by an additional symmetric aspect of the mean flow distortion under the condition of [Formula see text]. Our findings confirm that, with a finite [Formula see text], all flows satisfying [Formula see text] approach the [Formula see text] axis, effectively reproducing the plane Couette flow system in the absence of a gap. The centennial of Taylor's seminal Philosophical Transactions paper, concerning Taylor-Couette and related flows, is marked by this article, part 2 of the dedicated issue.

This study investigates the observed flow regimes in Taylor-Couette flow, considering a radius ratio of [Formula see text], across a range of Reynolds numbers up to [Formula see text]. We utilize a visualization technique to study the flow's patterns. An investigation is performed into the flow states of centrifugally unstable flows, specifically for counter-rotating cylinders and the situation of inner cylinder rotation alone. The cylindrical annulus shows a range of new flow patterns, in addition to the established Taylor vortex and wavy vortex flow, particularly during the transition towards turbulence. The system exhibits a coexistence of turbulent and laminar regions, as evidenced by observation. One can observe turbulent spots and bursts, an irregular Taylor-vortex flow, and non-stationary turbulent vortices. A distinguishing aspect is the presence of a solitary vortex aligned axially, situated precisely between the inner and outer cylinder. The flow patterns between independently rotating cylinders, categorized as principal regimes, are displayed in a flow-regime diagram. The 'Taylor-Couette and related flows' theme issue, part 2, features this article, commemorating the centennial of Taylor's landmark Philosophical Transactions paper.

The dynamic study of elasto-inertial turbulence (EIT) employs a Taylor-Couette geometrical arrangement. EIT's chaotic flow dynamic is predicated on both notable inertia and the manifestation of viscoelasticity. Direct flow visualization, complemented by torque measurement, confirms the earlier initiation of EIT in comparison to purely inertial instabilities (and inertial turbulence). Herein, for the first time, we delve into the scaling of the pseudo-Nusselt number, considering its dependence on inertia and elasticity. Before reaching its fully developed chaotic state, which hinges on both high inertia and elasticity, EIT exhibits an intermediate behavior, as revealed by variations in its friction coefficient, temporal frequency spectra, and spatial power density spectra.