The observed pattern changes are a consequence of low-frequency velocity modulations, which are induced by the interplay of two opposing spiral wave modes. A parametric investigation of the SRI, conducted through direct numerical simulations, evaluates the impact of Reynolds numbers, stratification, and container geometry on the observed low-frequency modulations and spiral pattern transformations. Analysis of the parameter study suggests that modulations emerge as a secondary instability, not universally observed in SRI unstable regimes. The findings regarding the TC model's correlation with star formation processes in accretion discs are significant. In a special issue (part 2) focused on Taylor-Couette and related flows, this article observes the one hundredth anniversary of Taylor's groundbreaking Philosophical Transactions paper.

Experiments and linear stability analysis are employed to investigate the critical modes of instabilities in viscoelastic Taylor-Couette flow, specifically when one cylinder rotates and the other remains stationary. According to a viscoelastic Rayleigh circulation criterion, polymer solution elasticity can induce flow instability despite the stability of the Newtonian counterpart. The rotation of the inner cylinder, in isolation, produces experimental results revealing three critical flow states: stationary axisymmetric vortices, or Taylor vortices, at low elasticity; standing waves, or ribbons, at intermediate elasticity; and disordered vortices (DV) at high elasticity. High elasticity, coupled with the rotation of the outer cylinder and the fixed inner cylinder, leads to critical modes taking the DV form. Theoretical and experimental results exhibit a high degree of concurrence, contingent upon the precise quantification of the polymer solution's elasticity. biodeteriogenic activity This piece contributes to a themed section devoted to Taylor-Couette and related flows, marking a century since Taylor's influential Philosophical Transactions publication (Part 2).

The flow of fluid between rotating concentric cylinders showcases two distinct pathways leading to turbulence. Inner-cylinder rotational flows experience a series of linear instabilities, eventually leading to temporally unpredictable dynamics as the rotational speed increases. Throughout the system, the resulting flow patterns evolve, exhibiting a sequential loss of spatial symmetry and coherence during the transition. Abrupt transitions to turbulent flow regions, challenging the persistence of laminar flow, occur in flows significantly influenced by outer-cylinder rotation. This analysis details the major attributes of the two turbulent trajectories. Both cases of temporal chaos are fundamentally explained by the principles of bifurcation theory. Yet, the catastrophic transition within flow systems, driven by outer-cylinder rotation, requires a statistical analysis of the spatial proliferation of turbulent regions for full comprehension. The rotation number, derived from the ratio of Coriolis to inertial forces, is shown to delimit the lower limit of conditions under which intermittent laminar-turbulent patterns can arise. This second part of the theme issue, 'Taylor-Couette and related flows,' honors the centennial of Taylor's pioneering Philosophical Transactions paper.

Taylor-Gortler (TG) instability and centrifugal instability, along with the vortices they generate, are phenomena frequently studied using the canonical Taylor-Couette flow. The phenomenon of TG instability is typically observed when fluids flow past curved surfaces or shapes. Our computational work confirms that the lid-driven cavity flow, alongside the Vogel-Escudier flow, displays TG-similar near-wall vortical structures. Within a circular cylinder, a rotating lid (specifically the top lid) produces the VE flow, while a linearly moving lid creates the LDC flow within a square or rectangular cavity. Epigenetics inhibitor The emergence of these vortical structures, as indicated by reconstructed phase space diagrams, reveals TG-like vortices appearing in the chaotic regimes of both flows. In the VE flow, instabilities within the side-wall boundary layer manifest as these vortices at high values of [Formula see text]. The observed sequence of events shows the VE flow changing from a steady state at low [Formula see text] to a chaotic state. In contrast to the behavior of VE flows, LDC flows, characterized by the absence of curved boundaries, show the emergence of TG-like vortices at the point of instability within a limit cycle. From a steady state, the LDC flow demonstrated a periodic oscillatory pattern before ultimately entering a chaotic state. To determine the presence of TG-like vortices, cavities with diverse aspect ratios are examined in each of the two flow patterns. Included in the second section of the theme issue 'Taylor-Couette and related flows', this article relates to the centennial of Taylor's seminal paper in Philosophical Transactions.

The study of stably stratified Taylor-Couette flow, a canonical example of the complex interplay between rotation, stable stratification, shear, and container boundaries, has attracted significant research interest due to its potential applications in geophysics and astrophysics. 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. Part 2 of the special issue 'Taylor-Couette and related flows' commemorates the centennial of Taylor's seminal Philosophical transactions paper, encompassing this article.

Through numerical means, the Taylor-Couette flow of concentrated non-colloidal suspensions is examined, with the inner cylinder rotating and the outer cylinder stationary. We investigate suspensions of bulk particle volume fraction b = 0.2 and 0.3, confined within a cylindrical annulus with a radius ratio of 60 (annular gap to particle radius). For every 0.877 units of inner radius, there is one unit of outer radius. By implementing suspension-balance models and rheological constitutive laws, numerical simulations are undertaken. Flow patterns induced by suspended particles are scrutinized by varying the Reynolds number of the suspension, a parameter derived from the bulk particle volume fraction and the rotational velocity of the inner cylinder, up to a maximum of 180. At high Reynolds numbers, the flow of a semi-dilute suspension displays modulated patterns beyond the confines of the wavy vortex flow. Therefore, the flow transforms, starting from circular Couette flow through ribbons, spiral vortex flow, wavy spiral vortex flow, wavy vortex flow, ultimately resulting in a modulated wavy vortex flow, particularly for concentrated suspensions. Additionally, the suspension's friction and torque coefficients are estimated. Suspended particles were found to substantially augment the torque experienced by the inner cylinder, simultaneously decreasing the friction coefficient and the pseudo-Nusselt number. A reduction in coefficients is observed within the flow of more dense suspensions. This piece contributes to a special issue, 'Taylor-Couette and related flows', celebrating the centennial of Taylor's pivotal Philosophical Transactions publication, part 2.

From a statistical standpoint, the large-scale laminar/turbulent spiral patterns in the linearly unstable regime of counter-rotating Taylor-Couette flow are investigated through direct numerical simulation. Diverging from the majority of previous numerical studies, we investigate the flow behavior in periodically configured parallelogram-annular domains, utilizing a coordinate transformation that aligns one parallelogram side with the spiral pattern. Experimentation with diverse domain sizes, shapes, and spatial resolutions was undertaken, and the corresponding outputs were evaluated against those from a sufficiently comprehensive computational orthogonal domain exhibiting inherent axial and azimuthal periodicity. The computational cost is significantly decreased by using a minimal parallelogram of the right tilt, without impairing the statistical properties of the supercritical turbulent spiral. Employing the slice method on extremely long time integrations in a co-rotating frame, the mean structure shows a striking resemblance to the turbulent stripes seen in plane Couette flow, the role of centrifugal instability being comparatively minor. Celebrating the centennial of Taylor's Philosophical Transactions paper, this article is included in the 'Taylor-Couette and related flows' theme issue (Part 2).

Using a Cartesian coordinate system, the Taylor-Couette system is examined in the vanishing gap limit between the coaxial cylinders. The ratio [Formula see text] of the angular velocities of the inner and outer cylinders, respectively, dictates the axisymmetric flow patterns. Our numerical stability study achieves an impressive concordance with previous research regarding the critical Taylor number, [Formula see text], representing the initiation of axisymmetric instability. Probiotic characteristics The relationship between the Taylor number, [Formula see text], and the expression [Formula see text] involves the rotation number, [Formula see text], and the Reynolds number, [Formula see text], both within the Cartesian coordinate framework. These values are, respectively, dependent on the average and the difference between [Formula see text] and [Formula see text]. The region [Formula see text] exhibits instability, with the finite product of [Formula see text] and [Formula see text] maintained. A numerical code for calculating nonlinear axisymmetric flows was subsequently developed by our team. Studies demonstrate that the axisymmetric flow's mean flow distortion is antisymmetrical across the gap, contingent upon [Formula see text], while also displaying a symmetric portion of mean flow distortion when [Formula see text]. Our investigation further demonstrates that, for a finite [Formula see text], all flows subject to [Formula see text] tend toward the [Formula see text] axis, thus recovering the plane Couette flow system in the limiting case of a vanishing gap. 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.