In moves ruled by outer-cylinder rotation, the change is abrupt and leads right to turbulent circulation regions that contend with laminar people. We right here review the primary top features of both of these channels to turbulence. Bifurcation theory rationalizes the origin of temporal chaos in both situations. However, the catastrophic transition of flows dominated hepatobiliary cancer by outer-cylinder rotation can simply be understood by accounting when it comes to spatial proliferation of turbulent regions with a statistical strategy. We stress the part for the rotation quantity (the ratio of Coriolis to inertial causes) and show so it determines the low edge for the presence of periodic laminar-turbulent patterns. This article is part of this motif issue ‘Taylor-Couette and related flows from the centennial of Taylor’s seminal Philosophical deals paper (Part 2)’.Taylor-Couette movement is a canonical circulation to examine Taylor-Görtler (TG) instability or centrifugal uncertainty and the connected vortices. TG instability has been typically associated with circulation over curved areas or geometries. Within the computational research, we verify the current presence of TG-like near-wall vortical structures in 2 lid-driven circulation methods, the Vogel-Escudier (VE) and also the lid-driven cavity (LDC) flows. The VE movement is created inside a circular cylinder by a rotating lid (top cover in today’s research), whilst the LDC movement is generated inside a square or rectangular hole because of the linear movement of this cover. We look at the emergence of those vortical structures through reconstructed phase room diagrams and find that the TG-like vortices are seen into the chaotic regimes both in flows. Within the Helicobacter hepaticus VE circulation, these vortices are seen once the side-wall boundary level instability units in at-large [Formula see text]. The VE flow is observed to attend a chaotic condition in a sequence of occasions from a stable state at reduced [Formula see text]. As opposed to VE flows, into the LDC movement with no curved boundaries, TG-like vortices are noticed in the emergence of unsteadiness when the flow displays a limit period. The LDC circulation is observed to have transitioned to chaos from the steady state through a periodic oscillatory condition. Numerous aspect proportion cavities tend to be examined both in flows for the existence of TG-like vortices. This informative article is a component of the theme issue ‘Taylor-Couette and associated flows on the centennial of Taylor’s seminal Philosophical deals paper (Part 2)’.Stably stratified Taylor-Couette circulation has attracted much attention because of its relevance as a canonical exemplory instance of the interplay among rotation, steady stratification, shear and container boundaries, in addition to its potential programs in geophysics and astrophysics. In this article, we review the present knowledge on this topic, emphasize unanswered questions and propose directions for future research. This informative article is part for the motif issue ‘Taylor-Couette and relevant flows in the centennial of Taylor’s seminal Philosophical deals paper (Part 2)’.Taylor-Couette circulation of concentrated non-colloidal suspensions with a rotating inner cylinder and a stationary external one is numerically examined. We start thinking about suspensions for the bulk particle volume fraction ϕb = 0.2, 0.3 aided by the proportion of annular space to the particle radius ε = 60 restricted in a cylindrical annulus of the radius ratio (for example. ratio of internal and external radii) η = 0.877. Numerical simulations are carried out by applying suspension-balance model and rheological constitutive laws. To see movement patterns caused by suspended particles, the Reynolds quantity of the suspension system, based on the bulk particle volume small fraction as well as the rotating velocity for the internal cylinder, is varied as much as 180. At high Reynolds number, modulated patterns undiscovered within the circulation of a semi-dilute suspension emerge beyond a wavy vortex flow. Therefore, a transition happens from the circular Couette circulation via ribbons, spiral vortex flow, wavy spiral vortex flow, wavy vortex circulation and modulated wavy vortex flow for the concentrated suspensions. Additionally, friction and torque coefficients for suspensions are estimated. As it happens that suspended particles significantly boost the torque in the inner cylinder while lowering friction coefficient in addition to pseudo-Nusselt number. In specific, the coefficients tend to be lower in the flow of more thick suspensions. This informative article is a component associated with the motif concern ‘Taylor-Couette and associated flows in the centennial of Taylor’s seminal Philosophical deals report (Part 2)’.The large-scale laminar/turbulent spiral patterns that appear in the linearly unstable regime of counter-rotating Taylor-Couette circulation are examined from a statistical perspective by way of direct numerical simulation. Unlike almost all previous numerical studies, we analyse the flow in regular parallelogram-annular domains, after a coordinate modification that aligns one of the parallelogram sides with the spiral pattern. The domain size, form and spatial quality have already been varied while the outcomes compared with those who work in a sufficiently huge computational orthogonal domain with natural axial and azimuthal periodicity. We discover that a minimal parallelogram regarding the right tilt notably decreases the computational price without notably limiting the statistical properties for the supercritical turbulent spiral. Its mean structure, obtained from acutely compound library chemical long time integrations in a co-rotating research frame using the method of cuts, holds remarkable similarity using the turbulent stripes noticed in jet Couette circulation, the centrifugal uncertainty playing just a secondary part.