Recent experiments have reported a novel transition to elasto-inertial turbulence in the Taylor--Couette flow of a dilute polymer solution. Unlike previously reported transitions, this newly discovered scenario, dubbed vortex merging and splitting (VMS) transition, occurs in the centrifugally unstable regime and the mechanisms underlying it are two-dimensional: the flow becomes chaotic due to the proliferation of events where axisymmetric vortex pairs may be either created (vortex splitting) or annihilated (vortex merging). In this paper, we present direct numerical simulations, using the FENE-P constitutive equation to model polymer dynamics, which reproduce the experimental observations with great accuracy and elucidate the reasons for the onset of this surprising dynamics. Starting from the Newtonian limit and increasing progressively the fluid's elasticity, we demonstrate that the VMS dynamics is not associated with the well-known Taylor vortices, but with a steady pattern of elastically induced axisymmetric vortex pairs known as diwhirls. The amount of angular momentum carried by these elastic vortices becomes increasingly small as the fluid's elasticity increases and it eventually reaches a marginal level. When this occurs, the diwhirls become dynamically disconnected from the rest of the system and move independently from each other in the axial direction. It is shown that vortex merging and splitting events, along with local transient chaotic dynamics, result from the interactions among diwhirls, and that this complex spatio-temporal dynamics persists even at elasticity levels twice as large as those investigated experimentally.
We report the onset of elastic turbulence in a two-dimensional Taylor-Couette geometry using numerical solutions of the Oldroyd-B model, also performed at high Weissenberg numbers with the program OpenFOAM. Beyond a critical Weissenberg number, an elastic instability causes a supercritical transition from the laminar Taylor-Couette to a turbulent flow. The order parameter, the time average of secondary-flow strength, follows the scaling law $Φ\propto (\mathrm{Wi} -\mathrm{Wi}_c)^γ$ with $\mathrm{Wi}_c=10$ and $γ= 0.45$. The power spectrum of the velocity fluctuations shows a power-law decay wi…
Dynamic properties of elasto-inertial turbulence (EIT) are studied in a Taylor-Couette geometry. EIT is a chaotic flow state that develops upon both non-negligible inertia and viscoelasticity. A combination of direct flow visualisation and torque measurement allows to verify the earlier onset of EIT compared to purely inertial instabilities (and inertial turbulence). The scaling of the pseudo-Nusselt number with inertia and elasticity is discussed here for the first time. Variations in the friction coefficient, temporal frequency spectra, and spatial power density spectra highlight that EIT un…
A new mixing layer can be generated if the rotation of either of the two cylinders in a Taylor--Couette apparatus varies discontinuously along the symmetry axis. The mixing zone between the two resulting co-current streams gives rise to radial vorticity in addition to the primary axial vorticity. An analytic solution for the azimuthal velocity has been derived from which we show that the width of the mixing zone varies only with radial position.
We study the stability of cylindrical Taylor-Couette flow in the presence of azimuthal magnetic fields, and show that one obtains non-axisymmetric magnetorotational instabilities, having azimuthal wavenumber m=1. For Omega_o/Omega_i only slightly greater than the Rayleigh value (r_i/r_o)^2, the critical Reynolds and Hartmann numbers are Re_c ~ 10^3 and Ha_c ~ 10^2, independent of the magnetic Prandtl number Pm. These values are sufficiently small that it should be possible to obtain these instabilities in the PROMISE experimental facility.
Turbulent Taylor-Couette flow between counter-rotating cylinders develops intermittently fluctuating boundary layers for sufficient counter-rotation. We demonstrate the phenomenon in direct numerical simulations for radius ratios η=0.5 and 0.71 and propose a theoretical model for the critical value in the rotation ratio. Numerical results as well as experiments show that the onset of this intermittency coincides with the maximum in torque. The variations in torque correlate with the variations in mean Taylor vortex flow which is first enhanced for weak counter-rotation, and then reduced as int…
Transient growth due to non-normality is investigated for the Taylor-Couette problem with counter-rotating cylinders as a function of aspect ratio eta and Reynolds number Re. For all Re < 500, transient growth is enhanced by curvature, i.e. is greater for eta < 1 than for eta = 1, the plane Couette limit. For fixed Re < 130 it is found that the greatest transient growth is achieved for eta between the Taylor-Couette linear stability boundary, if it exists, and one, while for Re > 130 the greatest transient growth is achieved for eta on the linear stability boundary. Transient growth is shown t…
Recent work suggests unstable recurrent solutions of the equations governing fluid flow can play an important role in structuring the dynamics of turbulence. Here we present a method for detecting intervals of time where turbulence "shadows" (spatially and temporally mimics) recurrent solutions. We find that shadowing occurs frequently and repeatedly in both numerical and experimental observations of counter-rotating Taylor-Couette flow, despite the relatively small number of known recurrent solutions in this system. Our results set the stage for experimentally-grounded dynamical descriptions …
Recent studies have brought into question the view that at sufficiently high Reynolds number turbulence is an asymptotic state. We present the first direct observation of the decay of turbulent states in Taylor-Couette flow with lifetimes spanning five orders of magnitude. We also show that there is a regime where Taylor-Couette flow shares many of the decay characteristics observed in other shear flows, including Poisson statistics and the coexistence of laminar and turbulent patches. Our data suggest that characteristic decay times increase super-exponentially with increasing Reynolds number…
We numerically compute axisymmetric Taylor-Couette flow in the presence of axially periodic magnetic fields, with Hartmann numbers up to $Ha^2=10^7$. The geometry of the field singles out special field lines on which Shercliff layers form. These are simple shear layers for insulating boundaries, versus super-rotating or counter-rotating layers for conducting boundaries. Some field configurations have previously studied spherical analogs, but fundamentally new configurations also exist, having no spherical analogs. Finally, we explore the influence of azimuthal fields $B_ϕ\sim r^{-1}{\bf\hat e}…
In the present work it will be shown how the curvature of the outer cylinder affects Laser Doppler anemometry measurements inside a Taylor-Couette apparatus. The measurement position and the measured velocity are altered by curved surfaces. Conventional methods for curvature correction are not applicable to our setup, and it will be shown how a ray-tracer can be used to solve this complication. By using a ray-tracer the focal position can be calculated, and the velocity can be corrected. The results of the ray-tracer are verified by measuring an a priori known velocity field, and after applyin…
We study the stability of the Couette-Taylor flow between porous cylinders with radial throughflow. It had been shown earlier that this flow can be unstable with respect to non-axisymmetric (azimuthal or helical) waves provided that the radial Reynolds number, $R$ (constructed using the radial velocity at the inner cylinder and its radius), is high. In this paper, we present a very detailed and, in many respects, novel chart of critical curves in a region of moderate values of $R$, and we show that, starting from values of $R$, as low as $10$, the critical modes inherited from the inviscid ins…
Taylor-Couette flow -- the flow between two coaxial co- or counter-rotating cylinders -- is one of the paradigmatic systems in physics of fluids. The (dimensionless) control parameters are the Reynolds numbers of the inner and outer cylinder, the ratio of the cylinder radii, and the aspect ratio. The response of the system is the torque required to retain constant angular velocities, which can be connected to the angular velocity transport through the gap. While the low Reynolds number regime has been very well explored in the '80s and '90s of the last century, in the fully turbulent regime ma…
Taylor-Couette flow is often used as a simplified model for complex rotating flows in the interior of stars and accretion disks. The flow dynamics in these objects is influenced by magnetic fields. For example, quasi-Keplerian flows in Taylor-Couette geometry become unstable to a travelling or standing wave in an external magnetic field if the fluid is conducting; there is an instability even when the flow is hydrodynamically stable. This magnetorotational instability leads to the development of chaotic states and, eventually, turbulence, when the cylinder rotation is sufficiently fast. The tr…
Emulsions are common in many natural and industrial settings. Recently, much attention has been put on understanding the dynamics of turbulent emulsions. This paper reviews some recent studies of emulsions in turbulent Taylor-Couette flow, mainly focusing on the statistics of the dispersed phase and the global momentum transport of the system. We first study the size distribution and the breakup mechanism of the dispersed droplets for turbulent emulsions with a low volume-fraction (dilute) of the dispersed phase. For systems with a high volume-fraction of the dispersed phase (dense), we addres…
The flow structure of strongly turbulent Taylor-Couette flow with Reynolds numbers up to Re_i = 2*10^6 of the inner cylinder is experimentally examined with high-speed particle image velocimetry (PIV). The wind Reynolds numbers Re_w of the turbulent Taylor-vortex flow is found to scale as Re_w ~ Ta^(1/2), exactly as predicted for the ultimate turbulence regime, in which the boundary layers are turbulent. The dimensionless angular velocity flux has an effective scaling of Nu_ω ~ Ta^0.38, also in correspondence with turbulence in the ultimate regime. The scaling of Nu_ω is confirmed by local ang…
We investigate the existence of multiple turbulent states in highly turbulent Taylor-Couette flow in the range of $\mathrm{Ta}=10^{11}$ to $9\cdot10^{12}$, by measuring the global torques and the local velocities while probing the phase space spanned by the rotation rates of the inner and outer cylinder. The multiple states are found to be very robust and are expected to persist beyond $\mathrm{Ta}=10^{13}$. The rotation ratio is the parameter that most strongly controls the transitions between the flow states; the transitional values only weakly depend on the Taylor number. However, complex p…
Starting from stationary bifurcations in Couette-Dean flow, we compute nontrivial stationary solutions in inertialess viscoelastic circular Couette flow. These solutions are strongly localized vortex pairs, exist at arbitrarily large wavelengths, and show hysteresis in the Weissenberg number, similar to experimentally observed ``diwhirl'' patterns. Based on the computed velocity and stress fields, we elucidate a heuristic, fully nonlinear mechanism for these flows. We propose that these localized, fully nonlinear structures comprise fundamental building blocks for complex spatiotemporal dynami…
We numerically investigate Taylor-Couette flow in a wide-gap configuration, with $r_i/r_o=1/2$, the inner cylinder rotating, and the outer cylinder stationary. The fluid is taken to be electrically conducting, and a magnetic field of the form $B_z\approx(1 + \cos(2πz/z_0))/2$ is externally imposed, where the wavelength $z_0=50(r_o-r_i)$. Taylor vortices form where the field is weak, but not where it is strong. As the Reynolds number measuring the rotation rate is increased, the initial onset of vortices involves phase slip events, whereby pairs of Taylor vortices are periodically formed and th…
We provide direct measurements of the boundary layer properties in highly turbulent Taylor-Couette flow up to $\text{Ta}=6.2 \times 10^{12}$ using high-resolution particle image velocimetry (PIV). We find that the mean azimuthal velocity profile at the inner and outer cylinder can be fitted by the von Kármán log law $u^+ = \frac 1κ\ln y^+ +B$. The von Kármán constant $κ$ is found to depend on the driving strength $\text{Ta}$ and for large $\text{Ta}$ asymptotically approaches $κ\approx 0.40$. The variance profiles of the local azimuthal velocity have a universal peak around $y^+ \approx 12$ an…
The ubiquity of turbulent flows in nature and technology makes it of utmost importance to fundamentally understand turbulence. Kolmogorov's 1941 paradigm suggests that for strongly turbulent flows with many degrees of freedom and its large fluctuations, there would only be \emph{one} turbulent state as the large fluctuations would explore the entire higher-dimensional phase space. Here we report the first conclusive evidence of multiple turbulent states for large Reynolds number $\text{Re}=\mathcal{O}(10^6)$ (Taylor number $\text{Ta}=\mathcal{O}(10^{12})$) Taylor-Couette flow in the regime of …
We numerically compute the flow of an electrically conducting fluid in a Taylor-Couette geometry where the rotation rates of the inner and outer cylinders satisfy $Ω_o/Ω_i=(r_o/r_i)^{-3/2}$. In this quasi-Keplerian regime a non-magnetic system would be Rayleigh-stable for all Reynolds numbers $Re$, and the resulting purely azimuthal flow incapable of kinematic dynamo action for all magnetic Reynolds numbers $Rm$. For $Re=10^4$ and $Rm=10^5$ we demonstrate the existence of a finite-amplitude dynamo, whereby a suitable initial condition yields mutually sustaining turbulence and magnetic fields, …
A new turbulent Taylor-Couette system consisting of two independently rotating cylinders has been constructed. The gap between the cylinders has a height of 0.927 m, an inner radius of 0.200 m, and a variable outer radius (from 0.279 to 0.220 m). The maximum angular rotation rates of the inner and outer cylinder are 20 and 10 Hz, respectively, resulting in Reynolds numbers up to 3.4 x 10^6 with water as working fluid. With this Taylor-Couette system, the parameter space (Re_i, Re_o, η) extends to (2.0 x 10^6, {\pm}1.4 x 10^6, 0.716-0.909). The system is equipped with bubble injectors, temperat…
We discuss the flow between concentric rotating cylinders in the limit of large radii where the system approaches plane Couette flow. We discuss how in this limit the linear instability that leads to the formation of Taylor vortices is lost and how the character of the transition approaches that of planar shear flows. In particular, a parameter regime is identified where fractal distributions of life times and spatiotemporal intermittency occur. Experiments in this regime should allow to study the characteristics of shear flow turbulence in a closed flow geometry.
The magnetorotational instability (MRI) is thought to be a powerful source of turbulence and momentum transport in astrophysical accretion discs, but obtaining observational evidence of its operation is challenging. Recently, laboratory experiments of Taylor--Couette flow with externally imposed axial and azimuthal magnetic fields have revealed the kinematic and dynamic properties of the MRI close to the instability onset. While good agreement was found with linear stability analyses, little is known about the transition to turbulence and transport properties of the MRI. We here report on a nu…
We study liquid-liquid dispersions in a turbulent Taylor-Couette flow, produced between two counterrotating coaxial cylinders. In pure Water and in counterrotation, Reynolds numbers up to 1.4 10^5 are reached. The liquids we use are a low-viscous Oil and pure Water or a Sodium Iodide solution with a refractive index matched to that of Oil, in order to get transparent dispersions. We first characterize the single-phase flow, in terms of threshold for transition to turbulence, scaling of the torque and measurements of the mean flow and of the Reynolds stress by stereoscopic PIV. We then study th…
The transition to turbulence in Taylor-Couette flow often occurs via a sequence of supercritical bifurcations to progressively more complex, yet stable, flows. We describe a subcritical laminar-turbulent transition in the counter-rotating regime mediated by an unstable intermediate state in a system with an axial aspect ratio of $Γ=5.26$ and a radius ratio of $η=0.905$. In this regime, flow visualization experiments and numerical simulations indicate the intermediate state corresponds to an aperiodic flow featuring interpenetrating spirals. Furthermore, the reverse transition out of turbulence…
We analyze the global transport properties of turbulent Taylor-Couette flow in the strongly turbulent regime for independently rotating outer and inner cylinders, reaching Reynolds numbers of the inner and outer cylinders of Re_i = 2 x 10^6 and Re_o = 1.4 x 10^6, respectively. For all Re_i, Re_o, the dimensionless torque G scales as a function of the Taylor number Ta (which is proportional to the square of the difference between the angular velocities of the inner and outer cylinders) with a universal effective scaling law G \propto Ta^{0.88}, corresponding to Nu_omega \propto Ta^{0.38} for th…
We derive the velocity profiles in strongly turbulent Taylor-Couette flow for the general case of independently rotating cylinders. The theory is based on the Navier-Stokes equations in the appropriate (cylinder) geometry. In particular, we derive the axial and the angular velocity profiles as functions of distance from the cylinder walls and find that both follow a logarithmic profile, with downwards-bending curvature corrections, which are more pronounced for the angular velocity profile as compared to the axial velocity profile, and which strongly increase with decreasing ratio $η$ between …
We investigate the quasi two-dimensional Taylor-Couette system in the regime where the radius ratio is close to unity - a transitional regime between three and two dimensions. By systematically increasing the Reynolds number we observe a number of standard transitions, such as one from the classical Taylor vortex flow (TVF) to wavy vortex flow (WVF), as well as the transition to fully developed turbulence. Prior to the onset of turbulence we observe intermittent burst patterns of localized turbulent patches, confirming the experimentally observed pattern of very short wavelength bursts (VSWBs)…
We study magnetic Taylor-Couette flow in a system having nondimensional radii $r_i=1$ and $r_o=2$, and periodic in the axial direction with wavelengths $h\ge100$. The rotation ratio of the inner and outer cylinders is adjusted to be slightly in the Rayleigh-stable regime, where magnetic fields are required to destabilize the flow, in this case triggering the axisymmetric helical magnetorotational instability (HMRI). Two choices of imposed magnetic field are considered, both having the same azimuthal component $B_ϕ=r^{-1}$, but differing axial components. The first choice has $B_z=0.1$, and yie…
The transition from Tayor vortex flow to wavy-vortex flow is revisited. The Self-Sustaining Process (SSP) of Waleffe [Phys. Fluids 9, 883-900 (1997)] proposes that a key ingredient in transition to turbulence in wall-bounded shear flows is a three-step process involving rolls advecting streamwise velocity, leading to streaks which become unstable to a wavy perturbation whose nonlinear interaction with itself feeds the rolls. We investigate this process in Taylor-Couette flow. The instability of Taylor-vortex flow to wavy-vortex flow, a process which is the inspiration for the second phase of t…
We present azimuthal velocity profiles measured in a Taylor-Couette apparatus, which has been used as a model of stellar and planetary accretion disks. The apparatus has a cylinder radius ratio of $η= 0.716$, an aspect-ratio of $Γ= 11.74$, and the plates closing the cylinders in the axial direction are attached to the outer cylinder. We investigate angular momentum transport and Ekman pumping in the Rayleigh-stable regime. The regime is linearly stable and is characterized by radially increasing specific angular momentum. We present several Rayleigh-stable profiles for shear Reynolds numbers $…
In search for the cheapest but still reliable numerical simulation, a systematic study on the effect of the computational domain ("box") size on direct numerical simulations of Taylor-Couette flow was performed. Four boxes, with varying azimuthal and axial extents were used. The radius ratio between the inner cylinder and the outer cylinder was fixed to $η=r_i/r_o=0.909$, and the outer was kept stationary, while the inner rotated at a Reynolds number $Re_i=10^5$. Profiles of mean and fluctuation velocities are compared, as well as autocorrelations and velocity spectra. The smallest box is foun…
We create a highly controlled lab environment-accessible to both global and local monitoring-to analyse turbulent boiling flows and in particular their shear stress in a statistically stationary state. Namely, by precisely monitoring the drag of strongly turbulent Taylor-Couette flow (the flow in between two co-axially rotating cylinders, Reynolds number $\textrm{Re}\approx 10^6$) during its transition from non-boiling to boiling, we show that the intuitive expectation, namely that a few volume percent of vapor bubbles would correspondingly change the global drag by a few percent, is wrong. Ra…
In this paper I analyze the onset of Rayleigh-Taylor instability between two linear viscoelastic fluids assuming that the perturbations at the interface are small. In the first half, the paper analyzes a stratified viscoelastic fluid in which I prove that the perturbations rise or fall exponentially without oscillating. The second half of the paper examines the effect of electric and magnetic fields on viscoelastic fluids. I show that it is possible to choose electric or magnetic field gradient such that the effective acceleration due to gravity is zero. If a heavy Newtonian fluid rests on top…
Emulsions are omnipresent in the food industry, health care, and chemical synthesis. In this Letter the dynamics of meta-stable oil-water emulsions in highly turbulent ($10^{11}\leq\text{Ta}\leq 3\times 10^{13}$) Taylor--Couette flow, far from equilibrium, is investigated. By varying the oil-in-water void fraction, catastrophic phase inversion between oil-in-water and water-in-oil emulsions can be triggered, changing the morphology, including droplet sizes, and rheological properties of the mixture, dramatically. The manifestation of these different states is exemplified by combining global to…
We report on the modification of drag by neutrally buoyant spherical particles in highly turbulent Taylor-Couette flow. These particles can be used to disentangle the effects of size, deformability, and volume fraction on the drag, when contrasted with the drag for bubbly flows. We find that rigid spheres hardly change the drag of the system beyond the trivial viscosity effects caused by replacing the working fluid with particles. The size of the particle has a marginal effect on the drag, with smaller diameter particles showing only slightly lower drag. Increasing the particle volume fraction…
We study the nonlinear mode competition of various spiral instabilities in magnetised Taylor-Couette flow. The resulting finite-amplitude mixed-mode solution branches are tracked using the annular-parallelogram periodic domain approach developed by Deguchi & Altmeyer (2013). Mode competition phenomena are studied in both the anti-cyclonic and cyclonic Rayleigh-stable regimes. In the anti-cyclonic sub-rotation regime, with the inner cylinder rotating faster than the outer, Hollerbach, Teeluck & Rudiger (2010) found competing axisymmetric and non-axisymmetric magneto-rotational linearly unstable…
Direct numerical simulations of turbulent Taylor-Couette flow are performed up to inner cylinder Reynolds numbers of {Re_i=10^5} for a radius ratio of {η=r_i/r_o=0.714} between the inner and outer cylinder. With increasing {Re_i}, the flow undergoes transitions between three different regimes: (i) a flow dominated by large coherent structures, (ii) an intermediate transitional regime, and (iii) a flow with developed turbulence. In the first regime the large--scale rolls completely drive the meridional flow while in the second one the coherent structures recover only on average. The presence of…
We study the decay of high-Reynolds number Taylor-Couette turbulence, i.e. the turbulent flow between two coaxial rotating cylinders. To do so, the rotation of the inner cylinder (Re$_i=2 \times 10^6$, the outer cylinder is at rest) is stopped within 12 s, thus fully removing the energy input to the system. Using a combination of laser Doppler anemometry and particle image velocimetry measurements, six decay decades of the kinetic energy could be captured. First, in the absence of cylinder rotation, the flow-velocity during the decay does not develop any height dependence in contrast to the we…
We investigate numerically a traveling wave pattern observed in experimental magnetized Taylor-Couette flow at low magnetic Reynolds number. By accurately modeling viscous and magnetic boundaries in all directions, we reproduce the experimentally measured wave patterns and their amplitudes. Contrary to previous claims, the waves are shown to be transiently amplified disturbances launched by viscous boundary layers rather than globally unstable magnetorotational modes.
We numerically simulate turbulent Taylor-Couette flow for independently rotating inner and outer cylinders, focusing on the analogy with turbulent Rayleigh-Bénard flow. Reynolds numbers of $Re_i=8\cdot10^3$ and $Re_o=\pm4\cdot10^3$ of the inner and outer cylinders, respectively, are reached, corresponding to Taylor numbers Ta up to $10^8$. Effective scaling laws for the torque and other system responses are found. Recent experiments with the Twente turbulent Taylor-Couette ($T^3C$) setup and with a similar facility in Maryland at very high Reynolds numbers have revealed an optimum transport at…
We present direct numerical simulations of Taylor-Couette flow with grooved walls at a fixed radius ratio $η=r_i/r_o=0.714$ with inner cylinder Reynolds number up to $Re_i=3.76\times10^4$, corresponding to Taylor number up to $Ta=2.15\times10^9$. The grooves are axisymmetric V-shaped obstacles attached to the wall with a tip angle of $90^\circ$. Results are compared to the smooth wall case in order to investigate the effects of grooves on Taylor-Couette flow. We focus on the effective scaling laws for the torque, flow structures, and boundary layers. It is found that, when the groove height is…
A counter-rotating Taylor-Couette flow with relatively small radius ratios of $η$ = 0.2--0.5 was investigated over a wide range of the Reynolds number, from laminar to turbulent regime, by means of three-dimensional direct numerical simulations. We investigated the $η$ dependence of the flow structure and determined a critical value between $η$ = 0.2 and 0.3, below which, the stable outer cylinder side exhibited a modal structure that was different from the Taylor-vortex flow on the inner side. At $η\geq$ 0.3, the Taylor-vortex on the unstable inner side dominated the entire flow field between…
We consider the nonaxisymmetric modes of instability present in Taylor-Couette flow under the application of helical magnetic fields, mainly for magnetic Prandtl numbers close to the inductionless limit, and conduct a full examination of marginal stability in the resulting parameter space. We allow for the azimuthal magnetic field to be generated by a combination of currents in the inner cylinder and fluid itself, and introduce a parameter governing the relation between the strength of these currents. A set of governing eigenvalue equations for the nonaxisymmetric modes of instability are deri…
In the past twenty years, shear-banding flows have been probed by various techniques, such as rheometry, velocimetry and flow birefringence. In micellar solutions, many of the data collected exhibit unexplained spatio-temporal fluctuations. Recently, it has been suggested that those fluctuations originate from a purely elastic instability of the flow. In cylindrical Couette geometry, the instability is reminiscent of the Taylor-like instability observed in viscoelastic polymer solutions. In this letter, we describe how the criterion for purely elastic Taylor-Couette instability should be adapt…
We provide experimental measurements for the effective scaling of the Taylor-Reynolds number within the bulk $\text{Re}_{λ,\text{bulk}}$, based on local flow quantities as a function of the driving strength (expressed as the Taylor number Ta), in the ultimate regime of Taylor-Couette flow. The data are obtained through flow velocity field measurements using Particle Image Velocimetry (PIV). We estimate the value of the local dissipation rate $ε(r)$ using the scaling of the second order velocity structure functions in the longitudinal and transverse direction within the inertial range---without…
This paper is the first part of a two-fold study of mixing, i.e. the formation of layers and upwelling of buoyancy, in axially stratified Taylor--Couette flow, with fixed outer cylinder. Using linear analysis and direct numerical simulation, we show the critical role played by non-axisymmetric instability modes, despite the fact that the flow is centrifugally unstable in the sense of Rayleigh's criterion. Interactions between helical modes of opposite handedness leads to the formation of nonlinear coherent structures: (mixed)-ribbons and (mixed)-cross-spirals. These give birth to complex densi…
Although inertial particle-laden flows occur in a wide range of industrial and natural processes, there is both a lack of fundamental understanding of these flows and continuum-level governing equations needed to predict transport and particle distribution. Towards this effort, the Taylor-Couette flow (TCF) system has been used recently to study the flow behavior of particle-laden fluids under inertia. This article provides an overview of experimental, theoretical, and computational work related to the TCF of neutrally buoyant non-Brownian suspensions, with an emphasis on the effect of finite-…
We consider the effect of radial fluid injection and suction on Taylor-Couette flow. Injection at the outer cylinder and suction at the inner cylinder generally results in a linearly unstable steady spiralling flow, even for cylindrical shears that are linearly stable in the absence of a radial flux. We study nonlinear aspects of the unstable motions with the energy stability method. Our results, though specialized, may have implications for drag reduction by suction, accretion in astrophysical disks, and perhaps even in the flow in the earth's polar vortex.
