We present numerical simulations of vortices that appear via primary bifurcations out of the unstructured circular Couette flow in the Taylor-Couette system with counter-rotating as well as with co-rotating cylinders. The full, time dependent Navier-Stokes equations are solved with a combination of a finite difference and a Galerkin method for a fixed axial periodicity length of the vortex patterns and for a finite system of aspect ratio 12 with rigid nonrotating ends in a setup with radius ratio eta=0.5. Differences in structure, dynamics, symmetry properties, bifurcation and stability behavior between spiral vortices with azimuthal wave numbers M=+-1 and M=0 Taylor vortices are elucidated and compared in quantitative detail. Simulations in axially periodic systems and in finite systems with stationary rigid ends are compared with experimental spiral data. In a second part of the paper we determine how the above listed properties of the M=-1,0,1 vortex structures are changed by an externally imposed axial through-flow with Reynolds numbers in the range -40 <= Re <= 40. Among others we investigate when left handed or right handed spirals or toroidally closed vortices are preferred.
We study the steady streaming between two infinitely long circular cylinders produced by small amplitude transverse vibrations of the inner cylinder about the axis of the outer cylinder. The Vishik-Lyusternik method is employed to construct an asymptotic expansion of the solution of the Navier-Stokes equations in the limit of high-frequency vibrations for Reynolds numbers of order of unity. The effect of the Stokes drift of fluid particles is also studied. It is shown that it is nonzero not only within the boundary layers but also in higher order terms of the expansion of the averaged outer fl…
Natural convection in a cylinder with an internally slotted annulus was solved by SIMPLE algorithm, and the effects of different slotted structures on nonlinear characteristics of natural convection were investigated. The results show that the equivalent thermal conductivity Keq increases with Rayleigh number, and reaches the maximum in the vertical orientation. Nonlinear results were obtained by simulating the fluid flow at different conditions. With increasing Rayleigh number, heat transfer is intensified and the state of heat transfer changes from the steady to unsteady. We investigated dif…
We consider the stability of two-dimensional viscous flows in an annulus with permeable boundary. In the basic flow, the velocity has nonzero azimuthal and radial components, and the direction of the radial flow can be from the inner cylinder to the outer one or vice versa. In most earlier studies, all components of the velocity were assumed to be given on the entire boundary of the flow domain. Our aim is to study the effect of different boundary conditions on the stability of such flows. We focus on the following boundary conditions: at the inflow part if the boundary (which may be either in…
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…
We analyze the stability of a cylindrical Couette flow under the imposition of a weak axial flow in case of a very short cylinder with a narrow annulus gap. We consider an incompressible viscous fluid which is contained in the narrow gap between two concentric short cylinders, where the inner cylinder rotates with constant angular velocity. The caps of the cylinders have narrow tubes conically tapering to super narrow slits which allow for an axial flow along the surface of the inner cylinder. The approximated solution for the Couette flow for short cylinders was found and used for the stabili…
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…
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…
The nonaxisymmetric azimuthal magnetorotational instability is studied for hydromagnetic Taylor-Couette flows between cylinders of finite electrical conductivity. We find that the magnetic Prandtl number Pm determines whether perfectly conducting or insulating boundary conditions lead to lower Hartmann numbers for the onset of instability. Regardless of the imposed rotation profile, for small Pm the solutions for perfectly conducting cylinders become unstable for weaker magnetic fields than the solutions for insulating cylinders. The critical Hartmann and Reynolds numbers form monotonic functi…
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…
The stability of two-dimensional diverging and converging flows in an annulus between two permeable cylinders is examined. The basic flow is irrotational and has both the radial and azimuthal components. It is shown that for a wide range of the parameters of the problem, the basic flow is unstable to small two-dimensional perturbations. The instability is inviscid and oscillatory and persists if the viscosity of the fluid is taken into consideration.
A series of direct numerical simulations of Taylor-Couette (TC) flow, the flow between two coaxial cylinders, with the outer cylinder rotating and the inner one fixed, were performed. Three cases, with outer cylinder Reynolds numbers $Re_o$ of $Re_o=5.5\cdot10^4$, $Re_o=1.1\cdot10^5$ and $Re_o=2.2\cdot10^5$ were considered. The radius ratio $η=r_i/r_o$ was fixed to $η=0.909$ to mitigate the effects of curvature. The vertical aspect ratio $Γ$ was fixed to $Γ=2.09$. Being linearly stable, outer cylinder rotation TC flow is known to have very different behavior than pure inner cylinder rotation T…
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…
The distribution of energy loss due to viscosity friction in plane Couette flow and Taylor-Couette Flow between concentric rotating cylinders are studied in detail for various flow conditions. The energy loss is related to the industrial processes in some fluid delivery devices and has significant influence on the flow efficiency, flow stability, turbulent transition, mixing, and heat transfer behaviours, etc. Therefore, it is important to know about the energy loss distribution in the flow domain and to know its influence on the flow for better understanding of the flow physics. The calculati…
We experimentally study the influence of wall roughness on bubble drag reduction in turbulent Taylor-Couette flow, i.e.\ the flow between two concentric, independently rotating cylinders. We measure the drag in the system for the cases with and without air, and add roughness by installing transverse ribs on either one or both of the cylinders. For the smooth wall case (no ribs) and the case of ribs on the inner cylinder only, we observe strong drag reduction up to $DR=33\%$ and $DR=23\%$, respectively, for a void fraction of $α=6\%$. However, with ribs mounted on both cylinders or on the outer…
We present wall-resolved large-eddy simulations (LES) of the incompressible Navier-Stokes equations together with empirical modeling for {turbulent} Taylor-Couette {(TC)} flow where the inner cylinder is rotating with angular velocity $Ω_i$ and the outer cylinder is stationary. A simple empirical model of the turbulent, TC flow is developed consisting of near-wall, log-like turbulent wall layers separated by an annulus of constant angular momentum. The model is closed by a proposed scaling relation concerning the thickness of the wall layer on the inner cylinder. Model results include the Nuss…
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 $…
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…
The energy gradient theory is used to study the instability of Taylor-Couette flow between concentric rotating cylinders. This theory has been proposed in our previous works. In our previous studies, the energy gradient theory was demonstrated to be applicable for wall-bounded parallel flows. It was found that the critical value of the energy gradient parameter Kmax at turbulent transition is about 370-389 for wall-bounded parallel flows (which include plane Poiseuille flow, pipe Poiseuille flow and plane Couette flow) below which no turbulence occurs. In this paper, the detailed derivation fo…
A new Taylor-Couette system has been designed and constructed with precise temperature control. Two concentric independently rotating cylinders are able to rotate at maximum rates of $f_i = \pm20$ Hz for the inner cylinder and $f_o = \pm10$ Hz for the outer cylinder. The inner cylinder has an outside radius of $r_i = 75$ mm, and the outer cylinder has an inside radius of $r_o = 105$ mm, resulting in a gap of $d=30$ mm. The height of the gap $L =549$ mm, giving a volume of $V=9.3$l. The geometric parameters are $η= r_i/r_o = 0.714$ and $Γ= L/d = 18.3$. With water as working fluid at room temper…
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 …
Using high-resolution particle image velocimetry we measure velocity profiles, the wind Reynolds number and characteristics of turbulent plumes in Taylor-Couette flow for a radius ratio of 0.5 and Taylor number of up to $6.2\cdot10^9$. The extracted angular velocity profiles follow a log-law more closely than the azimuthal velocity profiles due to the strong curvature of this $η=0.5$ setup. The scaling of the wind Reynolds number with the Taylor number agrees with the theoretically predicted 3/7-scaling for the classical turbulent regime, which is much more pronounced than for the well-explore…
We consider a Taylor-Dean-type flow of an electrically conducting liquid in an annulus between two infinitely long perfectly conducting cylinders subject to a generally helical magnetic field. The cylinders are electrically connected through a remote, perfectly conducting endcap, which allows a radial electric current to pass through the liquid. The radial current interacting with the axial component of magnetic field gives rise to the azimuthal electromagnetic force, which destabilizes the base flow by making its angular momentum decrease radially outwards. This instability, which we refer to…
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…
Air cavities, i.e. air layers developed behind cavitators, are seen as a promising drag reducing method in the maritime industry. Here we utilize the Taylor-Couette (TC) geometry, i.e. the flow between two concentric, independently rotating cylinders, to study the effect of air cavities in this closed setup, which is well-accessible for drag measurements and optical flow visualizations. We show that stable air cavities can be formed, and that the cavity size increases with Reynolds number and void fraction. The streamwise cavity length strongly depends on the axial position due to buoyancy for…
We study numerically the induction mechanisms generated from an array of helical motions distributed along a cylinder. Our flow is a very idealized geometry of the columnar structure that has been proposed for the convective motion inside the Earth core. Using an analytically prescribed flow, we apply a recently introduced iterative numerical scheme to solve the induction equation and analyze the flow response to externally applied fields with simple geometries (azimuthal, radial, etc.). Symmetry properties allow us to build selected induction modes whose interactions lead to dynamo mechanisms…
Numerical calculations of vortex flows in Taylor-Couette systems with counter rotating cylinders are presented. The full, time dependent Navier-Stokes equations are solved with a combination of a finite difference and a Galerkin method. Annular gaps of radius ratio $η=0.5$ and of several heights are simulated. They are closed by nonrotating lids that produce localized Ekman vortices in their vicinity and that prevent axial phase propagation of spiral vortices. Existence and spatio temporal properties of rotating defects, of modulated Ekman vortices, and of the spiral vortex structures in the b…
In this study we experimentally investigate bubbly drag reduction in a highly turbulent flow of water with dispersed air at $5.0 \times 10^{5} \leq \text{Re} \leq 1.7 \times 10^{6}$ over a non-wetting surface containing micro-scale roughness. To do so, the Taylor-Couette geometry is used, allowing for both accurate global drag and local flow measurements. The inner cylinder - coated with a rough, hydrophobic material - is rotating, whereas the smooth outer cylinder is kept stationary. The crucial control parameter is the air volume fraction $α$ present in the working fluid. For small volume fr…
Strongly turbulent Taylor-Couette flow with independently rotating inner and outer cylinders with a radius ratio of η= 0.716 is experimentally studied. From global torque measurements, we analyse the dimensionless angular velocity flux Nu_ω(Ta, a) as a function of the Taylor number Ta and the angular velocity ratio a = -ω_o/ω_i in the large-Taylor-number regime 10^{11} \lesssim Ta \lesssim 10^{13}. We analyse the data with the common power-law ansatz for the dimensionless angular velocity transport flux Nu_ω(Ta, a) = f(a)Ta^γ, with an amplitude f(a) and an exponent γ. The data are consistent w…
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.
We report on the mobility and orientation of finite-size, neutrally buoyant prolate ellipsoids (of aspect ratio $Λ=4$) in Taylor-Couette flow, using interface resolved numerical simulations. The setup consists of a particle-laden flow in between a rotating inner and a stationary outer cylinder. We simulate two particle sizes $\ell/d=0.1$ and $\ell/d=0.2$, $\ell$ denoting the particle major axis and $d$ the gap-width between the cylinders. The volume fractions are $0.01\%$ and $0.07\%$, respectively. The particles, which are initially randomly positioned, ultimately display characteristic spati…
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…
In this paper, we study the nonlinear stability of a steady circular flow created between two rotating concentric cylinders. The dynamics of the viscous fluid are described by 2D Navier-Stokes equations. We adopt scaling variables. For the rescaled equations, we prove that the steady flow (Taylor-Couette flow) is asymptotically stable up to a large perturbation of initial data. Back to the original 2D Navier-Stokes equations, this implies an improved transition threshold for the Taylor-Couette flow. The improvement is due to enhanced dissipation and new observations and constructions of weight…
Direct numerical simulations of the Taylor-Couette (TC) problem, the flow between two coaxial and independently rotating cylinders, have been performed. The study focuses on TC flow with mild curvature (small gap) with a radius ratio of $η=r_i/r_o=0.909$, an aspect ratio of $Γ=L/d=2π/3$, and a stationary outer cylinder. Three inner cylinder Reynolds of $1\cdot10^5$, $2\cdot10^5$ and $3\cdot 10^5$ were simulated, corresponding to frictional Reynolds numbers between $Re_τ\approx 1400$ and $Re_τ\approx 4000$. An additional case with a large gap, $η=0.5$ and driving of $Re=2\cdot10^5$ was also per…
The statistics of velocity fluctuations of turbulent Taylor-Couette flow are examined. The rotation rate of the inner and outer cylinder are varied while keeping the Taylor number fixed to $1.49 \times 10^{12}$ ($\mathcal{O}(\text{Re})=10^6$). The azimuthal velocity component of the flow is measured using laser Doppler anemometry (LDA). For each experiment $5\times10^6$ datapoints are acquired and carefully analysed. Using extended self-similarity (ESS) \cite{ben93b} the longitudinal structure function exponents are extracted, and are found to weakly depend on the ratio of the rotation rates. …
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 experimentally and numerically investigate the angular momentum transport in turbulent Taylor-Couette flow for independently rotating cylinders at a small radius ratio of $η=0.357$ for various shear Reynolds numbers ($4.5\times 10^3 \leq Re_S \leq 1.2 \times 10^5$) and ratios of angular velocities ($-0.5 \leq μ\leq 0.2$). \red{The momentum transport in terms of the pseudo-Nusselt number ${Nu}_ω$ does not show a pure power law scaling with the forcing $Re_S$ and features non-constant effective scaling between $1.3\times 10^4 \leq Re_S \leq 4 \times 10^4$. This transition lies in the classica…
Hollerbach and Rudiger have reported a new type of magnetorotational instability (MRI) in magnetized Taylor-Couette flow in the presence of combined axial and azimuthal magnetic fields. The salient advantage of this "helical'' MRI (HMRI) is that marginal instability occurs at arbitrarily low magnetic Reynolds and Lundquist numbers, suggesting that HMRI might be easier to realize than standard MRI (axial field only). We confirm their results, calculate HMRI growth rates, and show that in the resistive limit, HMRI is a weakly destabilized inertial oscillation propagating in a unique direction al…
The phenomenon of drag reduction induced by injection of bubbles into a turbulent carrier fluid has been known for a long time; the governing control parameters and underlying physics is however not well understood. In this paper, we use three dimensional numerical simulations to uncover the effect of deformability of bubbles injected in a turbulent Taylor-Couette flow on the overall drag experienced by the system. We consider two different Reynolds numbers for the carrier flow, i.e. $Re_i=5\times 10^3$ and $Re_i=2\times 10^4$; the deformability of the bubbles is controlled through the Weber n…
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…
Direct numerical simulations of Taylor-Couette flow (TC). Shear Reynolds numbers of up to $3\cdot10^5$, corresponding to Taylor numbers of $Ta=4.6\cdot10^{10}$, were reached. Effective scaling laws for the torque are presented. The transition to the ultimate regime, in which asymptotic scaling laws (with logarithmic corrections) for the torque are expected to hold up to arbitrarily high driving, is analysed for different radius ratios $η$, different aspect ratios $Γ$ and different rotation ratios $Ro$. It is shown that the transition is approximately independent of $Ro$ and $Γ$, but depends si…
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 study periodically driven Taylor-Couette turbulence, i.e. the flow confined between two concentric, independently rotating cylinders. Here, the inner cylinder is driven sinusoidally while the outer cylinder is kept at rest (time-averaged Reynolds number is $Re_i = 5 \times 10^5$). Using particle image velocimetry (PIV), we measure the velocity over a wide range of modulation periods, corresponding to a change in Womersley number in the range $15 \leq Wo \leq 114$. To understand how the flow responds to a given modulation, we calculate the phase delay and amplitude response of the azimuthal …
We present a new lattice kinetic method to simulate fluid dynamics in curvilinear geometries. A suitable discrete Boltzmann equation is solved in contravariant coordinates, and the equilibrium distribution function is obtained by a Hermite polynomials expansion of the Maxwell-Boltzmann distribution, expressed in terms of the contravariant coordinates and the metric tensor. To validate the model, we calculate the critical Reynolds number for the onset of the Taylor-Couette instability between two concentric cylinders, obtaining excellent agreement with the theory. In order to extend this study …
The `Rayleigh line' $μ=η^2$, where $μ=Ω_o/Ω_i$ and $η=r_i/r_o$ are respectively the rotation and radius ratios between inner (subscript `i') and outer (subscript `o') cylinders, is regarded as marking the limit of centrifugal instability (CI) in unstratified inviscid Taylor-Couette flow, for both axisymmetric and non-axisymmetric modes. Non-axisymmetric stratorotational instability (SRI) is known to set in for anticyclonic rotation ratios beyond that line, i.e. $η^2<μ<1$ for axially stably-stratified Taylor-Couette flow, but the competition between CI and SRI in the range $μ<η^2$ has not yet b…
Taylor-Couette (TC) flow, the flow between two independently rotating and co-axial cylinders is commonly used as a canonical model for shear flows. Unlike plane Couette, pinned secondary flows can be found in TC flow. These are known as Taylor rolls and drastically affect the flow behaviour. We study the possibility of modifying these secondary structures using patterns of stress-free and no-slip boundary conditions on the inner cylinder. For this, we perform direct numerical simulations of narrow-gap TC flow with pure inner cylinder rotation at four different shear Reynolds numbers up to $Re_…
A series of direct numerical simulations in large computational domains has been performed in order to probe the spatial feature robustness of the Taylor rolls in turbulent Taylor-Couette (TC) flow. The latter is the flow between two coaxial independently rotating cylinders of radius $r_i$ and $r_o$, respectively. Large axial aspect ratios $Γ= 7$-$8$ (with $Γ= L/(r_o-r_i)$, and $L$ the axial length of the domain) and a simulation with $Γ=14$ were used in order to allow the system to select the most unstable wavenumber and to possibly develop multiple states. The radius ratio was taken as $η=r_…
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…
The instability of a supercritical Taylor-Couette flow of a conducting fluid with resting outer cylinder under the influence of a uniform axial electric current is investigated for magnetic Prandtl number Pm=1. In the linear theory the critical Reynolds number for axisymmetric perturbations is not influenced by the current-induced axisymmetric magnetic field but all axisymmetric magnetic perturbations decay. The nonaxisymmetric perturbations with m=1 are excited even without rotation for large enough Hartmann numbers ("Tayler instability"). For slow rotation their growth rates scale with the A…
