Browsing by Author "Verzicco, Roberto"
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Item A multiple-resolution strategy for Direct Numerical Simulation of scalar turbulence(Journal of Computational Physics, 2015-02) Ostilla-Mónico, Rodolfo; Yang, Yantao; Van Der Poel, Erwin P.; Lohse, Detlef; Verzicco, RobertoIn this paper a numerical procedure to simulate low diffusivity scalar turbulence is presented. The method consists of using a grid for the advected scalar with a higher spatial resolution than that of the momentum. The latter usually requires a less refined mesh and integrating both fields on a single grid tailored to the most demanding variable produces an unnecessary computational overhead. A multiple resolution approach is used also in the time integration in order to maintain the stability of the scalars on the finer grid. The method is the more advantageous the less diffusive the scalar is with respect to momentum, therefore it is particularly well suited for large Prandtl or Schmidt number flows. However, even in the case of equal diffusivities the present procedure gives CPU time and memory occupation savings, due to the increased gradients and more intermittent behaviour of the scalars when compared to momentum.Item A parallel interaction potential approach coupled with the immersed boundary method for fully resolved simulations of deformable interfaces and membranes(Journal of Computational Physics, 2016-12) Spandan, Vamsi; Meschini, Valentina; Ostilla-Mónico, Rodolfo; Lohse, Detlef; Querzolo, Giorgio; De Tulio, Marco D.; Verzicco, RobertoIn this paper we show and discuss how the deformation dynamics of closed liquid–liquid interfaces (for example drops and bubbles) can be replicated with use of a phenomenological interaction potential model. This new approach to simulate liquid–liquid interfaces is based on the fundamental principle of minimum potential energy where the total potential energy depends on the extent of deformation of a spring network distributed on the surface of the immersed drop or bubble. Simulating liquid–liquid interfaces using this model require computing ad-hoc elastic constants which is done through a reverse-engineered approach. The results from our simulations agree very well with previous studies on the deformation of drops in standard flow configurations such as a deforming drop in a shear flow or cross flow. The interaction potential model is highly versatile, computationally efficient and can be easily incorporated into generic single phase fluid solvers to also simulate complex fluid–structure interaction problems. This is shown by simulating flow in the left ventricle of the heart with mechanical and natural mitral valves where the imposed flow, motion of ventricle and valves dynamically govern the behaviour of each other. Results from these simulations are compared with ad-hoc in-house experimental measurements. Finally, we present a simple and easy to implement parallelisation scheme, as high performance computing is unavoidable when studying large scale problems involving several thousands of simultaneously deforming bodies in highly turbulent flows.Item A pencil distributed finite difference code for strongly turbulent wall-bounded flows(Computers and Fluids, 2015-01) Van Der Poel, Erwin P.; Ostilla-Mónico, Rodolfo; Donners, John; Verzicco, RobertoWe present a numerical scheme geared for high performance computation of wall-bounded turbulentflows. The number of all-to-all communications is decreased to only six instances by using a two-dimensional (pencil) domain decomposition and utilizing the favourable scaling of the CFL time-stepconstraint as compared to the diffusive time-step constraint. As the CFL condition is more restrictiveat high driving, implicit time integration of the viscous terms in the wall-parallel directions is no longerrequired. This avoids the communication of non-local information to a process for the computation ofimplicit derivatives in these directions. We explain in detail the numerical scheme used for the integra-tion of the equations, and the underlying parallelization. The code is shown to have very good strong andweak scaling to at least 64 K cores.Item AFiD-GPU: A versatile Navier–Stokes solver for wall-bounded turbulent flows on GPU clusters(Computer Physics Communications, 2017-05) Zhu, Xiaojue; Phillips, Everett; Spandan, Vamsi; Donners, John; Ruetsch, Gregory; Romero, Joshua; Ostilla-Mónico, Rodolfo; Yang, Yantao; Lohse, Detlef; Verzicco, Roberto; Fatica, Massimiliano; Stevens, Richard J. A. M.The AFiD code, an open source solver for the incompressible Navier–Stokes equations (http://www.afid.eu), has been ported to GPU clusters to tackle large-scale wall-bounded turbulent flow simulations. The GPU porting has been carried out in CUDA Fortran with the extensive use of kernel loop directives (CUF kernels) in order to have a source code as close as possible to the original CPU version; just a few routines have been manually rewritten. A new transpose scheme has been devised to improve the scaling of the Poisson solver, which is the main bottleneck of incompressible solvers. For large meshes the GPU version of the code shows good strong scaling characteristics, and the wall-clock time per step for the GPU version is an order of magnitude smaller than for the CPU version of the code. Due to the increased performance and efficient use of memory, the GPU version of AFiD can perform simulations in parameter ranges that are unprecedented in thermally-driven wall-bounded turbulence. To verify the accuracy of the code, turbulent Rayleigh–Bénard convection and plane Couette flow are simulated and the results are in excellent agreement with the experimental and computational data that have been published in literature.Item Boundary layer dynamics at the transition between the classical and the ultimate regime of Taylor-Couette flow(Physics of Fluids, 2014) Ostilla-Mónico, Rodolfo; Van Der Poel, Erwin P.; Verzicco, Roberto; Grossmann, Siegfried; Lohse, DetlefDirect numerical simulations of turbulent Taylor-Couette flow are performed up to inner cylinder Reynolds numbers of Rei = 105 for a radius ratio of ? = ri/ro = 0.714 between the inner and outer cylinders. With increasing Rei, 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 a mean flow allows for the coexistence of laminar and turbulent boundary layer dynamics. In the third regime, the mean flow effects fade away and the flow becomes dominated by plumes. The effect of the local driving on the azimuthal and angular velocity profiles is quantified, in particular, we show when and where those profiles developItem Direct numerical simulation of Taylor–Couette flow with grooved walls: torque scaling and flow structure(Journal of Fluid Mechanics, 2016-03) Zhu, Xiaojue; Ostilla-Mónico, Rodolfo; Verzicco, Roberto; Lohse, DetlefWe present direct numerical simulations of Taylor–Couette flow with grooved walls at a fixed radius ratio n=ri/r0=0.714 with inner cylinder Reynolds number up to rei=3.76x10^4 , corresponding to Taylor number up to Ta=2.15x10^9 . The grooves are axisymmetric V-shaped obstacles attached to the wall with a tip angle of 90°. 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 smaller than the boundary layer thickness, the torque is the same as that of the smooth wall cases. With increasing Ta , the boundary layer thickness becomes smaller than the groove height. Plumes are ejected from the tips of the grooves and secondary circulations between the latter are formed. This is associated with a sharp increase of the torque, and thus the effective scaling law for the torque versus Ta becomes much steeper. Further increasing Ta does not result in an additional slope increase. Instead, the effective scaling law saturates to the ‘ultimate’ regime effective exponents seen for smooth walls. It is found that even though after saturation the slope is the same as for the smooth wall case, the absolute value of torque is increased, and more so with the larger size of the grooves.Item Drag reduction in numerical two-phase Taylor–Couette turbulence using an Euler–Lagrange approach(Journal of Fluid Mechanics, 2016-05) Spandan, Vamsi; Ostilla-Mónico, Rodolfo; Verzicco, Roberto; Lohse, DetlefTwo-phase turbulent Taylor–Couette (TC) flow is simulated using an Euler–Lagrange approach to study the effects of a secondary phase dispersed into a turbulent carrier phase (here bubbles dispersed into water). The dynamics of the carrier phase is computed using direct numerical simulations (DNS) in an Eulerian framework, while the bubbles are tracked in a Lagrangian manner by modelling the effective drag, lift, added mass and buoyancy force acting on them. Two-way coupling is implemented between the dispersed phase and the carrier phase which allows for momentum exchange among both phases and to study the effect of the dispersed phase on the carrier phase dynamics. The radius ratio of the TC setup is fixed to ? = 0.833, and a maximum inner cylinder Reynolds number of Rei = 8000 is reached. We vary the Froude number (Fr), which is the ratio of the centripetal to the gravitational acceleration of the dispersed phase and study its effect on the net torque required to drive the TC system. For the two-phase TC system, we observe drag reduction, i.e. the torque required to drive the inner cylinder is lower compared with that of the single-phase system. The net drag reduction decreases with increasing Reynolds number Rei, which is consistent with previous experimental findings (Murai et al., J. Phys.: Conf. Ser., vol. 14, 2005, pp. 143–156; Phys. Fluids, vol. 20(3), 2008, 034101). The drag reduction is strongly related to the Froude number: for fixed Reynolds number we observe higher drag reduction when Fr < 1 than for with Fr > 1. This buoyancy effect is more prominent in low Rei systems and decreases with increasing Reynolds number Rei. We trace the drag reduction back to the weakening of the angular momentum carrying Taylor rolls by the rising bubbles. We also investigate how the motion of the dispersed phase depends on Rei and Fr, by studying the individual trajectories and mean dispersion of bubbles in the radial and axial directions. Indeed, the less buoyant bubbles (large Fr) tend to get trapped by the Taylor rolls, while the more buoyant bubbles (small Fr) rise through and weaken themItem Effect of roll number on the statistics of Taylor-Couette flow(Physical Review Fluids, 2016-09) Ostilla-Mónico, Rodolfo; Lohse, Detlef; Verzicco, RobertoA 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 flow. The latter is the flow between two coaxial independently rotating cylinders of radius ri and ro, respectively. Large axial aspect ratios ?=7–8 [with ?=L/(ro?ri), and L the axial length of the domain] and a simulation with ?=14were used in order to allow the system to select the most unstable wave number and to possibly develop multiple states. The radius ratio was taken as ?=ri/ro= 0.909, the inner cylinder Reynolds number was fixed to Rei=3.4×10^4, and the outer cylinder was kept stationary, resulting in a frictional Reynolds number of Re??500, except for the ?=14simulation where Rei=1.5×10^4 and Re??240. The large-scale rolls were found to remain axially pinned for all simulations. Depending on the initial conditions, stable solutions with different number of rolls nrand roll wavelength ?z were found for ?=7.The effect of ?z and nron the statistics was quantified. The torque and mean flow statistics were found to be independent of both ?z and nr, while the velocity fluctuations and energy spectra showed some box-size dependence. Finally, the axial velocity spectra were found to have a very sharp dropoff for wavelengths larger than ?z, while for the small wavelengths they collapse.Item Effect of vapor bubbles on velocity fluctuations and dissipation rates in bubbly Rayleigh-B ?enard convection(Physical Review E, 9/19/2011) Lakkaraju, Rajaram; Schmidt, Laura E.; Oresta, Paolo; Toschi, Federico; Verzicco, Roberto; Lohse, Detlef; Prosperetti, AndreaNumerical results for kinetic and thermal energy dissipation rates in bubbly Rayleigh-Bénard convection are reported. Bubbles have a twofold effect on the flow: on the one hand, they absorb or release heat to the surrounding liquid phase, thus tending to decrease the temperature differences responsible for the convective motion; but on the other hand, the absorbed heat causes the bubbles to grow, thus increasing their buoyancy and enhancing turbulence (or, more properly, pseudoturbulence) by generating velocity fluctuations. This enhancement depends on the ratio of the sensible heat to the latent heat of the phase change, given by the Jakob number, which determines the dynamics of the bubble growth.Item Effect of velocity boundary conditions on the heat transfer and flow topology in two-dimensional Rayleigh-Bénard convection(Physical Review E, 2014-07) Van Der Poel, Erwin P.; Ostilla-Mónico, Rodolfo; Verzicco, Roberto; Lohse, DetlefThe effect of various velocity boundary condition is studied in two-dimensional Rayleigh-Bénard convection. Combinations of no-slip, stress-free, and periodic boundary conditions are used on both the sidewalls and the horizontal plates. For the studied Rayleigh numbers Ra between 10^8 and 10^11 the heat transport is lower for ?=0.33 than for ?=1in case of no-slip sidewalls. This is, surprisingly, the opposite for stress-free sidewalls, where the heat transport increases for a lower aspect ratio. In wider cells the aspect-ratio dependence is observed to disappear for Ra?10^10. Two distinct flow types with very different dynamics can be seen, mostly dependent on the plate velocity boundary condition, namely roll-like flow and zonal flow, which have a substantial effect on the dynamics and heat transport in the system. The predominantly horizontal zonal flow suppresses heat flux and is observed for stress-free and asymmetric plates. Low aspect-ratio periodic sidewall simulations with a no-slip boundary condition on the plates also exhibit zonal flow. In all the other cases, the flow is roll like. In two-dimensional Rayleigh-Bénard convection, the velocity boundary conditions thus have large implications on both roll-like and zonal flow that have to be taken into consideration before the boundary conditions are imposed.Item Effects of the computational domain size on DNS of Taylor-Couette turbulence with stationary outer cylinder(Physics of Fluids, 2015) Ostilla-Mónico, Rodolfo; Verzicco, Roberto; Lohse, DetlefIn 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 ? = ri/ro = 0.909. The outer cylinder was kept stationary, while the inner rotated at a Reynolds number Rei = 105. Profiles of mean and fluctuation velocities are compared, as well as autocorrelations and velocity spectra. The smallest box is found to accurately reproduce the torque and mean azimuthal velocity profiles of larger boxes, while having smaller values of the fluctuations than the larger boxes. The axial extent of the box directly reflects on the Taylor-rolls and plays a crucial role on the correlations and spectra. The azimuthal extent is found to play a minor role in the simulations, as the boxes are large enough. For all boxes studied, the spectra do not reach a box independent maximum.Item Exploring the large-scale structure of Taylor–Couette turbulence through Large-Eddy Simulations(Journal of Physics: Conference Series, 2018) Ostilla-Mónico, Rodolfo; Zhu, Xiaojue; Verzicco, RobertoLarge eddy simulations (LES) of Taylor-Couette (TC) flow, the flow between two co-axial and independently rotating cylinders are performed in an attempt to explore the large-scale axially-pinned structures seen in experiments and simulations. Both static and dynamic LES models are used. The Reynolds number is kept fixed at Re = 3.4 centerdot 104, and the radius ratio ? = ri /ro is set to ? = 0.909, limiting the effects of curvature and resulting in frictional Reynolds numbers of around Re ? ? 500. Four rotation ratios from Rot = ?0.0909 to Rot = 0.3 are simulated. First, the LES of TC is benchmarked for different rotation ratios. Both the Smagorinsky model with a constant of cs = 0.1 and the dynamic model are found to produce reasonable results for no mean rotation and cyclonic rotation, but deviations increase for increasing rotation. This is attributed to the increasing anisotropic character of the fluctuations. Second, "over-damped" LES, i.e. LES with a large Smagorinsky constant is performed and is shown to reproduce some features of the large-scale structures, even when the near-wall region is not adequately modeled. This shows the potential for using over-damped LES for fast explorations of the parameter space where large-scale structures are found.Item Exploring the phase diagram of fully turbulent Taylor–Couette flow(Journal of Fluid Mechanics, 2014-10) Ostilla-Mónico, Rodolfo; Van Der Poel, Erwin P.; Verzicco, Roberto; Grossmann, SiegfriedDirect numerical simulations of Taylor–Couette flow, i.e. the flow between two coaxial and independently rotating cylinders, were performed. Shear Reynolds numbers of up to 3 × 10^5, corresponding to Taylor numbers of Ta = 4.6 × 10^10, 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, different aspect ratios and different rotation ratios. It is shown that the transition is approximately independent of the aspect and rotation ratios, but depends significantly on the radius ratio. We furthermore calculate the local angular velocity profiles and visualize different flow regimes that depend both on the shearing of the flow, and the Coriolis force originating from the outer cylinder rotation. Two main regimes are distinguished, based on the magnitude of the Coriolis force, namely the co-rotating and weakly counter-rotating regime dominated by Rayleigh-unstable regions, and the strongly counter-rotating regime where a mixture of Rayleigh-stable and Rayleigh-unstable regions exist. Furthermore, an analogy between radius ratio and outer-cylinder rotation is revealed, namely that smaller gaps behave like a wider gap with co-rotating cylinders, and that wider gaps behave like smaller gaps with weakly counter-rotating cylinders. Finally, the effect of the aspect ratio on the effective torque versus Taylor number scaling is analysed and it is shown that different branches of the torque-versus-Taylor relationships associated to different aspect ratios are found to cross within 15 % of the Reynolds number associated to the transition to the ultimate regime. The paper culminates in phase diagram in the inner versus outer Reynolds number parameter space and in the Taylor versus inverse Rossby number parameter space, which can be seen as the extension of the Andereck et al. (J. Fluid Mech., vol. 164, 1986, pp. 155–183) phase diagram towards the ultimate regime.Item Heat transfer mechanisms in bubbly Rayleigh-Benard convection(Physical Review E, 8/17/2009) Oresta, Paolo; Verzicco, Roberto; Lohse, Detlef; Prosperetti, AndreaThe heat transfer mechanism in Rayleigh-Bénard convection in a liquid with a mean temperature close to its boiling point is studied through numerical simulations with pointlike vapor bubbles, which are allowed to grow or shrink through evaporation and condensation and which act back on the flow both thermally and mechanically. It is shown that the effect of the bubbles is strongly dependent on the ratio of the sensible heat to the latent heat as embodied in the Jakob number Ja. For very small Ja the bubbles stabilize the flow by absorbing heat in the warmer regions and releasing it in the colder regions. With an increase in Ja, the added buoyancy due to the bubble growth destabilizes the flow with respect to single-phase convection and considerably increases the Nusselt number.Item Heat transport in bubbling turbulent convection(Proceedings of the National Academy of Sciences, 6/4/2013) Lakkaraju, Rajaram; Stevens, Richard J.A.M.; Oresta, Paolo; Verzicco, Roberto; Lohse, Detlef; Prosperetti, AndreaBoiling is an extremely effective way to promote heat transfer from a hot surface to a liquid due to numerous mechanisms, many of which are not understood in quantitative detail. An important component of the overall process is that the buoyancy of the bubble compounds with that of the liquid to give rise to a much-enhanced natural convection. In this article, we focus specifically on this enhancement and present a numerical study of the resulting two-phase Rayleigh–Bénard convection process in a cylindrical cell with a diameter equal to its height. We make no attempt to model other aspects of the boiling process such as bubble nucleation and detachment. The cell base and top are held at temperatures above and below the boiling point of the liquid, respectively. By keeping this difference constant, we study the effect of the liquid superheat in a Rayleigh number range that, in the absence of boiling, would be between 2 × 106 and 5 × 109. We find a considerable enhancement of the heat transfer and study its dependence on the number of bubbles, the degree of superheat of the hot cell bottom, and the Rayleigh number. The increased buoyancy provided by the bubbles leads to more energetic hot plumes detaching from the cell bottom, and the strength of the circulation in the cell is significantly increased. Our results are in general agreement with recent experiments on boiling Rayleigh–Bénard convection.Item Identifying coherent structures and vortex clusters in Taylor-Couette turbulence(Journal of Physics: Conference Series, 2016) Spandan, Vamsi; Ostilla-Mónico, Rodolfo; Lohse, Detlef; Verzicco, RobertoThe nature of the underlying structures in Taylor-Couette (TC) flow, the flow between two co-axial and independently rotating cylinders is investigated by two methods. First, the quadrant analysis technique for identifying structures with intense radial-azimuthal stresses (also referred to as 'Q's) of Lozano-Durán et al., (J. Fluid Mech. 694, 100-130) is used to identify the main structures responsible for the transport of angular velocity. Second, the vortex clusters are identified based on the analysis by del Álamo et al., (J. Fluid. Mech., 561, 329-358). In order to test these criteria, two different radius ratios ? = ri/ro are considered, where ri and ro are the radii of inner and outer cylinder, respectively: (i) ? = 0.5 and (ii) ? = 0.909, which correspond to high and low curvature geometries, respectively and have different underlying structures. The Taylor rolls, i.e. the large-scale coherent structures, are effectively captured as 'Q's for the low curvature setup and it is observed that curvature plays a dominant role in influencing the size and volumes of these 'Q's. On the other hand, the vortex clusters are smaller in size when compared to the 'Q' structures. These vortex clusters are found to be taller in the case of ? = 0.909, while the distribution of the lengths of these clusters is almost homogenous for both radius ratios.Item Life stages of wall-bounded decay of Taylor-Couette turbulence(Physical Review Fluids, 2017-11) Ostilla-Mónico, Rodolfo; Zhu, Xiaojue; Spandan, Vamsi; Verzicco, Roberto; Lohse, DetlefThe decay of Taylor-Couette turbulence, i.e., the flow between two coaxial and independently rotating cylinders, is numerically studied by instantaneously stopping the forcing from an initially statistically stationary flow field at a Reynolds number of Re =3.5×10^4.The effect of wall friction is analyzed by comparing three separate cases, in which the cylinders are either suddenly made no-slip or stress-free. Different life stages are observed during the decay. In the first stage, the decay is dominated by large-scale rolls. Counterintuitively, when these rolls fade away, if the flow inertia is small a redistribution of energy occurs and the energy of the azimuthal velocity behaves nonmonotonically, first decreasing by almost two orders of magnitude and then increasing during the redistribution. The second stage is dominated by non-normal transient growth of perturbations in the axial (spanwise) direction. Once this mechanism is exhausted, the flow enters the final life stage, viscous decay, which is dominated by wall friction. We show that this stage can be modeled by a one-dimensional heat equation, and that self-similar velocity profiles collapse onto the theoretical solution.Item Logarithmic Mean Temperature Profiles and Their Connection to Plume Emissions in Turbulent Rayleigh-Bénard Convection(Physical Review Letters, 2015-10) Van Der Poel, Erwin P.; Ostilla-Mónico, Rodolfo; Verzicco, Roberto; Grossmann, Siegfried; Lohse, DetlefTwo-dimensional simulations of Rayleigh-Bénard convection at Ra=5×10^10 show that vertical logarithmic mean temperature profiles can be observed in regions of the boundary layer where thermal plumes are emitted. The profile is logarithmic only in these regions and not in the rest of the boundary layer where it is sheared by the large-scale wind and impacted by plumes. In addition, the logarithmic behavior is not visible in the horizontal average. The findings reveal that the temperature profiles are strongly connected to thermal plume emission, and they support a perception that parts of the boundary layer can be turbulent while others are not. The transition to the ultimate regime, in which the boundary layers are considered to be fully turbulent, can therefore be understood as a gradual increase in the fraction of the plume-emitting (“turbulent”) regions of the boundary layerItem Modification of turbulence in Rayleigh-B ?enard convection by phase change(New Journal of Physics, 2/3/2011) Schmidt, Laura E.; Oresta, Paolo; Toschi, Federico; Verzicco, Roberto; Lohse, Detlef; Prosperetti, AndreaHeavy or light particles introduced into a liquid trigger motion due to their buoyancy, with the potential to drive flow to a turbulent state. In the case of vapor bubbles present in a liquid near its boiling point, thermal coupling between the liquid and vapor can moderate this additional motion by reducing temperature gradients in the liquid. Whether the destabilizing mechanical feedback or stabilizing thermal feedback will dominate the system response depends on the number of bubbles present and the properties of the phase change. Here we study thermal convection with phase change in a cylindrical Rayleigh–Bénard cell to examine this competition. Using the Reynolds number of the flow as a signature of turbulence and the intensity of the flow, we show that in general the rising vapor bubbles destabilize the system and lead to higher velocities. The exception is a limited regime corresponding to phase change with a high latent heat of vaporization (corresponding to low Jakob number), where the vapor bubbles can eliminate the convective flow by smoothing temperature differences of the fluid.Item Optimal Taylor–Couette flow: direct numerical simulations(Journal of Fluid Mechanics, 2012-10) Ostilla-Mónico, Rodolfo; Stevens, Richard J. A. M.; Grossmann, Siegfried; Verzicco, Roberto; Lohse, DetlefWe 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 Rei= 8 x 10^3 and Reo=+/-4 x 10^3 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 a certain non-zero rotation rate ratio a=-wo/wi of about aopt=0.33 . For large enough Ta in the numerically accessible range we also find such an optimum transport at non-zero counter-rotation. The position of this maximum is found to shift with the driving, reaching a maximum of a(opi)=0.15 for Ta=2.5 x 10^7. An explanation for this shift is elucidated, consistent with the experimental result that a(opt) becomes approximately independent of the driving strength for large enough Reynolds numbers. We furthermore numerically calculate the angular velocity profiles and visualize the different flow structures for the various regimes. By writing the equations in a frame co-rotating with the outer cylinder a link is found between the local angular velocity profiles and the global transport quantities.