# Browsing by Author "Grossmann, Siegfried"

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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, DetlefShow more Direct 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 developShow more 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, SiegfriedShow more Direct 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.Show more 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, DetlefShow more Two-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 layerShow more 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, DetlefShow more 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 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.Show more Item Optimal Taylor–Couette flow: radius ratio dependence(Journal of Fluid Mechanics, 2013-10) Ostilla-Mónico, Rodolfo; Huisman, Sander G.; Jannink, Tim J. G.; Van Gils, Dennis P. M.; Verzicco, Roberto; Grossmann, Siegfried; Sun, Chao; Lohse, DetlefShow more Taylor–Couette flow with independently rotating inner ( i ) and outer ( o ) cylinders is explored numerically and experimentally to determine the effects of the radius ratio on the system response. Numerical simulations reach Reynolds numbers of up to Rei=9.5 x 10^3 and Re0= 5 x 10^3 , corresponding to Taylor numbers of up to Ta=10^8 for four different radius ratios n=ri/ro between 0.5 and 0.909. The experiments, performed in the Twente Turbulent Taylor–Couette ( T^3C ) set-up, reach Reynolds numbers of up to Rei= 2 x 10^6 and Reo= 1.5 x 10^6 , corresponding to Ta= 5 x 10^12 for n=.714--0.909 . Effective scaling laws for the torque J^w(Ta) are found, which for sufficiently large driving Ta are independent of the radius ratio n . As previously reported for n=0.714 , optimum transport at a non-zero Rossby number Ro=ri|wi-wo|/ ]2(ro-ri)wo] is found in both experiments and numerics. Here Ro(opt) is found to depend on the radius ratio and the driving of the system. At a driving in the range between Ta~3 x 10^8 and Ta~10^10 , Ro(opt) saturates to an asymptotic n -dependent value. Theoretical predictions for the asymptotic value of Ro(opt) are compared to the experimental results, and found to differ notably. Furthermore, the local angular velocity profiles from experiments and numerics are compared, and a link between a flat bulk profile and optimum transport for all radius ratios is reported.Show more Item Salinity transfer in bounded double diffusive convection(Journal of Fluid Mechanics, 2015-03) Yang, Yantao; Van Der Poel, Erwin P.; Ostilla-Mónico, Rodolfo; Sun, Chao; Verzicco, Roberto; Grossmann, Siegfried; Lohse, DetlefShow more The double diffusive convection between two parallel plates is numerically studied for a series of parameters. The flow is driven by the salinity difference and stabilised by the thermal field. Our simulations are directly compared with experiments by Hage & Tilgner (Phys. Fluids, vol. 22, 2010, 076603) for several sets of parameters and reasonable agreement is found. This, in particular, holds for the salinity flux and its dependence on the salinity Rayleigh number. Salt fingers are present in all simulations and extend through the entire height. The thermal Rayleigh number seems to have a minor influence on the salinity flux but affects the Reynolds number and the morphology of the flow. In addition to the numerical calculation, we apply the Grossmann–Lohse theory for Rayleigh–Bénard flow to the present problem without introducing any new coefficients. The theory successfully predicts the salinity flux both with respect to the scaling and even with respect to the absolute value for the numerical and experimental results.Show more Item Spatial dependence of fluctuations and flux in turbulent Rayleigh-B ?enard convection(Physical Review E, 11/26/2012) Lakkaraju, Rajaram; Stevens, Richard J.A.M.; Verzicco, Roberto; Grossmann, Siegfried; Prosperetti, Andrea; Sun, Chao; Lohse, DetlefShow more Item The near-wall region of highly turbulent Taylor–Couette flow(Journal of Fluid Mechanics, 2017-04) Ostilla-Mónico, Rodolfo; Verzicco, Roberto; Grossmann, Siegfried; Lohse, DetlefShow more 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 n=ri/ro=0.909 , an aspect ratio of r=L/d=2(pie)/3 , and a stationary outer cylinder. Three inner cylinder Reynolds numbers of 1x10^5 , 2x10^5 and 3x10^5 were simulated, corresponding to frictional Reynolds numbers between Rer=1400 and Rer=4000 . An additional case with a large gap, n=0.5 and driving of was also investigated. Small-gap TC was found to be dominated by spatially fixed large-scale structures, known as Taylor rolls (TRs). TRs are attached to the boundary layer, and are active, i.e. they transport angular velocity through Reynolds stresses. An additional simulation was also conducted with inner cylinder Reynolds number of Re=1x10^5 and fixed outer cylinder with an externally imposed axial flow of comparable strength to the wind of the TRs. The axial flow was found to convect the TRs without any weakening effect. For small-gap TC flow, evidence was found for the existence of logarithmic velocity fluctuations, and of an overlap layer, in which the velocity fluctuations collapse in outer units. Profiles consistent with a logarithmic dependence were also found for the angular velocity in large-gap TC flow, albeit in a very reduced range of scales. Finally, the behaviour of both small- and large-gap TC flow was compared to other canonical flows. Small-gap TC flow has similar behaviour in the near-wall region to other canonical flows, while large-gap TC flow displays very different behaviour.Show more Item Turbulence decay towards the linearly stable regime of Taylor–Couette flow(Journal of Fluid Mechanics, 2013-11) Ostilla-Mónico, Rodolfo; Verzicco, Roberto; Grossmann, Siegfried; Lohse, DetlefShow more Taylor–Couette (TC) flow is used to probe the hydrodynamical (HD) stability of astrophysical accretion disks. Experimental data on the subcritical stability of TC flow are in conflict about the existence of turbulence (cf. Ji et al. (Nature, vol. 444, 2006, pp. 343–346) and Paoletti et al. (Astron. Astroph., vol. 547, 2012, A64)), with discrepancies attributed to end-plate effects. In this paper we numerically simulate TC flow with axially periodic boundary conditions to explore the existence of subcritical transitions to turbulence when no end plates are present. We start the simulations with a fully turbulent state in the unstable regime and enter the linearly stable regime by suddenly starting a (stabilizing) outer cylinder rotation. The shear Reynolds number of the turbulent initial state is up to Res(less than or equal to)10^5 and the radius ratio is n=0.714 . The stabilization causes the system to behave as a damped oscillator and, correspondingly, the turbulence decays. The evolution of the torque and turbulent kinetic energy is analysed and the periodicity and damping of the oscillations are quantified and explained as a function of shear Reynolds number. Though the initially turbulent flow state decays, surprisingly, the system is found to absorb energy during this decay.Show more