Turbulence decay towards the linearly stable regime of Taylor–Couette flow

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 $Re_s \lesssim 10^5$$Re_s \lesssim 10^5$ and the radius ratio is $\eta =0.714$$\eta =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

Optimal Taylor–Couette flow: radius ratio dependence

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 η on the system response. Numerical simulations reach Reynolds numbers of up to Rei=9.5×10^3 and Reo=5×10^3, corresponding to Taylor numbers of up to Ta=10^8 for four different radius ratios η=ri/ro between 0.5 and 0.909. The experiments, performed in the Twente Turbulent Taylor–Couette (T3C) set-up, reach Reynolds numbers of up to Rei=2×10^6 and Reo=1.5×10^6, corresponding to Ta=5×10^12 for η=0.714--0.909. Effective scaling laws for the torque Jω(Ta) are found, which for sufficiently large driving Ta are independent of the radius ratio η. As previously reported for η=0.714, optimum transport at a non-zero Rossby number Ro=ri|ωi−ωo|/[2(ro−ri)ωo] is found in both experiments and numerics. Here Roopt is found to depend on the radius ratio and the driving of the system. At a driving in the range between Ta∼3×10^8 and Ta∼10^10, Roopt saturates to an asymptotic η-dependent value. Theoretical predictions for the asymptotic value of Roopt 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

Wall roughness induces asymptotic ultimate turbulence

Turbulence is omnipresent in Nature and technology, governing the transport of heat, mass, and momentum on multiple scales. For real-world applications of wall-bounded turbulence, the underlying surfaces are virtually always rough; yet characterizing and understanding the effects of wall roughness for turbulence remains a challenge, especially for rotating and thermally driven turbulence. By combining extensive experiments and numerical simulations, here, taking as example the paradigmatic Taylor-Couette system (the closed flow between two independently rotating coaxial cylinders), we show how wall roughness greatly enhances the overall transport properties and the corresponding scaling exponents. If only one of the walls is rough, we reveal that the bulk velocity is slaved to the rough side, due to the much stronger coupling to that wall by the detaching flow structures. If both walls are rough, the viscosity dependence is thoroughly eliminated in the boundary layers and we thus achieve asymptotic ultimate turbulence, i.e. the upper limit of transport, whose existence had been predicted by Robert Kraichnan in 1962 (Phys. Fluids {\bf 5}, 1374 (1962)) and in which the scalings laws can be extrapolated to arbitrarily large Reynolds numbers

Physical and geometric constraints shape the labyrinth-like nasal cavity

The nasal cavity is a vital component of the respiratory system that heats and humidifies inhaled air in all vertebrates. Despite this common function, the shapes of nasal cavities vary widely across animals. To understand this variability, we here connect nasal geometry to its function by theoretically studying the airflow and the associated scalar exchange that describes heating and humidification. We find that optimal geometries, which have minimal resistance for a given exchange efficiency, have a constant gap width between their side walls, while their overall shape can adhere to the geometric constraints imposed by the head. Our theory explains the geometric variations of natural nasal cavities quantitatively, and we hypothesize that the trade-off between high exchange efficiency and low resistance to airflow is the main driving force shaping the nasal cavity. Our model further explains why humans, whose nasal cavities evolved to be smaller than expected for their size, become obligate oral breathers in aerobically challenging situations

Boundary layer dynamics at the transition between the classical and the ultimate regime of Taylor-Couette flow

Direct numerical simulations of turbulent Taylor-Couette flow are performed up to inner cylinder Reynolds numbers of Rei = 105 for a radius ratio of η = ri/ro = 0.714 between the inner and outer cylinders. With increasing Rei, the flow under- goes transitions between three different regimes: (i) a flow dominated by large coher- ent 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 develop

Transition to geostrophic convection : the role of the boundary conditions

Rotating Rayleigh–Bénard convection, the flow in a rotating fluid layer heated from below and cooled from above, is used to analyse the transition to the geostrophic regime of thermal convection. In the geostrophic regime, which is of direct relevance to most geo- and astrophysical flows, the system is strongly rotating while maintaining a sufficiently large thermal driving to generate turbulence. We directly simulate the Navier–Stokes equations for two values of the thermal forcing, i.e. Ra = 1010 and Ra = 5 × 1010, at constant Prandtl number Pr = 1, and vary the Ekman number in the range Ek = 1.3 × 10-7 to Ek = 2 × 10-6, which satisfies both requirements of supercriticality and strong rotation. We focus on the differences between the application of no-slip versus stress-free boundary conditions on the horizontal plates. The transition is found at roughly the same parameter values for both boundary conditions, i.e. at Ek ≈ 9 × 10-7 for Ra = 1 × 1010 and at Ek ≈ 3 × 10-7 for Ra = 5 × 1010. However, the transition is gradual and it does not exactly coincide in Ek for different flow indicators. In particular, we report the characteristics of the transitions in the heat-transfer scaling laws, the boundary-layer thicknesses, the bulk/boundary-layer distribution of dissipations and the mean temperature gradient in the bulk. The flow phenomenology in the geostrophic regime evolves differently for no-slip and stress-free plates. For stress-free conditions, the formation of a large-scale barotropic vortex with associated inverse energy cascade is apparent. For no-slip plates, a turbulent state without large-scale coherent structures is found; the absence of large-scale structure formation is reflected in the energy transfer in the sense that the inverse cascade, present for stress-free boundary conditions, vanishes

Double maxima of angular momentum transport in small gap Taylor–Couette turbulence

We use experiments and direct numerical simulations to probe the phase space of low-curvature Taylor–Couette flow in the vicinity of the ultimate regime. The cylinder radius ratio is fixed at η = ri/ro = 0.91, where ri (ro) is the inner (outer) cylinder radius. Non-dimensional shear drivings (Taylor numbers Ta) in the range 107 ≤ Ta ≤ 1011 are explored for both co- and counter-rotating configurations. In the Ta range 108 ≤ Ta ≤ 1010, we observe two local maxima of the angular momentum transport as a function of the cylinder rotation ratio, which can be described as either ‘co-’ or ‘counter-rotating’ due to their location or as ‘broad’ or ‘narrow’ due to their shape. We confirm that the broad peak is accompanied by the strengthening of the large-scale structures, and that the narrow peak appears once the driving (Ta) is strong enough. As first evidenced in numerical simulations by Brauckmann et al. (J. Fluid Mech., vol. 790, 2016, pp. 419–452), the broad peak is produced by centrifugal instabilities and that the narrow peak is a consequence of shear instabilities. We describe how the peaks change with Ta as the flow becomes more turbulent. Close to the transition to the ultimate regime when the boundary layers (BLs) become turbulent, the usual structure of counter-rotating Taylor vortex pairs breaks down and stable unpaired rolls appear locally. We attribute this state to changes in the underlying roll characteristics during the transition to the ultimate regime. Further changes in the flow structure around Ta ≈ 1010 cause the broad peak to disappear completely and the narrow peak to move. This second transition is caused when the regions inside the BLs which are locally smooth regions disappear and the whole boundary layer becomes active