We report an investigation of temperature profiles in turbulent Rayleigh–Bénard convection of water based on direct numerical simulations (DNS) for a cylindrical cell with unit aspect ratio for the same Prandtl number Pr and similar Rayleigh numbers Ra as used in recent high-precision measurements by Funfschilling et al. (J. Fluid Mech., vol. 536, 2005, p. 145). The Nusselt numbers Nu computed for Pr = 4.38 and Ra = 108, 3 × 108, 5 × 108, 8 × 108 and 109 are found to be in excellent agreement with the experimental data corrected for finite thermal conductivity of the walls. Based on this successful validation of the numerical approach, the DNS data are used to extract vertical profiles of the mean temperature. We find that near the heating and cooling plates the non-dimensional temperature profiles Θ(y) (where y is the non-dimensional vertical coordinate), obey neither a logarithmic nor a power law. Moreover, we demonstrate that the Prandtl–Blasius boundary layer theory cannot predict the shape of the temperature profile with an error less than 7.9% within the thermal boundary layers (TBLs). We further show that the profiles can be approximated by a universal stretched exponential of the form Θ(y) ≈ 1 − exp(−y − 0.5y2) with an absolute error less than 1.1% within the TBLs and 5.5% in the whole Rayleigh cell. Finally, we provide more accurate analytical approximations of the profiles involving higher order polynomials in the approximation.

Recently there has been remarkable progress made in the direct numerical simulation (DNS) of wall-bounded turbulence, particularly of turbulent channel flow, with numerical data now available above Reτ ≈ 2000 (Hoyas & Jiménez, Phys. Fluids, vol. 18, 2006, p. 011702; Iwamoto et al., Proceedings of the Sixth Symposium Smart Control of Turbulence, 2005). Much knowledge has been gained from these results, particularly in the areas of flow structure and dynamics. Yet, while the value of such simulations is undoubted, only very limited comparisons with experimental data have been documented. Although the physics of the flow are captured correctly in an ideal DNS, as with any real numerical or physical experiment, there are opportunities for misrepresentation of the characteristics of turbulence. As such, this article seeks to make a comparison between a well-documented high Reynolds number (Reτ = 934), large box size (8πh × 2h × 3πh) DNS from del Álamo et al. (J. Fluid Mech., vol. 500, 2004, p. 135) and laboratory channel flow data measured by the authors. Results show that there is excellent agreement between the streamwise velocity statistics of the two data sets. The spectra are also very similar, however, throughout the logarithmic region the secondary peak in energy is clearly reduced in the DNS results. Although the source of the difference is not certain, the wavelengths concerned are close to the DNS box length, leading to the recommendation that longer box lengths should be investigated. Another large-scale spectral discrepancy near the wall results from the incorrect assumption of a constant convection velocity used to infer spatial information from the temporal. A near-wall convection velocity modification function is tentatively proposed. While the modification gives good agreement between the data sets, higher Reynolds number comparisons are required to better understand the intricate convection velocity issue.

In this study, we present experimental results on particle-wall collision in viscoelastic fluids. A sphere is released in a tank filled with poly(ethylene-oxide) (PEO) mixed with water with varying concentrations up to 1.5%. The effect of Stokes and Deborah numbers on the rebound velocity of a spherical particle colliding onto a wall is considered. It has been observed that the slope at which the coefficient of restitution increases with Stokes number is smaller for higher Deborah numbers. Higher rebound occurs for higher PEO concentration at the same stokes number. However, the results for the coefficient of restitution in polymeric liquids can be collapsed together with the Newtonian fluid behaviour if one defines the Stokes number based on the local strain rate.

The selection of long air bubbles propagating steadily in a strongly collapsed fluid-filled elastic tube is investigated experimentally in a benchtop model of airway reopening. Localized regions of strong collapse are likely in the lung, because collapsing fluid-elastic instabilities promote extensive deformation of the airway cross-section beyond the point of opposite wall contact. We find that radical changes in the reopening mechanics occur at this point. We build on the recent identification by Heap & Juel (Phys. Fluids, vol. 20, 2008, article no. 081702) of three different steadily propagating bubbles (asymmetric, double-tipped and pointed) that are selected successively for increasing values of the capillary number (Ca, ratio of viscous to surface tension forces) in tubes initially collapsed beyond the point of opposite wall contact. The asymmetric bubble is also observed in less collapsed tubes for small values of Ca, and we show that it bifurcates super-critically from the usual parabolic-tipped bubble as Ca increases. We also characterize the mechanisms underlying the discontinuous transitions between asymmetric and double-tipped bubbles, and double-tipped and pointed bubbles. In particular, we find that the tube must reopen to a critical height for double-tipped bubbles to be selected. The length of the precursor fingers in the double-tipped bubble decreases with Ca, and the bubble loses stability to pointed bubbles when this length is less than the height of the tube at the point where the fingers merge. By contrast with the asymmetric and double-tipped bubbles, the pointed bubble infiltrates the most collapsed part of the tube to yield the rapid reopening of the airway at low pressure, with the potential to reduce ventilation-induced lung damage.