Shear flow over a solid surface containing perforations or patches of zero shear stress is discussed with a view to evaluating the slip velocity. In both cases, the functional dependence of the slip velocity on the solid fraction of the surface strongly depends on the surface geometry, and a universal law cannot be established. Numerical results for flow over a plate with circular or square perforations or patches of zero shear stress, and flow over a plate consisting of separated square or circular tiles corroborate the assertion.

Do tidal channels have a characteristic length? Given the sediment characteristics, the inlet conditions and the degree of channel convergence, can we predict it? And how is this length affected by the presence of tidal flats adjacent to the channel? We answer the above questions on the basis of a fully analytical treatment, appropriate for the short channels typically observed in coastal wetlands. The equilibrium length of non-convergent tidal channels is found to be proportional to the critical flow speed for channel erosion. Channel convergence causes concavity of the bed profile. Tidal flats shorten equilibrium channels significantly. Laboratory and field observations substantiate our findings.

Results from direct numerical simulation (DNS) for three-dimensional Rayleigh–Bénard convection in a cylindrical cell of aspect ratio 1/2 and Prandtl number Pr=0.7 are presented. They span five decades of Rayleigh number Ra from 2 × 106 to 2 × 1011. The results are in good agreement with the experimental data of Niemela et al. (Nature, vol. 404, 2000, p. 837). Previous DNS results from Amati et al. (Phys. Fluids, vol. 17, 2005, paper no. 121701) showed a heat transfer that was up to 30% higher than the experimental values. The simulations presented in this paper are performed with a much higher resolution to properly resolve the plume dynamics. We find that in under-resolved simulations the hot (cold) plumes travel further from the bottom (top) plate than in the better-resolved ones, because of insufficient thermal dissipation mainly close to the sidewall (where the grid cells are largest), and therefore the Nusselt number in under-resolved simulations is overestimated. Furthermore, we compare the best resolved thermal boundary layer profile with the Prandtl–Blasius profile. We find that the boundary layer profile is closer to the Prandtl–Blasius profile at the cylinder axis than close to the sidewall, because of rising plumes close to the sidewall.

An experimental investigation of the flow generated by a homogeneous population of bubbles rising in water is reported for three different bubble diameters (d = 1.6, 2.1 and 2.5 mm) and moderate gas volume fractions (0.005 ≤ α ≤ 0.1). The Reynolds numbers, Re = V0d/ν, based on the rise velocity V0 of a single bubble range between 500 and 800. Velocity statistics of both the bubbles and the liquid phase are determined within the homogeneous bubble swarm by means of optical probes and laser Doppler anemometry. Also, the decaying agitation that takes place in the liquid just after the passage of the bubble swarm is investigated from high-speed particle image velocimetry measurements. Concerning the bubbles, the average velocity is found to evolve as V0α−0.1 whereas the velocity fluctuations are observed to be almost independent of α. Concerning the liquid fluctuations, the probability density functions adopt a self-similar behaviour when the gas volume fraction is varied, the characteristic velocity scaling as V0α0.4. The spectra of horizontal and vertical liquid velocity fluctuations are obtained with a resolution of 0.6 mm. The integral length scale Λ is found to be proportional to V02/g or equivalently to d/Cd0, where g is the gravity acceleration and Cd0 the drag coefficient of a single rising bubble. Normalized by using Λ, the spectra are independent on both the bubble diameter and the volume fraction. At large scales, the spectral energy density evolves as the power −3 of the wavenumber. This range starts approximately from Λ and is followed for scales smaller than Λ/4 by a classic −5/3 power law. Although the Kolmogorov microscale is smaller than the measurement resolution, the dissipation rate is however obtained from the decay of the kinetic energy after the passage of the bubbles. It is found to scale as α0.9V03/Λ. The major characteristics of the agitation are thus expressed as functions of the characteristics of a single rising bubble. Altogether, these results provide a rather complete description of the bubble-induced turbulence.