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This paper presents numerical results for Rayleigh–Bénard convection with suspended particles at Rayleigh numbers $Ra=10^7$ and $10^8$, and unit Prandtl number. Accounting for their finite size makes it possible to investigate in detail the mechanism by which the particles, which are 10% heavier than the fluid, get resuspended after settling, thus maintaining a two-phase circulating flow. It is shown that an essential component of this mechanism is the formation of particle accumulations, or ‘dunes’, on the bottom of the Rayleigh–Bénard cell. Ascending plumes become localised on these dunes. Particles are dragged up the dune slopes, and when they reach the top, are entrained into the rising plumes. Direct resuspension of particles from the cell bottom, if it happens at all, is very rare. For $Ra=10^7$, aspect ratios (width/height) $$\Gamma =1,2,4$$ are considered. It is found that in these and in the other cases simulated, at steady state, a single dune evolves, the largest linear dimension of which is comparable to the cell size. A remarkable consequence is that even at the low volume fraction considered here, 3.27%, the particles are able to structure the flow and to determine the size and position of the largest ascending plumes. Their effect on the Nusselt number, however, remains small. This and other results are explained on the basis of the ratio of the cell-bottom viscous boundary-layer thickness to the particle diameter. 

A direct numerical simulation of incompressible channel flow at a friction Reynolds number (Reτ) of 5186 has been performed, and the flow exhibits a number of the characteristics of high-Reynolds-number wall-bounded turbulent flows. For example, a region where the mean velocity has a logarithmic variation is observed, with von Kármán constant k = 0.384 ± 0.004. There is also a logarithmic dependence of the variance of the spanwise velocity component, though not the streamwise component. A distinct separation of scales exists between the large outer-layer structures and small inner-layer structures. At intermediate distances from the wall, the one-dimensional spectrum of the streamwise velocity fluctuation in both the streamwise and spanwise directions exhibits k-1 dependence over a short range in wavenumber (k) . Further, consistent with previous experimental observations, when these spectra are multiplied by k (premultiplied spectra), they have a bimodal structure with local peaks located at wavenumbers on either side of the k-1 range. 

The turbulent channel flow database is produced from a direct numerical simulation (DNS) of wall bounded flow with periodic boundary conditions in the longitudinal and transverse directions, and no-slip conditions at the top and bottom walls. In the simulation, the Navier-Stokes equations are solved using a wall {normal, velocity {vorticity formulation. Solutions to the governing equations are provided using a Fourier-Galerkin pseudo-spectral method for the longitudinal and transverse directions and seventh-order Basis-splines (B-splines) collocation method in the wall normal direction. De-aliasing is performed using the 3/2-rule [3]. Temporal integration is performed using a low-storage, third-order Runge-Kutta method. Initially, the flow is driven using a constant volume flux control (imposing a bulk channel mean velocity of U = 1) until stationary conditions are reached. Then the control is changed to a constant applied mean pressure gradient forcing term equivalent to the shear stress resulting from the prior steps. Additional iterations are then performed to further achieve statistical stationarity before outputting fields.