We report high-precision measurements of the Nusselt number Nu as a function of the Rayleigh number Ra in water-filled rectangular Rayleigh-Bénard convection cells. The horizontal length L and width W of the cells are 50.0 and 15.0 cm, respectively, and the heights H = 49.9, 25.0, 12.5, 6.9, 3.5, and 2.4 cm, corresponding to the aspect ratios (Γ x ≡ L/H, Γ y ≡ W/H) ). The measurements were carried out over the Rayleigh number range 6 × 10 5 Ra 10 11 and the Prandtl number range 5.2 Pr 7. Our results show that for rectangular geometry turbulent heat transport is independent of the cells' aspect ratios and hence is insensitive to the nature and structures of the large-scale mean flows of the system. This is slightly different from the observations in cylindrical cells where Nu is found to be in general a decreasing function of Γ , at least for Γ = 1 and larger. Such a difference is probably a manifestation of the finite plate conductivity effect. Corrections for the influence of the finite conductivity of the top and bottom plates are made to obtain the estimates of Nu ∞ for plates with perfect conductivity. The local scaling exponents β l of Nu ∞ ∼ Ra β l are calculated and found to increase from 0.243 at Ra 9 × 10 5 to 0.327 at Ra 4 × 10 10 .

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Contaminants released from sediment into rivers are one of the main problems to study in environmental hydrodynamics. For contaminants released into the overlying water under different hydrodynamic conditions, the mechanical mechanisms involved can be roughly divided into convective diffusion, molecular diffusion, and adsorption/desorption. Because of the obvious environmental influence of fine sediment (D 90 = 0.06 mm), non-cohesive fine sediment, and cohesive fine sediment are researched in this paper, and phosphorus is chosen for a typical adsorption of a contaminant. Through theoretical analysis of the contaminant release process, according to different hydraulic conditions, the contaminant release coupling mathematical model can be established by the N-S equation, the Darcy equation, the solute transport equation, and the adsorption/desorption equation. Then, the experiments are completed in an open water flume. The simulation results and experimental results show that convective diffusion dominates the contaminant release both in non-cohesive and cohesive fine sediment after their suspension, and that they contribute more than 90 % of the total release. Molecular diffusion and desorption have more of a contribution for contaminant release from unsuspended sediment. In unsuspension sediment, convective diffusion is about 10-50 times larger than molecular diffusion during the initial stages under high velocity; it is close to molecular diffusion in the later stages. Convective diffusion is about 6 times larger than molecular diffusion during the initial stages under low velocity, it is about a quarter of molecular diffusion in later stages, and has a similar level with desorption/adsorption. In unsuspended sediment, a seepage boundary layer exists below the water-sediment interface, and various release mechanisms in that layer mostly dominate the contaminant release process. In non-cohesive fine sediment, the depth of that layer increases linearly with shear stress. In cohesive fine sediment, the range seepage boundary is different from that in non-cohesive sediment, and that phenomenon is more obvious under a lower shear stress.

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