A two-layer approach for depth-limited open-channel flow with submerged vegetation is described. A momentum balance is applied to each layer and expressions for the mean velocities are proposed. The velocity is assumed to be uniform in the vegetation layer and logarithmic in the upper layer. The proposed relationship successfully predicts the mean velocity distribution when compared with the measured data. Using the velocity formula, the layer-averaged mean velocities in the upper layer and over the entire layer are derived. An expression for the roughness coefficient increased by vegetation is also presented, performing better for the roughness coefficient than other formulas. Another relationship is proposed for predicting the distribution of suspended sediment in depth-limited flow with submerged vegetation by using an eddy-viscosity profile. The predicted profiles moderately agree with the measured data. Comparisons with simulated data from the Reynolds-averaged Navier–Stokes equations with the k–ϵ model suggest that these proposals successfully predict suspended sediment transport in a depth-limited flow with submerged vegetation.

A Reynolds stress model for the numerical simulation of partly-vegetated flows is presented. The model uses Speziale, Sarkar, and Gatski's model for the pressure–strain correlation, Mellor and Herring's model and Rotta's model for the diffusion and the dissipation rate of the Reynolds stress, respectively. The model is applied to partly-vegetated rectangular open-channel flows, and simulated results are compared with experimental data. The model satisfactorily predicts mean flow and turbulence statistics. Through numerical experiments, the evolution of secondary current patterns and mean flow structure are presented for different densities of vegetation. A budget analysis of the streamwise vorticity equation is also performed to investigate the mechanism by which secondary currents in a partly-vegetated open-channel flow are generated. In the vegetated zone, the production by anisotropy is important in generating secondary currents over the entire depth, except for regions close to the free surface and the bottom where Reynolds shear stress plays a key role. This is different from the vortical structure of plain open-channel flows.

This study presents the results of laboratory experiments on depth-limited open channel flow with submerged vegetation. To investigate the impact of stem flexibility on the mean flow and turbulence structures, two flow types with similar drags but with flexible and rigid stems are compared. It is found that the stem flexibility hardly affects the mean flow but increases the peak value of the Reynolds shear stress. In addition, the stem flexibility increases and decreases the streamwise component of the turbulent intensity in the upper and vegetation layers, respectively. However, the stem flexibility increases the vertical component of the turbulent intensity over the whole depth. General profiles of the mean flow, the Reynolds shear stress, and the turbulent intensity are presented. The results of a quadrant analysis and a budget analysis are also provided.

Shredded rubber tire is a geomaterial that is potentially useful in environmental and engineering projects. Here, we study the effect of particle size ratio on the thermal conductivity of granular mixtures containing rubber tire particles. Glass beads were mixed at various volume fractions with rubber particles of varying size. The 3D network model analysis using synthetic packed assemblies was used to determine the dominant factors influencing the thermal conduction of the mixtures. Results present that mixtures with varying size ratios exhibit different nonlinear evolutions of thermal conductivity values with mixture fractions. In particular, mixtures with large insulating materials (e.g., rubber particles) have higher thermal conduction that those with small ones. This is because the larger insulating particles allow better interconnectivity among the conductive particles, thereby avoiding the interruption of the thermal conduction of the conductive particles. Similar tests conducted with natural sand corroborate the significant effect of the relative size of the insulating particles. The 3D network model identifies the heterogeneity of local and effective thermal conductivity and the influence of connectivity among conductive particles. A supplementary examination of electrical conductivity highlights the significance of local and long-range connectivity on conduction paths in granular mixtures.