Donghuo Zhou

A dynamic approach to sediment‐laden turbulent flows

An approach that studies the effects of the dynamic coupling between turbulent flow and sediment in suspension on the mean velocity and the sediment concentration profiles of sediment-laden open-channel flows is systematically developed. The analysis is based on the Boussinesq approximation to the governing equations that treats the mixture of the liquid and sediment as a single fluid with changing density over the flow depth. As a result, it permits the direct systematic comparison between the turbulent flow of clear water and that with suspended sediment. By further employing the mixing length approach for the related turbulent closure problem, the coupling effects on mean velocity and concentration profiles are evaluated, and the resulting distributions are compared with available experimental data. The derived mean velocity distribution contains profiles of existing models as special cases and thus unifies the results of existing major models conceptually and quantitatively. Moreover, the analysis clearly demonstrates the importance of the coupling effect on the suspended sediment concentration profile and, consequently, a more generalized formula of concentration profile is obtained. Although the mean velocity and concentration profiles are the main concern of this paper, the approach establishes a framework for further study of the effects of the dynamic interaction on other physical quantities.

Low-Reynolds-number turbulent channel flows

An analysis - valid for the flow of incompressible fluids through closed and open channels - of the maintenance of the Reynolds stresses, which starts from the Navier-Stokes and mass conservation equations, is applied to steady, two-dimensional, fully developed, low-Reynolds-number turbulent channel flows. The approach adopted considers the Reynolds stresses to depend on the structure of the turbulent components over the entire flow field. As a result of the analysis, the distributions of the mean velocity, the Reynolds stress and the turbulence intensities are found in the inner and outer region in which the shear flow is divided. By matching the solutions in the two regions, new uniform approximations for the distributions are obtained. The derived profiles are compared with available experimental data and the agreement is found to be satisfactory.

Energetics of sediment-laden streamflows

The present approach, which considers a diluted sediment suspension as a perturbation to a clear-water flow, permits a direct comparison of the energetics of turbulent sediment-laden and clear-water open-channel flows of constant slope and depth. On the basis of the Boussinesq approximation to the momentum equations for the flow with sediment in suspension and the Navier-Stokes equations for the clear-water flow, a depth-averaged equation for the change in turbulence energy dissipation rate and an equation for the flow energy budget are obtained. From the analysis of these equations it becomes clear that the presence of the suspension affects the distribution of energy in the flow; also, the turbulence kinetic energy can increase, decrease, or remain the same depending on the sediment loading conditions, and its rate of dissipation can increase, decrease, or remain the same depending on the magnitude of the flow hydraulic parameters relative to that of the loading conditions. These findings provide additional insight into the energetics of these complex flows, agree qualitatively with experimental data, and complement available models.

Surface drift effect on wind energy transfer to waves

The effect of surface drift velocity on the energy transfer from the wind to ocean waves and the growth rate of the dominant surface wave was studied analytically. The model analyzed considered first the airflow above the surface wave to be turbulent, the thin drift shear layer to be viscous, and the flow beneath the drift flow to be potential. Then an extension of the analysis was made for the case of a drift shear layer of considerable thickness. The analysis clearly demonstrated the important role that air turbulence and water surface drift play in the wind energy transfer to waves. It was also found that the exponential growth dominated the process of the wind energy transfer to waves. In general, the presence of surface drift increased the wave energy growth rate. The present analysis predicted the existence of a critical value of the normalized surface drift velocity, at which the increment of wave energy growth due to surface drift reached a maximum. When the surface drift exceeded the critical value, there was an adverse effect on the wave energy growth. In the extreme condition in which the surface drift matched the phase speed, it set up the upper limit of the wave energy growth rate. The numerical estimates computed with the theory were consistent with experimental measurements, and with the results obtained with more complex analyses based on numerical models.