Structural ensemble dynamics based closure model for wall-bounded turbulent flow

Wall-bounded turbulent flow involves the development of multi-scale turbulent eddies, as well as a sharply varying boundary layer. Its theoretical descriptions are yet phenomenological. We present here a new framework called structural ensemble dynamics （SED）, which aims at using systematically all relevant statistical properties of turbulent structures for a quantitative description of ensemble means. A new set of closure equations based on the SED approach for a turbulent channel flow is presented. SED order functions are defined, and numerically determined from data of direct numerical simulations （DNS）. Computational results show that the new closure model reproduces accurately the solution of the original Navier-Stokes simulation, including the mean velocity profile, the kinetic energy of the streamwise velocity component, and every term in the energy budget equation. It is suggested that the SED-based studies of turbulent structure builds a bridge between the studies of physical mechanisms of turbulence and the development of accurate model equations for engineering predictions.

The influence of upstream slope on the local scour at drop structure

The drop structure will fail as a result of local scoring downstream.This paper discusses the influence of a drop structures' upstream slope to local scour.Empirical equations of the scour hole were developed by laboratory experiment,theoretical assumptions,and regression analysis.These equations include the maximum scour depth and length during the scouring period,the maximum equilibrium scour depth and length,and the unit width scour rate.The four channel slopes(0%,2%,4%,and 6%) before the drop structure has been included in the analysis.A series of laboratory experiments were conducted to obtain 48 groups of experiments and 419 scour hole profiles during the scouring period.The material used in the scour section is uniform non-cohesive and with a median diameter of d50 = 0.5 mm.The results have been used to develop empirical equations via regression analysis to determine the coefficients of theoretical equations.The high correlation coefficient indicates that the equations developed in this study are suitable for verifying the characteristics of a scour hole at drop structure in the sloped channel.The semi-empirical equation is more accurate than the empirical equation.Compared to a horizontal channel,a sloped channel tends to cause a greater equilibriummaximum scour length,shorter equilibrium maximum scour depth,and faster unit-wide scour rate.

Spatial relationship between energy dissipation and vortex tubes in channel flow

The spatial relationship between the energy dissipation slabs and the vortex tubes is investigated based on the direct numerical simulation（DNS） of the channel flow. The spatial distance between these two structures is found to be slightly greater than the vortex radius. Comparison of the core areas of the vortex tubes and the dissipation slabs gives a mean ratio of 0.16 for the mean swirling strength and that of 2.89 for the mean dissipation rate. These results verify that in the channel flow the slabs of intense dissipation and the vortex tubes do not coincide in space. Rather they appear in pairs offset with a mean separation of approximately 10η.