A Compositional Analysis of Unbalanced Usages of Multiple Left-turn Lanes

Lane usage measures distribution of a specific traffic movement across multiple available lanes in a given time. Unbalanced lane usages decrease the capacity of subject segment. This paper took multiple left-turn lanes at signalized intersections as case study, and explored the influences of some factors on the lane usage balance. Lane usages were calculated from field collected lane volumes and the constant-sum constraint among them was explicitly considered in the statistical analysis. Classical and compositional analysis of variance was respectively conducted to identify significant influential factors. By comparing the results of compositional analysis and those of the classical one, the former ones have better interpretability. It was found that left-turn lane usages could be affected by parameter variance of geometric design or traffic control, such as length of turning curve, length of upstream segment, length of signal phase or cycle. These factors could make the lane usages achieve relative balance at different factor levels.</p

Aspect ratio dependence of heat transport by turbulent Rayleigh-B\'{e}nard convection in rectangular cells

We report high-precision measurements of the Nusselt number $Nu$ as a function of the Rayleigh number $Ra$ in water-filled rectangular Rayleigh-B\'{e}nard convection cells. The horizontal length $L$ and width $W$ of the cells are 50.0 cm 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 $(\Gamma_x\equiv L/H,\Gamma_y\equiv W/H)=(1,0.3)$, $(2,0.6)$, $(4,1.2)$, $(7.3,2.2)$, $(14.3,4.3)$, and $(20.8,6.3)$. The measurements were carried out over the Rayleigh number range $6\times10^5\lesssim Ra\lesssim10^{11}$ and the Prandtl number range $5.2\lesssim Pr\lesssim7$. 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 $\Gamma$, at least for $\Gamma=1$ 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 $Nu_{\infty}$ for plates with perfect conductivity. The local scaling exponents $\beta_l$ of $Nu_{\infty}\sim Ra^{\beta_l}$ are calculated and found to increase from 0.243 at $Ra\simeq9\times10^5$ to 0.327 at $Ra\simeq4\times10^{10}$.Comment: 15 pages, 7 figures, Accepted by Journal of Fluid Mechanic