Scaling of maximum probability density function of velocity increments in turbulent Rayleigh-Bénard convection

In this paper, we apply a scaling analysis of the maximum of the probability density function(pdf) of velocity increments, i.e., max() = max()up p u, for a velocity field of turbulent Rayleigh-Bénard convection obtained at the Taylor-microscale Reynolds number Re60. The scaling exponent is comparable with that of the first-order velocity structure function, (1), in which the large-scale effect might be constrained, showing the background fluctuations of the velocity field. It is found that the integral time T(x/ D) scales as T(x/ D)(x/ D), with a scaling exponent =0.25 0.01, suggesting the large-scale inhomogeneity of the flow. Moreover, the pdf scaling exponent (x, z) is strongly inhomogeneous in the x(horizontal) direction. The vertical-direction-averaged pdf scaling exponent (x) obeys a logarithm law with respect to x, the distance from the cell sidewall, with a scaling exponent 0.22 within the velocity boundary layer and 0.28 near the cell sidewall. In the cell's central region, (x, z) fluctuates around 0.37, which agrees well with (1) obtained in high-Reynolds-number turbulent flows, implying the same intermittent correction. Moreover, the length of the inertial range represented in decade()IT x is found to be linearly increasing with the wall distance x with an exponent 0.65 0.05.     

When large lakes respond fast: A parsimonious model for phosphorus dynamics

This article illustrates how the time scale of lake responses to external inputs of limiting nutrients, such as phosphorus, can be evaluated with minimum calculation from a simple mass balance model that takes into account nutrient recycling in sediments. The characteristic transient time can be estimated from

${\tau }_{\mathit{trans}}\equiv {\left[{\tau }^{?1}+\eta \left(1?k\right)\right]}^{?1}$

where τ (yr) is the hydrological residence time, η (yr^? 1) characterizes the rate of nutrient removal by settling from the water column, and k (between 0 and 1) is the efficiency of nutrient recycling in sediment. At steady state, τ_trans is equivalent to the nutrient residence time with respect to inputs I^st, so that, for given inputs, the steady state nutrient level (W^st) can be calculated as

$W^{\mathit{st}}={\tau }_{\mathit{trans}}{I}^{\mathit{st}}$

Application of the model to the Laurentian Great Lakes reproduces the historical data for total phosphorus levels and suggests changes in recent decades in the rate of P sequestration from the water column into sediments. The model demonstrates that lakes with sediment phosphorus recycling efficiencies of < 50%, such as many oligotrophic and well-oxygenated large lakes of the world, can respond to external P inputs quickly even when the hydrological residence time of water is long. Higher recycling efficiencies lead to a dominance by internal loading and increased response times. When net sedimentation is positive (k< 1), however, lakes should respond to changes in external P inputs faster than their hydrological residence time even when their P budgets are dominated by internal loading.     

Experimental study on discharge coefficient of a gear-shaped weir

This study focused on hydraulic characteristics around a gear-shaped weir in a straight channel. Systematic experiments were carried out for weirs with two different gear heights and eight groups of geometrical parameters. The impacts of various geometrical parameters of gear-shaped weirs on the discharge capacity were investigated. The following conclusions are drawn from the experimental study: (1) The discharge coefficient ($m_{\mathrm{c}}$) was influenced by the size of the gear: at a constant discharge, the weir with larger values of a/b (a is the width of the gear, and b is the width between the two neighboring gears) and a/c (c is the height of the gear) had a smaller value of $m_{\mathrm{c}}$. The discharge capacity of the gear-shaped weir was influenced by the water depth in the weir. (2) For type C1 with a gear height of 0.01 m, when the discharge was less than 60 m³/h and $H_{\mathrm{1}}/P$ < 1.0 ($H_{\mathrm{1}}$ is the water depth at the low weir crest, and P is the weir height), $m_{\mathrm{c}}$ significantly increased with the discharge and $H_{\mathrm{1}}/P$; with further increases of the discharge and $H_{\mathrm{1}}/P$, $m_{\mathrm{c}}$ showed insignificant decreases and fluctuated within small ranges. For type C2 with a gear height of 0.02 m, when the discharge was less than 60 m³/h and $H_{\mathrm{1}}/P$ < 1.0, $m_{\mathrm{c}}$ significantly increased with the discharge and $H_{\mathrm{1}}/P$; when the discharge was larger than 60 m³/h and $H_{\mathrm{1}}/P$ > 1.0, $m_{\mathrm{c}}$ slowly decreased with the increases of the discharge and $H_{\mathrm{1}}/P$ for $a/b$ ≤ 1.0 and $a/c$ ≤ 1.0, and slowly increased with the discharge and $H_{\mathrm{1}}/P$ for $a/b$ > 1.0 and $a/c$ > 1.0. (3) A formula of $m_{\mathrm{c}}$ for gear-shaped weirs was established based on the principle of weir flow, with consideration of the water depth in the weir, the weir height and width, and the height of the gear.