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.     

Three-dimensional modeling of sediment resuspension in a large shallow lake

We simulated bottom resuspension events in Lake Erie, using a coupled three-dimensional hydrodynamic and water quality model. Key parameters in the model, including critical bottom shear stress (${\tau }_{\mathit{cr}}$) and resuspension rate (α) were calibrated and validated by comparing the model output to observations. These included total suspended solid (TSS) concentrations in the bottom boundary layer (RMSE = 0.74 $\text{mg}{\text{L}}^{\text{-1}}$) and water column (RMSE = 0.81 $\text{mg}{\text{L}}^{\text{-1}}$), and to time series of acoustic backscatter signal (R² > 0.8) and turbidity (R² ≈ 0.4) from long-term moorings near the lakebed in 2008–09 and 2013. Signals from phytoplankton, in spring and summer, caused discrepancies between modeled TSS and the observed turbidity data. Although common practice, we show that literature-based or field-observed critical shear stress should not be directly applied in large-scale Reynolds-averaged sediment model as this will likely underestimate resuspension. In agreement with the literature, the model reproduced more frequent and intensive surface-wave driven resuspension in the shallow regions (< ~20 m), particularly in the western basin, compared to the deeper central and eastern basins, where bottom stresses induced by mean currents (${\tau }_c$) were comparable with those due to surface waves (${\tau }_w$). However, on the north-shore of the eastern basin, ${\tau }_c$ often predominated over ${\tau }_w$. We simulated thermocline motion, including up- and down-welling events and swashing of the internal Poincaré wave, to contribute to ${\tau }_c$ in the central basin and form nepheloid layers.