Environmental Fluid Mechanics

In the Earth’s atmosphere, Cumulus clouds are often modeled as an ensemble of statistically stationary moist plumes in a stratified environment. The entrainment rate coefficient for a plume relates the rate of change of volume flow rate along the plume axis to the center-line velocity and plume width. Its value determines the rate at which each plume gets diluted by the environment, and, consequently, the height of each plume. General Circulation Models typically assume a constant, empirically determined value of entrainment rate coefficient along cloud depth, which is the same for all plumes. In this work, data from Large Eddy Simulation of non-precipitating shallow Cumulus clouds is used to obtain an energy consistent closure for entrainment rate coefficient along the cloud depth in terms of the source terms in the mean momentum and vertical energy equation. The relative humidity of the environment is systematically varied over a set of three simulations, in which the control case corresponds to the Barbados oceanographic and meteorological experiment. A non-linear dependence of the local entrainment rate in terms of the local Richardson number is postulated for updraft patches, and the model constants are dynamically extracted from the relevant source terms in momentum and energy equation using the energy consistent approach. This model allows updraft patches to have a positive local entrainment rate even when the average entrainment rate for the ensemble of updrafts is negative. The resulting entrainment model for individual updraft patches may be used to obtain the fractional entrainment and detrainment rates of the cloud ensemble. The model yields reasonably low a posteriori error, especially for positively buoyant updrafts.

Sediment-laden turbulent flows are commonly encountered in natural and engineered environments. It is well known that turbulence generates fluctuations to the particle motion, resulting in modulation of the particle settling velocity. A novel stochastic particle tracking model is developed to predict the particle settling out and deposition from a sediment-laden jet. Particle velocity fluctuations in the jet flow are modelled from a Lagrangian velocity autocorrelation function that incorporates the physical mechanism leading to a reduction of settling velocity. The model is first applied to study the settling velocity modulation in a homogeneous turbulence field. Consistent with basic experiments using grid-generated turbulence and computational fluid dynamics (CFD) calculations, the model predicts that the apparent settling velocity can be reduced by as much as 30 % of the stillwater settling velocity. Using analytical solution for the jet mean flow and semi-empirical RMS turbulent velocity fluctuation and dissipation rate profiles derived from CFD predictions, model predictions of the sediment deposition and cross-sectional concentration profiles of horizontal sediment-laden jets are in excellent agreement with data. Unlike CFD calculations of sediment fall out and deposition from a jet flow, the present method does not require any a priori adjustment of particle settling velocity.

A number of experimental studies on submerged canopy flows have focused on fully-developed flow and turbulent characteristics. In many natural rivers, however, aquatic vegetation occurs in patches of finite length. In such vegetated flows, the shear layer is not formed at the upstream edge of the vegetation patch and coherent motions develop downstream. Therefore, more work is neededz to reveal the development process for large-scale coherent structures within vegetation patches. For this work, we considered the effect of a limited length vegetation patch. Turbulence measurements were intensively conducted in open-channel flows with submerged vegetation using Particle Image Velocimetry (PIV). To examine the transition from boundary-layer flow upstream of the vegetation patch to a mixing-layer-type flow within the patch, velocity profiles were measured at 33 positions in a longitudinal direction. A phenomenological model for the development process in the vegetation flow was developed. The model decomposed the entire flow region into four zones. The four zones are the following: (i) the smooth bed zone, (ii) the diverging flow zone, (iii) the developing zone and (iv) the fully-developed zone. The PIV data also confirmed the efficiency of the mixing-layer analogy and provided insight into the spatial evolution of coherent motions.

Experiments were conducted in order to characterize the distributions of concentrations of suspended particulate matter (SPM) in water columns of lakes and reservoirs. The experiments, in a reduced model of the water column, used a set of oscillating grids. Runs were done with particles denser than water as well as with light particles. The results were in good agreement with analytical solutions for steady-state, and non-steady-state conditions. An approximate analytical solution was derived and found to be in agreement with the full solution. The threshold for resuspension was measured, and characterized in terms of a modified Shields parameter, which is appropriate to a zero-shear environment. All experiments showed that the distribution of SPM exhibited a layer near the bottom that is thought to be analogous to the benthic nepheloid layer (BNL) observed in larger lakes. The thickness of the nepheloid layer increases with the turbulence intensity.

Due to the lack of data on hydraulic-jump dynamics in very large channels, the present paper describes the main characteristics of the velocity field and turbulence in a large rectangular channel with a width of 4 m. Although a hydraulic jump is always treated as a wave that is transversal to the channel wall, in the case of this study it has a trapezoidal front shape, first starting from a point at the sidewalls and then developing downstream in an oblique manner, finally giving rise to a trapezoidal shape. The oblique wave front may be regarded as a lateral shockwave that arises from a perturbation at a certain point of the lateral wall and travels obliquely toward the centreline of the channel. The experimental work was carried out at the Coastal Engineering Laboratory of the Water Engineering and Chemistry Department of the Technical University of Bari (Italy). In addition to the hydraulic jump formation, a large recirculating flow zone starts to develop from the separating point of the lateral shock wave and a separate boundary layer occurs. Intensive measurements of the streamwise and spanwise flow velocity components along one-half width of the channel were taken using a bidimensional Acoustic Doppler Velocimeter (ADV). The water surface elevation was obtained by means of an ultrasonic profiler. Velocity vectors, transversal velocity profiles, turbulence intensities and Reynolds shear stresses were all investigated. The experimental results of the separated boundary layer were compared with numerical predictions and related work presented in literature and showed good agreement. The transversal velocity profiles indicated the presence of adverse pressure gradient zones and the law of the wall appears to govern the region around the separated boundary layer.

In a chute aerator flow, a large air discharge that is introduced through an air supply duct is entrained into the flow and transported to the downstream zone. In this study, a series of experiments were conducted to quantify the two–phase flow properties, including air concentration, bubble frequency, and bubble diffusivity, and air entrainment flux for a wide range of Froude numbers (3.3 ≤ F0 ≤ 7.4) at relatively large Reynolds numbers (5 × 105 ≤ R ≤ 1.2 × 106). The distributions of air concentration and bubble frequency, which demonstrated two competitive turbulent processes, were presented. The air transport process of the chute aerator flow was quantitatively described based on the approach flow conditions and the aerator geometry. According to the characteristics of air discharge in the equilibrium zone, and based on the previous equation, qa = KV0L, the experimental results indicated that the dimensionless coefficient K was independent of the aerator structure and significantly increases with the flow Froude number.