George C. Christodoulou

Interfacial mixing in stratified flows

In this paper the phenomenon of turbulent mixing at a density interface is studied. Based on a unified view of the mixing processes, quantitative laws are sought, which would be generally valid in flows with mean motion in at least one of the layers. Re-examination of available experimental data from four types of stratified flow, supplemented by theoretical considerations, leads to the identification of four such governing laws, all of a power form, applicable in different ranges of the overall Richardson number, Ri 0. Two of these laws refer to supercritical and subcritical conditions and are considered as fundamental, being related to qualitatively different mechanisms of interfacial mixing. An intermediate law applies around the critical Ri 0 value of unity, while an asymptotic law corresponds to the limit of homogeneous flow as Ri 0 tends to zero. All the above laws are given by simple expressions in terms of the mean flow characteristics, allowing their straightforward application for the quantifica...

Inclined negatively buoyant jets 1: geometrical characteristics

Experimental results on inclined turbulent round jets with negative buoyancy discharging in a calm homogeneous fluid are presented. Six different discharge angles from 45° to 90° to the horizontal are studied, and the jet evolution is recorded by means of a video camera. Results concern the main geometrical characteristics of the jet trajectory, i.e. the initial terminal height of rise reached by the jet at flow initiation, the final terminal height of rise observed at steady state, the horizontal distance from the source at which the terminal height is observed and the horizontal distance to the point where the jet returns at the source elevation. The densimetric Froude number at the source ranges between 7 and 60, whereas the Reynolds number is generally higher than 6000. Results are given in dimensionless form and confirm theoretical considerations obtained by dimensional analysis.

Inclined negatively buoyant jets 2: concentration measurements

Experiments on concentration measurements in round turbulent negatively buoyant jets discharging into a calm homogeneous fluid at three different angles are presented. Detailed measurements using a micro-scale conductivity probe were carried out at the horizontal location of the terminal rise height, mostly along the vertical of the axial jet plane and in the transverse direction. The dimensionless vertical distribution of the mean concentration is found to be asymmetric, whereas the transverse distribution is approximately Gaussian. At the same horizontal location, the vertical distribution of the concentration turbulent intensity has a maximum at a point systematically higher than the jet axis. The width of the mean concentration distribution, the heights to the location of the maximum mean concentration and to the maximum turbulent intensity as well as the minimum dilution are determined. From measurements in the region where the jet returns to the source elevation, the minimum dilution and the horizontal distance to the return point are estimated.

On the entrainment coefficient in negatively buoyant jets

Integral models proposed to simulate positively buoyant jets are used to model jets with negative or reversing buoyancy issuing into a calm, homogeneous or density-stratified environment. On the basis of the self-similarity assumption, ‘top hat’ and Gaussian cross-sectional distributions are employed for concentration and velocity. The entrainment coefficient is considered to vary with the local Richardson number, between the asymptotic values for simple jets and plumes, estimated from earlier experiments in positively buoyant jets. Top-hat and Gaussian distribution models are employed in a wide range of experimental data on negatively buoyant jets, issuing vertically or at an angle into a calm homogeneous ambient, and on jets with reversing buoyancy, discharging into a calm, density-stratified fluid. It is found that geometrical characteristics such as the terminal (steady state) height of rise, the spreading elevation in stratified ambient and the distance to the point of impingement are considerably underestimated, resulting in lower dilution rates at the point of impingement, especially when the Gaussian formulation is applied. Reduction of the entrainment coefficient in the jet-like flow regime improves model predictions, indicating that the negative buoyancy reduces the entrainment in momentum-driven, negatively buoyant jets.

Apparent shear stress in smooth compound channels

A simple, dimensionally sound, formula is proposed for expressing the apparent shear stress on the vertical interface between main channel and flood plain in a compound channel. An apparent friction factor is introduced and its dependence on the cross-section shape is examined based on experimental results reported in previous studies. For symmetrical smooth channels, it is found that this friction factor is essentially independent of the flow depth and is well linearly correlated with the width ratio of the compound section, at least within the ranges of practical interest where data are available. Discharge estimates obtained by incorporating the predicted shear stress in the ϕ-index method compare well with experimental results. The suggested approach is sufficiently accurate for practical applications and may be extended to other channel shapes and roughnesses depending on the acquisition of adequate data.

3-D numerical modeling of supercritical flow in gradual expansions

A 3-D CFD model based on the Volume of Fluid method to calculate the free surface was used to study supercritical flow in gradual open channel expansions. The model was first applied to a modified Rouse expansion, for which extensive experimental data are available. A detailed comparison between the numerical and the experimental results concerning surface profiles, velocities, free surface uniformity, and shock front location showed satisfactory agreement, especially for lower supercritical Froude numbers. The model was subsequently applied to optimize and finalize the design of a compound expansion structure with variable bottom elevation, piers, and inner walls. CFD calculations showed that flow conditions in this structure are satisfactory, provided that bottom ramps are used to ensure a uniform variation of the bottom elevation

Dilution of dense effluents on a sloping bottom

A simple model is proposed for evaluating the dilution and other main characteristics of a dense boundaryattached 3-D plume, created by the disposal of heavier effluent into a quiescent homogeneous ambient. It is based on matching requirements between the near-and intermediate field, which allow the calculation of necessary quantities at the initiation of the bottom plume in terms of the initial discharge parameters. The subsequent spreading is described through a generalization of available data.