Mixing in Density-Stratified Conjugate Flows

Citation

Rasi, Marco (1989) Mixing in Density-Stratified Conjugate Flows. Dissertation (Ph.D.), California Institute of Technology. doi:10.7907/2s6d-kv47. https://resolver.caltech.edu/CaltechETD:etd-02152007-155510

Abstract

Two-layer stratified shear flows have been studied in the laboratory using combined laser-induced fluorescence and laser-Doppler velocimetry. Use of this high resolution, non-intrusive instrumentation has enabled new insight on the entraining characteristics of supercritical two-layer flows and the phenomenon known as an internal hydraulic jump.

In the experiments, salt water was discharged at a steady flowrate from a rectangular slot located at the bottom of the upstream end of a horizontal channel containing fresh water. The flow of the dense bottom layer was controlled at the downstream end of the channel by either a free overfall or a broad-crested weir. The transition between the wall-jet-like flow near the source and the subcritical downstream counterflow took place through an internal hydraulic jump, characterized by a steep interfacial slope and a local recirculating flow region.

A one-dimensional theory based on the assumptions of uniformity of velocity and density distributions downstream of the mixing region was discussed and extended to predict the overall internal flow geometry and the dilution attained by the source fluid across the mixing region. The analysis, which applies to the general case of a mixing channel of finite depth and length, was carried out in three stages. First, the flow at the upstream end of the channel was considered, and a conservation of flow force in the total channel depth across the jump was hypothesized. Second, the gradually-varied counterflow, governed by boundary shear and interfacial momentum transfer, as well as by the critical flow condition at the channel end, was studied by applying the momentum principle to both layers. Finally, the upstream and downstream equations were combined to obtain hydraulic solutions, in a way that clearly establishes that the overall problem can only be solved if the importance of the interplay between source and control is recognized.

An extensive series of experiments confirmed the general predictions of the one-dimensional theory. Four predicted mixing modes (free internal hydraulic jump, flooded jump, upstream-controlled instability, and downstream-controlled instability) were all observed in the experiments. The dependence of the entrainment rate, both on the depth of the ambient water and on the control establishing the critical flow at the end of the channel, has been documented with comprehensive experimental data.

The non-intrusive laser-based instrumentation used has enabled a detailed experimental description of the density and velocity distributions at several locations in the flow field and has pointed out some inaccuracies in the one-dimensional approach. A procedure to overcome these inaccuracies has been proposed.

The ideas developed and the experimental results obtained from this work can be readily extended to further the understanding of many of the two-layer stratified shear flows of interest to engineers and geophysicists.

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