Studies in density stratified flows. April 1970.

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Examines the rapidly varied flow phenomenon in a two layer density stratified system. Only one layer flows, the other being stationary. The flow regime changes from supercritical to subcritical across the region of rapidly varied flow. The analogous phenomenon in open channel hydraulics is the hydraulic jump. In stratified flows it will be referred to as a density jump because it is generally accompanied by a change in the density of the flowing layer. It is shown there is a fundamental difference between the hydraulic and the density jump in that the conjugate conditions on either side of a density jump are not uniquely related as they are with the hydraulic jump. There are a range of possible states which may be attained downstream of a density jump for a given upstream state. It is shown that the rate of entrainment of ambient fluid into a density jump and therefore the conditions downstream of the jump are a function of the downstream control. The limiting cases of maximum and minimum entrainment and control mechanisms within the jump are examined. Several forms of control are investigated among these being the broad crested weir, a free overfall and channel friction. An entrainment function is derived, relating a local entrainment parameter to a local Froude number within the entraining zone of a density jump. Some features of unsteady density flows are examined and it is shown that all the properties of strarting flow or nose are controlled by the following layer, which in turn is generally controlled by boundary friction. An approximate expression is derived for the fall in momentum flux across a density jump and this is compared with experimental data. Finally, experimental velocity and density distributions downstream of density jumps are presented, and are shown to be functions of the Froude number of the flow upstream of the density jump, and the rate of entrainment within the jump. The significant result arising from this work is that conditions downstream of density jump which will occur, for example, at power station cooling pond outfalls and some ocean sewage outfalls, can be predicted. A design example, showing how station cooling pond efficiencies can be optimised by the control of mixing at the outfall, is included in the appendices.
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Wilkinson, D. L.
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