A study of the effects of friction and mixing on the exchange flow through the Bosphorus (Strait of Istanbul)
Date
2018-04-05
Authors
Gerdes, Frank
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Abstract
This thesis presents observations from the Bosphorus (Strait of Istanbul), Turkey, made to study the effects of mixing, entrainment and frictionally induced shear on the dynamics of an exchange flow.
The well known two-layer structure with an upper layer of brackish Black Sea water over an opposing undercurrent of salty Mediterranean water was observed. It is likely that the exchange was maximal as it seemed to be bounded by two hydraulic controls at the strait's ends; a sill control at the Black Sea was readily identifiable and the exchange also appeared to be controlled at the south exit toward the Sea of Marmara. The lower layer lost 15 to 20% of its volume to the upper layer because of upward mixing caused by interfacial shear and turbulence created at bends and lateral protuberances. The exchange was quasi-steady, except during a so-called Orkoz when strong winds caused a reversal of the upper layer flow. Between the controls the interface sloped steeply throughout the strait indicating that mass and momentum exchange between the layers and friction along the interface and sidewalls were important.
The hydraulics of a single layer flow with entrainment is examined with a reduced gravity model. Expressions are derived for the local change of layer thickness and Froude number as function of the entrainment velocity. It is shown that entrainment, like friction, acts to force the flow toward criticality, although the layer thickness can increase if the Froude number is smaller than 1/2. For certain Froude numbers the effects of friction and entrainment on the layer thickness and the hydraulic state of the flow are found to be of comparable magnitude. A two-layer model with entrainment is developed. Predicted and observed interfacial slopes are found to be in reasonable agreement.
The classical definition of hydraulic control assumes layers with uniform velocity so that further consideration is required if there is frictionally induced shear as observed in the Bosphorus. If a shear flow preserves the shape of its velocity profile, a standard formula suggests that hydraulic control is achieved when the depth-averaged flow speed is less than ( gh)1/2. On the other hand, shallow water waves have a speed relative to the mean flow of more than (gh)1/2, suggesting that information could propagate upstream. This apparent paradox is solved by showing that the internal stress required to maintain a constant velocity profile depends on flow derivatives, thus altering the wave speed without introducing damping. By contrast, an inviscid shear flow does not maintain the same profile shape, but is shown to exhibit hydraulic control when the depth-averaged speed equals the inviscid long wave speed. In the Bosphorus the similarity assumption was found to approximately hold indicating that hydraulic control could not be defined using classical inviscid theory.
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Keywords
Hydraulics, Channels (Hydraulic engineering)