| Summary: | The gravitational exchange of fluids between two bodies of water of slightly different density
through a channel with a smooth two-dimensional underwater sill is studied theoretically and
experimentally. Internal hydraulic theory is extended to incorporate the effects of streamline
curvature caused by the sill. The extended theory is applied to both single and two-layer flows.
Unlike internal hydraulic theory which fails to predict a whole class of two-layer flows, namely,
approach-controlled flows, the extended theory with non-hydrostatic pressure considered
achieves excellent agreement with previous experimental measurements.
Internal hydraulic theory is further extended to incorporate the effects of friction caused by
the channel and the two-layer interface, as well as the streamline curvature. For the exchange
flow through a channel of constant width with a sill, maximal exchange occurs when both sill
and exit controls are present. With the effects of curvature and friction considered, the sill
control is shifted away from the sill crest, and the internal energy is no longer constant.
Exchange flows established in the laboratory are studied using flow visualization, particle
tracking, and image processing techniques. The friction factors for the sidewalls and bottom are
estimated using boundary layer theories, while the interfacial friction factor is determined
experimentally. The friction reduces the internal energy throughout the channel, significantly
increases the interface slope and reduces the flow rate. The frictional effect is important
throughout the channel, whereas the curvature effect is mainly important in the sill region. With
both effects included, the exchange flow over a sill is accurately predicted.
On the interface of exchange flows, interfacial instabilities are observed, with Kelvin-
Helmholtz instabilities at both ends of the channel where shear is strong, and Holmboe
instabilities in the middle region where shear is weaker. The Holmboe instabilities have been
studied in detail. The existence of the negative shift, i.e., the shear center being lower than the density interface, is confirmed. This shift initially results in non-symmetric Holmboe waves.
Later in the experiments, the shift reduces to zero and symmetric Holmboe waves are observed.
The growth rate, wave lengths, and wave speeds of the Holmboe instabilities are measured and
found to be in agreement with the linear stability theory of Haigh (1995). Variations in wave
speeds when the positive and negative waves pass through each other have been observed for the
first time experimentally. The Holmboe waves are stabilized when the bulk Richardson number
exceeds about 0.8. === Applied Science, Faculty of === Civil Engineering, Department of === Graduate
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