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UBC Theses and Dissertations

Exchange flow through a channel with an underwater sill Zhu, Zhiwei


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.

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