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Unstable waves on a sheared density interface

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Title: Unstable waves on a sheared density interface
Author: Carpenter, Jeffrey Richard
Degree Doctor of Philosophy - PhD
Program Civil Engineering
Copyright Date: 2009
Publicly Available in cIRcle 2009-08-17
Abstract: The Holmboe instability is known to occur in stratified shear layers that exhibit a relatively thin density interface compared to the shear layer thickness. At finite amplitude the instability appears as cusp-like propagating internal waves. The evolution and identification of these unstable waves is the subject of this thesis. The results are presented in four parts. First, the basic wave field resulting from Holmboe's instability is studied both numerically and experimentally. In comparing basic descriptors of the wave fields, a number of processes are identified that are responsible for differences between the simulations and experiments. These are related to variations in the mean flow that arise due to the different boundary conditions. Holmboe waves are known to produce vertical ejections of interfacial fluid from the wave crests. This `ejection process,' in which stratified fluid is transported against buoyancy forces, is caused by the formation of a vortex couple (i.e. two vorticies of opposite sign that travel as a pair). Results obtained by means of direct numerical simulations also show that the process is primarily two-dimensional and does not require the presence of both upper and lower Holmboe modes. Shear instability is then studied in the highly stratified Fraser River estuary. The observations are found to be in good agreement with the predictions of linear theory. When instability occurs, it is largely as a result of asymmetry between regions of strong shear and density stratification. The structure of the salinity intrusion is found to depend on the strength of the freshwater discharge, in addition to the phase of the tidal cycle. This has implications for whether estuarine mixing takes place through shear instability or boundary layer turbulence. Finally, the asymmetric stratified shear layer, which exhibits a vertical shift between the density interface and the shear layer centre, is examined by the formulation of a diagnostic that is based on the `wave interaction' mechanism of instability growth. This allows for a quantitative assessment of Kelvin-Helmhotz and Holmboe-type growth mechanisms in stratified shear layers. The predictions of the diagnostic are compared to results of nonlinear simulations and observations in the Fraser River estuary.
URI: http://hdl.handle.net/2429/12259

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