Gregory Lawrence

Professor

Relevant Degree Programs

 

Graduate Student Supervision

Doctoral Student Supervision (Jan 2008 - May 2019)
Assessing the impacts of free-stream turbines for electricity generation (2016)

Due to a number of factors including energy security and climate change, there is an urgent need to transition the global energy supply to renewables. Two potential sources are tidal-stream and hydrokinetic power, utilizing free-stream water turbines as generating devices. Much of the interest in tidal-stream power comes from resource assessments that suggest that significant amounts of electricity could be produced from tidal currents flowing through straits. These assessments inventoried the kinetic energy flux and do not account for flow reduction due to turbine resistance. As such, they do not present a realistic picture of the resource. An analytical model for flow reduction in tidal straits demonstrates that only 38% of the natural fluid power is theoretically extractible. This model does not capture the behaviour of bays, lagoons, or the open ocean. Maximum power production requires flows to be reduced to 58% of natural and if the flow is kept above 95% of nominal (due to environmental regulations) less than 10% of the total power is available. A large laboratory experiment was built to test the analytical model and the results agree with the analytical model. Predicted future levelized cost of energy from tidal generation in straits is an interplay of reduced production due flow reduction competing with decreasing technology costs. This is modelled, indicating levelized costs of energy will drop initially, then rise due to flow reduction. Considering hydrokinetic power near hydropower stations, a 1D model used Seton Canal data to simulate the installation of turbines. The results show that the installation of hydrokinetic turbines would decrease the output of the existing powerhouse. Furthermore, the decrease in hydroelectric production is greater than the hydrokinetic production. Thus, installing hydrokinetic turbines would cause a net energy loss. In conclusion, there are three key recommendations:1. Policy makers are cautioned in embracing tidal resource assessments that are based solely on kinetic energy flux. 2. Project proponents and regulators are advised to study far-field effects of any proposed free-stream turbine installation.3. Developers, investors, and policy makers are cautioned towards assuming that the long-term cost of energy from tidal power will decrease.

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Effect of spectral and temporal variation of subsurface irradiance on the heating of lakes (2013)

This dissertation illustrates how the vertical distribution of temperature in lakes can be affected by the fact that the attenuation coefficient of light is often strongly dependent on wavelength. The potential importance of this spectral effect is first examined by considering the solar radiation in isolation, and then by including all non–penetrative heat fluxes using a modified version of the numerical model, DYRESM. Comparing the subsurface spectral irradiance of different lakes reveals that the spectral variability of the attenuation coefficient is more significant when calculating the light intensity in relatively clear lakes than in turbid lakes. Comparisons made between field measurements and theoretical predictions of hypolimnetic heating show the importance of accounting for the spectral irradiance for two relatively clear lakes: Pavilion Lake and Crater Lake. A new parameterization that better describes the spectral attenuation coefficient and the distribution of subsurface irradiance is added to DYRESM. The results obtained, when running the original and the modified DYRESM on Pavilion Lake, show a significant improvement in predicting the thermal structure of the lake with the modified version.The effects of the variation in solar angle and the seasonal variation in water quality on the attenuation coefficient are also examined for Pavilion Lake using DYRESM modified to accept a time varying attenuation coefficient. Simulations were performed for Pavilion Lake using the original and modified versions of DYRESM on diurnal and seasonal scales. Results show no significant improvement in the thermal evolution of the lake when considering the diurnal variations, while slight improvement was shown on a seasonal scale.

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Two dimensional hydrodynamic instabilities in shear flows (2013)

Hydrodynamic instabilities occurring in two dimensional shear flows have been investigated. First, the process of resonant interaction between two progressive interfacial waves is studied. Such interaction produces exponentially growing instabilities in idealized, homogeneous or density stratified, inviscid shear layers. It is shown that two oppositely propagating interfacial waves, having arbitrary initial amplitudes and phases, eventually phase-lock, provided they satisfy a particular condition. Three types of shear instabilities - Kelvin Helmholtz, Holmboe and Taylor have been studied. The above-mentioned condition provides a range of unstable wavenumbers for each instability type, and this range matches the predictions of the canonical normal-mode based linear stability theory. The non-linear evolution of Kelvin-Helmholtz (KH) instability has been studied. The commonly known manifestation of KH is in the form of spiral billows. However, KH evolving from a piecewise linear shear layer is remarkably different; it is characterized by elliptical vortices of constant vorticity connected via thin braids. Using direct numerical simulation and contour dynamics, it is shown that the interaction between two counter-propagating vorticity waves is solely responsible for this KH formation. The oscillation of the vorticity wave amplitude, the rotation and nutation of the elliptical vortex, and straining of the braids have been investigated.Finally, the linear stability of plane Couette-Poiseuille flow in the presence of a cross-flow is studied. The base flow is characterized by the cross flow Reynolds number, Reinj and the dimensionless wall velocity, k. Corresponding to each dimensionless wall velocity, k ∈ [0,1], two ranges of Reinj exist where unconditional stability is observed. In the lower range of Reinj , for modest k we have a stabilization of long wavelengths leading to a cut-off Reinj. As Reinj is increased, we see first destabilization and then stabilization at very large Reinj. Analysis of the eigenspectrum suggests the cause of instability is due to resonant interactions of Tollmien-Schlichting waves.

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Kelvin-Helmholtz instabilities in sheared density stratified flows (2011)

Kelvin-Helmholtz instabilities are the most commonly studied type of instability in sheared density stratified flows. Turbulence caused by these instabilities is an important mechanism for mixing in geophysical flows. The primary objectives of this study are the evolution of these instabilities and quantifying the mixing they generate using direct numerical simulations. The results are presented in three chapters. First, the evolution of primary Kelvin-Helmhlotz instabilities in two dimensions is studied for a wide range of Reynolds and Prandtl numbers, representing real oceanic and atmospheric flows. The results suggest that some properties of KH billows are predictable by a semi-analytical model. It is shown that a new Corcos-Sherman scale is a useful guide when simulating turbulent KH flow fields. The details of the mixing process generated by the evolution of Kelvin-Helmholtz instabilities as it goes through different stages, is analyzed. As the Reynolds number increases a transition in the overall amount of mixing is found, which is in agreement with previous experimental studies. This transition is explained quantitatively by the entrainment and mixing caused by three-dimensional motions, in addition to those resulted from the two-dimensional growth of the instability.The effect of Prandtl number on mixing is studied to understand the characteristics of high Prandtl number mixing events in the ocean; these cases have usually been approximated by low Prandtl number simulations. The increase in the Pradtl number has some significant implications for the evolution of the billow, the time variation of mixing properties, and the overall mixing.

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Laboratory, field and numerical investigations of Holmboe's instability (2009)

The instabilities that occur at a sheared density interface are investigatedin the laboratory, the Fraser River estuary and with Direct Numerical Simulations (DNS).In the laboratory, symmetric Holmboe instabilities are observed duringsteady, maximal two-layer exchange flow in a long channel of rectangular cross section. Internal hydraulic controls at each end of the channel isolate the subcritical region within the channel from disturbances in the reservoirs. Inside the channel, the instabilities form cusp-like waves that propagate in both directions. The phase speed of the instabilities is consistent with linear theory, and increases along the length of the channel as a result of thegradual acceleration of each layer. This acceleration causes the wavelength of any given instability to increase in the direction of flow. As the instabilities are elongated new instabilities form, and as a consequence, the average wavelength is almost constant along the length of the channel. In the Fraser River estuary, a detailed stability analysis is conductedbased on the Taylor-Goldstein (TG) equation, and compared to direct observations in the estuary. We find that each set of instabilities observed coincides with an unstable mode predicted by the TG equation. Each of these instabilities occurs in a region where the gradient Richardson number is less than the critical value of 1/4. Both the TG predictions and echosoundingsindicate the instabilities are concentrated either above or below the density interface. These ‘one-sided’ instabilities are closer in structure to the Holmboe instability than to the Kelvin-Helmholtz instability. Although the dominant source of mixing in the estuary appears to be caused by shearinstability, there is also evidence of small-scale overturning due to boundarylayer turbulence when the tide produces strong near-bed velocities.Many features of the numerical simulations are consistent with lineartheory and the laboratory experiments. However, inherent differences between the DNS and the experiments are responsible for variations in thedominant wavenumber and amplitude of the wave field. The simulations exhibit a nonlinear ‘wave coarsening’ effect, whereby the energy is shifted to lower wavenumber in discrete jumps. This process is, in part, related to the occurrence of ejections of mixed fluid away from the density interface. In the case of the laboratory experiment, energy is transferred to lower wavenumber by the ‘stretching’ of the wave field by a gradually varying mean velocity. This stretching of the waves results in a reduction in amplitude compared to the DNS. The results of the comparison show the dependence of the nonlinear evolution of a Holmboe wave field on temporal and spatial variations of the mean flow.

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Unstable waves on a sheared density interface (2009)

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.

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Master's Student Supervision (2010 - 2018)
Wind waves and internal waves in Base Mine Lake (2017)

Syncrude's Base Mine Lake is the first commercial scale demonstration of end pit lake technology in the Canadian Oil Sands. Following its commissioning in 2012 significant efforts have been made to monitor and understand its evolution. Of particular interest is the impact of surface and internal waves on the resuspension of fluid fine tailings and the effect of hydrocarbons on surface wind wave formation and growth. In this study the first complete description of the wind and internal waves in Base Mine Lake is presented. Observations of surface wind waves were collected using two subsurface pressure gauges. Data revealed that wind waves in Base Mine Lake have short residence times and rarely generate bottom orbital velocities capable of resuspending fluid fine tailings. Additionally, numerical simulations of the wind waves in Base Mine Lake were performed with the SWAN model. Modeled wave heights were in good agreement with observations, and resuspension of fluid fine tailings was minimal even during the 10 year storm event. As the surface of Base Mine Lake contains a hydrocarbon film its impact on surface wind waves was investigated in the laboratory and field. It was found that the hydrocarbon film dampens high frequency wind waves and results in a slower growing wind wave field dominated by longer wavelengths. Additionally, the presence of hydrocarbons also increases the critical wind speed needed to initiate wave growth. From these findings it is postulated that the hydrocarbon film on Base Mine Lake acts to decrease the fluxes of momentum, gas, and heat. The internal waves in Base Mine Lake were simulated using Delft3D Flow. Simulated wave heights as large as 3 m were shown to oscillate for multiple days with little dampening, and despite the small surface area of Base Mine Lake (8 km²) the internal waves were significantly influenced by the Coriolis force. This influence was seen in the form of simulated Kelvin and Poincaré waves which resulted in complex circulation patterns within the lake. The findings presented here provide a first picture into the impacts of waves on the reclamation of Base Mine Lake.

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Factors affecting fall turnover in brackish lakes (2014)

This study investigates fall mixing in brackish lakes. Data from the Colomac Zone 2 Pit Lake is used to study the effects of salinity structure, and the ratio of runoff plus direct precipitation to evaporation (P*/E), on fall turnover. Zone 2 Pit Lake is currently not subject to turnover, but the model CE-QUAL-W2 is used to investigate conditions under which it, or other similar lakes, might turnover in fall. Accordingly, a curve is generated which separates meromictic and holomictic states for different combinations of salinity stratification and P*/E ratios given the bathymetry of Zone 2 Pit Lake, and the meteorological forcing it was subject to in 2010. It is shown that in brackish lakes, increases in the salinity of the surface layer due to evaporation can drive turnover.

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